CFRGInternet Research Task Force (IRTF) S. Smyshlyaev, Ed.Internet-DraftRequest for Comments: 8645 CryptoProIntended status:Category: InformationalMay 31, 2019 Expires: December 2,August 2019 ISSN: 2070-1721 Re-keying Mechanisms for Symmetric Keysdraft-irtf-cfrg-re-keying-17Abstract A certain maximum amount of data can be safely encrypted when encryption is performed under a single key. This amount is called the "key lifetime". This specification describes a variety of methodsto increasefor increasing the lifetime of symmetric keys. It provides two types of re-keying mechanisms based on hash functions andonblockciphers,ciphers that can be used with modes of operations such as CTR, GCM, CBC,CFBCFB, and OMAC. This document is a product of the Crypto Forum Research Group (CFRG) in the IRTF. Status of This Memo ThisInternet-Draftdocument issubmitted in full conformance withnot an Internet Standards Track specification; it is published for informational purposes. This document is a product of theprovisionsInternet Research Task Force (IRTF). The IRTF publishes the results ofBCP 78Internet-related research andBCP 79. Internet-Drafts are working documentsdevelopment activities. These results might not be suitable for deployment. This RFC represents the consensus of the Crypto Forum Research Group of the InternetEngineeringResearch Task Force(IETF). Note that other groups may also distribute working documents as Internet-Drafts. The list of current Internet- Drafts is at https://datatracker.ietf.org/drafts/current/. Internet-Drafts(IRTF). Documents approved for publication by the IRSG aredraft documents validnot candidates fora maximumany level of Internet Standard; see Section 2 of RFC 7841. Information about the current status ofsix monthsthis document, any errata, and how to provide feedback on it may beupdated, replaced, or obsoleted by other documentsobtained atany time. It is inappropriate to use Internet-Drafts as reference material or to cite them other than as "work in progress." This Internet-Draft will expire on December 2, 2019.https://www.rfc-editor.org/info/rfc8645. Copyright Notice Copyright (c) 2019 IETF Trust and the persons identified as the document authors. All rights reserved. This document is subject to BCP 78 and the IETF Trust's Legal Provisions Relating to IETF Documents (https://trustee.ietf.org/license-info) in effect on the date of publication of this document. Please review these documents carefully, as they describe your rights and restrictions with respect to this document.Code Components extracted from this document must include Simplified BSD License text as described in Section 4.e of the Trust Legal Provisions and are provided without warranty as described in the Simplified BSD License.Table of Contents 1. Introduction . . . . . . . . . . . . . . . . . . . . . . . .34 2. Conventions Used in This Document . . . . . . . . . . . . . .67 3. Basic Terms and Definitions . . . . . . . . . . . . . . . . .67 4. Choosing Constructions and Security Parameters . . . . . . .89 5. External Re-keying Mechanisms . . . . . . . . . . . . . . . .1011 5.1. Methods of Key Lifetime Control . . . . . . . . . . . . .1314 5.2. Parallel Constructions . . . . . . . . . . . . . . . . .1314 5.2.1. Parallel Construction Based on a KDF on a Block Cipher . . . . . . . . . . . . . . . . . . . . . . .1415 5.2.2. Parallel Construction Based on a KDF on a Hash Function . . . . . . . . . . . . . . . . . . . . . .1416 5.2.3.Tree-basedTree-Based Construction . . . . . . . . . . . . . . .1516 5.3. Serial Constructions . . . . . . . . . . . . . . . . . .1617 5.3.1. Serial Construction Based on a KDF on a Block Cipher1719 5.3.2. Serial Construction Based on a KDF on a Hash Function1819 5.4. Using Additional Entropy during Re-keying . . . . . . . .1819 6. Internal Re-keying Mechanisms . . . . . . . . . . . . . . . .1920 6.1. Methods of Key Lifetime Control . . . . . . . . . . . . .2122 6.2. Constructions that Do Not Require a Master Key . . . . .. 2223 6.2.1. ACPKM Re-keying Mechanisms . . . . . . . . . . . . .2223 6.2.2. CTR-ACPKM Encryption Mode . . . . . . . . . . . . . . 24 6.2.3. GCM-ACPKM Authenticated Encryption Mode . . . . . . . 26 6.3. Constructions that Require a Master Key . . . . . . . . .. 2829 6.3.1. ACPKM-Master Key Derivation from the Master Key . . . 29 6.3.2. CTR-ACPKM-Master Encryption Mode . . . . . . . . . . 31 6.3.3. GCM-ACPKM-Master Authenticated Encryption Mode . . . 33 6.3.4. CBC-ACPKM-Master Encryption Mode . . . . . . . . . .3536 6.3.5. CFB-ACPKM-Master Encryption Mode . . . . . . . . . .3837 6.3.6. OMAC-ACPKM-Master Authentication Mode . . . . . . . .4039 7. Joint Usage of External and Internal Re-keying . . . . . . . 41 8. Security Considerations . . . . . . . . . . . . . . . . . . . 42 9. IANA Considerations . . . . . . . . . . . . . . . . . . . . .4342 10. References . . . . . . . . . . . . . . . . . . . . . . . . .4342 10.1. Normative References . . . . . . . . . . . . . . . . . .4342 10.2. Informative References . . . . . . . . . . . . . . . . . 44 Appendix A. Test Examples . . . . . . . . . . . . . . . . . . .4647 A.1. Test Examples for External Re-keying . . . . . . . . . .4647 A.1.1. External Re-keying with a Parallel Construction . . .4647 A.1.2. External Re-keying with a Serial Construction . . . . 48 A.2. Test Examples for Internal Re-keying . . . . . . . . . . 51 A.2.1. Internal Re-keying Mechanisms that Do Not Require a Master Key . . . . . . . . . . . . . . . .. . . . .51 A.2.2. Internal Re-keying Mechanisms with a Master Key . . . 55Appendix B. ContributorsAcknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . 67Appendix C. AcknowledgmentsContributors . . . . . . . . . . . . . . . . . .68. . . . . . . . 67 Author's Address . . . . . . . . . . . . . . . . . . . . . . . . 68 1. Introduction A certain maximum amount of data can be safely encrypted when encryption is performed under a single key.HereinafterHereinafter, this amount will be referred to as the "key lifetime". The need for such a limitation is dictated by the following methods of cryptanalysis: 1. Methods based on the combinatorial properties of the used block cipher mode of operation These methods do not depend on the underlying block cipher. Commonmodesmode restrictions derived from such methods are of order 2^{n/2}, where n is a block size defined in Section 3. [Sweet32]isincludes an example of an attack that is based on such methods. 2. Methods based on side-channel analysis issues In mostcasescases, these methods do not depend on the used encryption modes and weakly depend on the usedblockcipher features. Limitations resulting from these considerations are usually the most restrictive ones. [TEMPEST] is an example of an attack that is based on such methods. 3. Methods based on the properties of the used block cipher The most common methods of this type are linear and differential cryptanalysis [LDC]. In mostcasescases, these methods do not depend on the used modes of operation. In the case of secure block ciphers, bounds resulting from such methods are roughly the same as the natural bounds of2^n,2^n and are dominated by the other bounds above. Therefore, they can be excluded from the considerations here. As a result, it is important to replace a key when the total size of the processed plaintext under that key approaches the lifetime limitation. A specific value of the key lifetime should be determined in accordance with some safety margin for protocol security and the methods outlined above. Suppose L is a key lifetime limitation in some protocol P. For simplicity, assume that all messages have the same length m. Hence, the number of messages q that can be processed with a single key K should be such that m * q <= L. This can be depicted graphically as a rectangle with sides m and qwhich isenclosed by area L (see Figure 1). +------------------------+ | L | | +--------m---------+ | | |==================| | | |==================| | | q==================| | m * q <= L | |==================| | | |==================| | | +------------------+ | +------------------------+ Figure 1: GraphicdisplayDisplay of thekey lifetime limitationKey Lifetime Limitation In practice,suchthe amount of data that corresponds to limitation L may not be enough. The simplest and obviouswaysolution in this situation is a regular renegotiation of an initial key after processing this threshold amount of data L. However, this reduces the total performance, since it usually entails termination of application data transmission, additional service messages, the use of a random numbergeneratorgenerator, and many other additional calculations, includingresource- intensiveresource-intensive public key cryptography. Fortheprotocols based on block ciphers or streamciphersciphers, a more efficient way toincreasingincrease the key lifetime is to use various re- keying mechanisms. This specification considersonly the case of re- keyingre-keying mechanisms for blockciphers, whileciphers only; re-keying mechanisms typical for stream ciphers (e.g., [Pietrzak2009], [FPS2012])case goare beyond the scope of this document. Re-keying mechanisms can be appliedonat the different protocol levels:onthe block cipher level (this approach is known as fresh re-keying and is described, for instance, in[FRESHREKEYING]), on[FRESHREKEYING]; the block cipher mode of operation level (see Section6), on6); and the protocol level above the block cipher mode of operation (see Section 5). The usage of the first approach is highly inefficient due to the key changing afterprocessingeach messageblock.block is processed. Moreover, fresh re-keying mechanisms can change the block cipher internalstructure,structure and, consequently, can requirethean additional security analysis for each particular block cipher. As a result, this approach depends on particular primitive properties andcan notcannot be applied to any arbitrary block cipher without additional securityanalysis, therefore,analysis. Therefore, fresh re-keying mechanisms go beyond the scope of this document. Thus, this document contains the list of recommended re-keying mechanisms that can be used in the symmetric encryption schemes based on the block ciphers. These mechanisms are independent from the particular block cipherspecificationspecification, and their security properties rely only on the standard block cipher security assumption. This specification presents two basic approaches toextendextending the lifetime of a key while avoidingrenegotiation thatrenegotiation, which were introduced in [AAOS2017]: 1. External re-keying External re-keying is performed by a protocol, and it is independent of the underlying block cipher and the mode of operation. External re-keying can use parallel and serial constructions. In the parallel case, data processing keys K^1, K^2, ... are generated directly from the initial key K independently of each other. In the serial case, everydatadata- processing key depends on the state that is updated after the generation of each newdata processingdata-processing key. As a generalization of external parallelre-keyingre-keying, an external tree-based mechanism can be considered. It is specified intheSection 5.2.3 and can be viewed as the[GGM]treegeneralization.generalization in [GGM]. Similar constructions are used in the one-way tree mechanism ([OWT]) and [AESDUKPT] standard. 2. Internal re-keying Internal re-keying is built into the mode, and it depends heavily on the properties of the mode of operation and the block size. The re-keying approaches extend the key lifetime for a single initialkey by providing the possibility to limitkey by allowing the leakages to be limited (via side channels) and by improving the combinatorial properties of the used block cipher mode of operation. In practical applications, re-keying can be useful for protocols that need to operate in hostile environments or under restricted resource conditions (e.g., those that require lightweight cryptography, where ciphers have a small blocksize,size that imposes strict combinatorial limitations). Moreover, mechanisms that use external or internal re- keying may provide some protection against possible future attacks (by limiting the number of plaintext-ciphertext pairs that an adversary can collect) and some properties of forward or backward security (meaning that past or futuredata processingdata-processing keys remain secure even if the current key iscompromised,compromised; see [AbBell] for moredetails [AbBell]).details). External or internal re-keying can be used in network protocols as well as in the systems for data-at-rest encryption. Depending on the concrete protocolcharacteristicscharacteristics, there might be situations in which both external and internal re-keying mechanisms (see Section 7) can be applied. For example,thea similar approach was used intheTaha's tree construction (see [TAHA]). Note that there arekey updatingkey-updating (key regression) algorithms (e.g., [FKK2005] and [KMNT2003])whichthat are called "re-keying" as well, but they pursuethe goal different fromgoals other than increasing the key lifetime. Therefore, key regression algorithms are excluded from the considerations here. This document represents the consensus of the Crypto Forum Research Group (CFRG). 2. Conventions Used in This Document The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT", "SHOULD", "SHOULD NOT", "RECOMMENDED", "NOT RECOMMENDED", "MAY", and "OPTIONAL" in this document are to be interpreted as described in[RFC2119].BCP 14 [RFC2119] [RFC8174] when, and only when, they appear in all capitals, as shown here. 3. Basic Terms and Definitions This document uses the following terms and definitions for the sets and operations on the elements of these sets: V* the set of all bit strings of a finite length (hereinafter referred to as strings), including the empty string; V_s the set of all bit strings of length s, where s is a non- negative integer; |X| the bit length of the bit string X; A | B the concatenation of strings A and B both belonging to V*, i.e., a string in V_{|A|+|B|}, where the left substring in V_|A| is equal toA,A and the right substring in V_|B| is equal to B; (xor) the exclusive-or of two bit strings of the same length; Z_{2^n} the ring of residues modulo 2^n; Int_s: V_s -> Z_{2^s} the transformation that mapsathe string a = (a_s, ... , a_1) in V_s into the integer Int_s(a) = 2^{s-1} * a_s + ... + 2 * a_2 + a_1 (the interpretation of the binary string as an integer); Vec_s: Z_{2^s} -> V_s the transformation inverse to the mapping Int_s (the interpretation of an integer as a binary string); MSB_i: V_s -> V_i the transformation that maps the string a = (a_s, ... , a_1) in V_s into the string MSB_i(a) = (a_s, ... , a_{s-i+1}) in V_i (most significant bits); LSB_i: V_s -> V_i the transformation that maps the string a = (a_s, ... , a_1) in V_s into the string LSB_i(a) = (a_i, ... , a_1) in V_i (least significant bits); Inc_c: V_s -> V_s the transformation that maps the string a = (a_s, ... , a_1) in V_s into the string Inc_c(a) = MSB_{|a|-c}(a) | Vec_c(Int_c(LSB_c(a)) + 1(mod 2^c)) in V_s (incrementing the least significant c bits of the bit string, regarded as the binary representation of an integer); a^s the string in V_s that consists of s 'a' bits; E_{K}: V_n -> V_n the block cipher permutation under the key K in V_k; ceil(x) the smallest integer that is greater than or equal to x; floor(x) the biggest integer that is less than or equal to x; k thebit-lengthbit length of the K; k is assumed to be divisible by 8; n the block size of the block cipher (in bits); n is assumed to be divisible by 8; b the number of data blocks in the plaintext P (b = ceil(|P|/n)); N the section size (the number of bits that are processed with one section key before this key is transformed). A plaintext message P and the corresponding ciphertext C are divided into b = ceil(|P|/n) blocks, denoted as P = P_1 | P_2 | ... | P_b and C = C_1 | C_2 | ... | C_b, respectively. The first b-1 blocks P_i and C_i are inV_n,V_n for i = 1, 2, ... , b-1. The b-th blocksP_b,P_b and C_b may beanincomplete blocks, i.e., in V_r, where r <= n if not otherwise specified. 4. Choosing Constructions and Security Parameters External re-keying is an approach assuming that a key is transformed after encrypting a limited number of entire messages.External re- keyingThe external re-keying method is chosen at the protocol level, regardless of the underlying block cipher or the encryption mode. External re-keying is recommended for protocols that process relatively short messages orforprotocols that have a way to divide a long message into manageable pieces. Through externalre-keyingre-keying, the number of messages that can be securely processed with a single initial key K is substantially increased without a lossinof message length. External re-keying has the followingadvantages:advantages 1.itIt increases the lifetime of an initial key by increasing the number of messages processed with thiskey;key. 2.itIt has minimal impact onperformance,performance when the number of messages processed under one initial key is sufficientlylarge;large. 3.itIt provides forward and backward security ofdata processingdata-processing keys. However, the use of external re-keying has the following disadvantage: incase ofcases with restrictive key lifetimelimitationslimitations, the message sizes can becomeinconvenientobstructive due to the impossibility of processing sufficiently large messages, so itcouldmay be necessary to perform additional fragmentation at the protocol level.E.g.For example, if the key lifetime L is 1 GB and the message length m = 3 GB, then this message cannot be processed as awholewhole, and it should be divided into three fragments that will be processed separately. Internal re-keying is an approach assuming that a key is transformed during each separate message processing. Such procedures are integrated into the base modes of operations, so every internal re- keying mechanism is defined for the particular operation mode and the block size of the used cipher. Internal re-keying is recommended for protocols that process long messages: the size of each single message can be substantially increased without loss in the number of messages that can be securely processed with a single initial key. Internal re-keying has the following advantages: 1.itIt increases the lifetime of an initial key by increasing the size of the messages processed with one initialkey;key. 2.itIt has minimal impact onperformance;performance. 3.internalInternal re-keying mechanisms without a master keydoesdo not affectshort messagesshort-message transformation atall;all. 4.itIt is transparent (works like any mode of operation): it does not require changes ofIV'sinitialization vectors (IVs) andrestartinga restart of MACing. However, the use of internal re-keying has the following disadvantages: 1. a specific method must not be chosen independently of a mode ofoperation;operation. 2. internal re-keying mechanisms without a master key do not provide backward security ofdata processingdata-processing keys. Any block cipher modes of operations with internal re-keying can be jointly used with any external re-keying mechanisms. Such joint usage increases both the number of messages processed with one initial key and their maximum possible size. If the adversary has access to thedata processing interfacedata-processing interface, the use of the same cryptographic primitives both fordata processingdata-processing and re- keying transformation decreases the code size but can lead to some possible vulnerabilities (the possibility of mounting a chosen- plaintext attack may lead to the compromise of the following keys). This vulnerability can be eliminated by using different primitives for data processing and re-keying, e.g., block cipher for data processing and hash for re-keying (see Section 5.2.2 and Section 5.3.2). However, in thiscasecase, the security of the whole scheme cannot be reduced to standard notions likePRFa pseudorandom function (PRF) orPRP,pseudorandom permutation (PRP), so security estimations become more difficult and unclear. Summing up theabove-mentionedabovementioned issues briefly: 1. If a protocol assumes processing of long records (e.g., [CMS]), internal re-keying should be used. If a protocol assumes processing of a significantamountnumber of ordered records, which can be considered as a single data stream (e.g., [TLS], [SSH]), internal re-keying may also be used. 2. For protocolswhichthat allow out-of-order delivery and lost records (e.g., [DTLS],[ESP])[ESP]), external re-keying should be usedasas, in thiscasecase, records cannot be considered as a single data stream. Ifatthesame timerecords are also long enough, internal re-keying should also beadditionallyused during each separate message processing. For external re-keying: 1. If it is desirable to separate transformations used for data processing andforkeyupdate,updates, hashfunction basedfunction-based re-keying should be used. 2. If parallel data processing is required, then parallel external re-keying should be used. 3.In case ofIf restrictive key lifetime limitations are present, externaltree- basedtree-based re-keying should be used. For internal re-keying: 1. If the property of forward and backward security is desirable fordata processingdata-processing keys and if additional key material can be easily obtained for thedata processingdata-processing stage, internal re-keying with a master key should be used. 5. External Re-keying Mechanisms This section presents an approach toincreaseincreasing the initial key lifetime by using a transformation of adata processingdata-processing key (frame key) after processing a limited number of entire messages (frame).ItThe approach provides external parallel and serial re-keying mechanisms (see [AbBell]). These mechanisms use initial key K only for framekeyskey generation and never use it directly for data processing. Such mechanisms operate outside of the base modes of operations and do not change them atall, thereforeall; therefore, they are called "external re-keying" mechanisms in this document. External re-keying mechanisms are recommended for usage in protocols that process quite small messages, since the maximum gain in increasing the initial key lifetime is achieved by increasing the number of messages. External re-keying increases the initial key lifetime through the following approach. Suppose there is a protocol P with some mode of operation (base encryption or authentication mode). Let L1 be a key lifetime limitation induced by side-channel analysis methods (side- channel limitation), let L2 be a key lifetime limitation induced by methods based on the combinatorial properties of a used mode of operation (combinatoriallimitation)limitation), and let q1, q2 be the total numbers of messages of lengthm,m that can be safely processed with an initial key K according to these limitations. Let L = min(L1, L2), q =min (q1,min(q1, q2), and q * m <= L. As the L1 limitation is usually much stronger than the L2 limitation (L1 < L2), the final key lifetime restriction is equal to the most restrictive limitation L1. Thus, as displayed in Figure 2, withoutre-keyingre-keying, only q1 (q1 * m <= L1) messages can be safely processed. <--------m-------> +----------------+ ^ ^ |================| | | |================| | | K-->|================| q1| |================| | | |==============L1| | | +----------------+ v | | | | | | | | | q2 | | | | | | | | | | | | | | | | | | | | | | | | | L2| | +----------------+ v Figure 2: BasicprinciplesPrinciples ofmessage processingMessage Processing withoutexternal re-keyingExternal Re-keying Suppose that the safety margin for the protocol P is fixed and the external re-keying approach is applied to the initial key K to generate the sequence of frame keys. The frame keys are generated in such a way that the leakage of a previous frame key does not have any impact on the following one, so theside channelside-channel limitation L1goesis switched off. Thus, the resulting key lifetime limitation of the initial key K can be calculated on the basis of a new combinatorial limitation L2'. It is proven (see [AbBell]) that the security of the mode of operation that uses external re-keying leads to an increase when compared to base mode without re-keying (thus, L2 < L2'). Hence, as displayed in Figure 3, the resulting key lifetime limitationin case ofif using external re-keying can be increased up to L2'. <--------m-------> K +----------------+ | |================| v |================| K^1--> |================| | |================| | |==============L1| | +----------------+ | |================| v |================| K^2--> |================| | |================| | |==============L1| | +----------------+ | |================| v |================| ... | . . . | | | | | | L2| +----------------+ | | ... ... | L2'| +----------------+ Figure 3: BasicprinciplesPrinciples ofmessage processingMessage Processing withexternal re-keyingExternal Re-keying Note:theThe key transformation process is depicted in a simplified form. A specific approach (parallel and serial) is described below. Consider an example. Let the message size in a protocol P be equal to 1 KB. Suppose L1 = 128 MB and L2 = 1 TB. Thus, if an external re-keying mechanism is not used, the initial key K must be renegotiated after processing 128 MB / 1 KB = 131072 messages. If an external re-keying mechanism is used, the key lifetime limitation L1 goes off.HenceHence, the resulting key lifetime limitation L2' can be set to morethenthan 1 TB.ThusThus, if an external re-keying mechanism is used, morethenthan 1 TB / 1 KB = 2^30 messages can be processed before the initial key K is renegotiated. This is 8192 times greater than the number of messages that can beprocessed,processed when an external re-keying mechanism is not used. 5.1. Methods of Key Lifetime Control Suppose L is an amount of data that can be safely processed with one frame key. For i in {1, 2, ... ,t}t}, the frame key K^i (seeFigureFigures 4 andFigure6) should be transformed after processing q_i messages, where q_i can be calculated in accordance with one of the following approaches: Explicit approach: q_i is such that |M^{i,1}| + ... + |M^{i,q_i}| <= L, |M^{i,1}| + ... + |M^{i,q_i+1}| > L. This approach allowstouse of the frame key K^i in an almost optimalwayway, but it can be applied onlyin casewhen messages cannot be lost or reordered (e.g., TLS records). Implicit approach: q_i = L / m_max, i = 1, ... , t. The amount of data processed with one frame key K^i is calculated under the assumption that every message has the maximum length m_max.HenceHence, this amount can be considerably less than the key lifetime limitation L. On the other hand, this approach can be appliedin casewhen messages may be lost or reordered (e.g., DTLS records). Dynamic key changes: We can organize the key change using the Protected Point to Point ([P3]) solution by building a protected tunnel between the endpoints in which the information about frame key updating can be safely passed across. This can be useful, for example, when wewishwant the adversarynotto not detect the key change during the protocol evaluation. 5.2. Parallel Constructions External parallel re-keying mechanisms generate frame keys K^1, K^2, ... directly from the initial key K independently of each other. The main idea behind external re-keying with a parallel construction is presented in Figure 4: Maximum message size = m_max. _____________________________________________________________ m_max <----------------> M^{1,1} |=== | M^{1,2} |=============== | +->K^1--> ... ... | M^{1,q_1} |======== | | | | M^{2,1} |================| | M^{2,2} |===== | K-----|->K^2--> ... ... | M^{2,q_2} |========== | | ... | M^{t,1} |============ | | M^{t,2} |============= | +->K^t--> ... ... M^{t,q_t} |========== | _____________________________________________________________ Figure 4: Externalparallel re-keying mechanismsParallel Re-keying Mechanisms The frame key K^i, i = 1, ... ,t-1,t - 1 is updated after processing a certainamountnumber of messages (see Section 5.1). 5.2.1. Parallel Construction Based on a KDF on a Block Cipher The ExtParallelC re-keying mechanism is based on the key derivation function on a block cipher and is used to generate t frame keys as follows: K^1 | K^2 | ... | K^t = ExtParallelC(K, t * k) = MSB_{t * k}(E_{K}(Vec_n(0)) | E_{K}(Vec_n(1)) | ... | E_{K}(Vec_n(R - 1))), where R = ceil(t * k/n). 5.2.2. Parallel Construction Based on a KDF on a Hash Function The ExtParallelH re-keying mechanism is based on the key derivation function HKDF-Expand, described in [RFC5869], and is used to generate t frame keys as follows: K^1 | K^2 | ... | K^t = ExtParallelH(K, t * k) = HKDF-Expand(K, label, t * k), where label is a string (may be a zero-length string) that is defined by a specific protocol. 5.2.3.Tree-basedTree-Based Construction The application of an external tree-based mechanism leads to the construction of the key tree with the initial key K (root key) at the0-level0 level and the frame keys K^1, K^2, ... at the lastlevellevel, as described in Figure 5. K_root = K ___________|___________ | ... | V V K{1,1} K{1,W1} ______|______ ______|______ | ... | | ... | V V V V K{2,1} K{2,W2} K{2,(W1-1)*W2+1} K{2,W1*W2} __|__ __|__ __|__ __|__ | ... | | ... | | ... | | ... | V V V V V V V V K{3,1} ... ... ... ... ... ... K{3,W1*W2*W3} ... ... __|__ ... __|__ | ... | | ... | V V V V K{h,1} K{h,Wh} K{h,(W1*...*W{h-1}-1)*Wh+1} K{h,W1*...*Wh} // \\ // \\ K^1 K^{Wh} K^{(W1*...*W{h-1}-1)*Wh+1} K^{W1*...*Wh} ____________________________________________________________________ Figure 5: ExternalTree-basedTree-Based Mechanism The tree height h and the number of keys Wj, j in {1, ... , h}, which can be partitioned from the "parent" key, are defined in accordance with a specific protocol and key lifetime limitations for the used derivation functions. Each j-level key K{j,w}, where j in {1, ... , h}, w in {1, ... , W1 * ... * Wj}, is derived from the (j-1)-level "parent" keyK{j-1,ceil(w/ Wi)}K{j-1, ceil(w/Wi)} (and other appropriate input data) using the j-th level derivation function. This functionthatcan be based on the block cipher function or on the hash function andthatis defined in accordance with a specific protocol. The i-th frame K^i, i in {1, 2, ... , W1*...*Wh}, can be calculated as follows: K^i = ExtKeyTree(K, i) = KDF_h(KDF_{h-1}(... KDF_1(K, ceil(i / (W2 * ... * Wh)) ... , ceil(i / Wh)), i), where KDF_j is the j-th level derivation function that takes two arguments (the parent key value and the integer in a range from 1 to W1 * ... * Wj) and outputs the j-th level key value. The frame key K^i is updated after processing a certainamountnumber of messages (see Section 5.1). In order to create an efficient implementation, during frame key K^igenerationgeneration, the derivation functions KDF_j, j in {1, ... ,h-1},h-1} should be used onlyin casewhen ceil(i / (W{j+1} * ... * Wh)) != ceil((i - 1) / (W{j+1} * ... * Wh));otherwiseotherwise, it is necessary to use a previously generated value. This approach also makes it possible to take countermeasures againstside channelsside-channel attacks. Consider an example. Suppose h = 3, W1 = W2 = W3 =WW, and KDF_1, KDF_2, KDF_3 are key derivation functions based on the KDF_GOSTR3411_2012_256 (hereafter simply KDF) function described in [RFC7836]. The resulting ExtKeyTree function can be defined as follows: ExtKeyTree(K, i) = KDF(KDF(KDF(K, "level1", ceil(i / W^2)), "level2", ceil(i / W)), "level3", i). where i in {1, 2, ... , W^3}.TheA structure similar to the external tree-based mechanism can be found in Section 6 of [NISTSP800-108]. 5.3. Serial Constructions External serial re-keying mechanisms generate frame keys, each of which depends on the secret state (K*_1, K*_2,..., see Figure 6)...) that is updated after the generation of each new framekey.key; see Figure 6. Similar approaches are used in the [SIGNAL]protocol, inprotocol and the [TLS] updating traffickeyskey mechanism and were proposed for use in the [U2F] protocol. External serial re-keying mechanisms have the obvious disadvantage ofthe impossibilitybeing impossible tobe implementedimplement in parallel, but theycanmay be the preferred option if additional forward secrecy isdesirable: in casedesirable. If all keys are securely deleted after usage, the compromise of a current secret state at sometimepoint does not lead to a compromise of all previous secret states and frame keys. In terms of [TLS], compromise of application_traffic_secret_N does not compromise all previous application_traffic_secret_i, i < N. The main idea behind external re-keying with a serial construction is presented in Figure 6: Maximum message size = m_max. _____________________________________________________________ m_max <----------------> M^{1,1} |=== | M^{1,2} |=============== | K*_1 = K --->K^1--> ... ... | M^{1,q_1} |======== | | | | M^{2,1} |================| v M^{2,2} |===== | K*_2 ------->K^2--> ... ... | M^{2,q_2} |========== | | ... | M^{t,1} |============ | v M^{t,2} |============= | K*_t ------->K^t--> ... ... M^{t,q_t} |========== | _____________________________________________________________ Figure 6: Externalserial re-keying mechanismsSerial Re-keying Mechanisms The frame key K^i, i = 1, ... , t - 1, is updated after processing a certainamountnumber of messages (see Section 5.1). 5.3.1. Serial Construction Based on a KDF on a Block Cipher The frame key K^i is calculated using the ExtSerialC transformation as follows: K^i = ExtSerialC(K, i) = MSB_k(E_{K*_i}(Vec_n(0)) |E_{K*_i}(Vec_n(1)) | ... | E_{K*_i}(Vec_n(J - 1))), where J = ceil(k / n), i = 1, ... , t, K*_i is calculated as follows: K*_1 = K, K*_{j+1} = MSB_k(E_{K*_j}(Vec_n(J)) | E_{K*_j}(Vec_n(J + 1)) | ... | E_{K*_j}(Vec_n(2 * J - 1))), where j = 1, ... , t - 1. 5.3.2. Serial Construction Based on a KDF on a Hash Function The frame key K^i is calculated using the ExtSerialH transformation as follows: K^i = ExtSerialH(K, i) = HKDF-Expand(K*_i, label1, k), where i = 1, ... ,t,t; HKDF-Expand is the HMAC-based key derivation function, as described in[RFC5869],[RFC5869]; and K*_i is calculated as follows: K*_1 = K, K*_{j+1} = HKDF-Expand(K*_j, label2, k), where j = 1, ... , t - 1, where label1 and label2 are different strings from V* that are defined by a specific protocol (see, for example,TLS 1.3the algorithm for updating traffic keysalgorithmin TLS 1.3 [TLS]). 5.4. Using Additional Entropy during Re-keying In manycasescases, using additional entropy during re-keying won't increasesecurity,security but may give a false sense ofthat, thereforethat. Therefore, one can rely on additional entropy only after conducting a deep security analysis. For example, good PRF constructions do not require additional entropy for the quality of keys,soso, in mostcasescases, there is no needfor usingto use additional entropy with external re-keying mechanisms based on secure KDFs. However, in somesituationssituations, mixed- in entropy can still increase security in the case of a time-limited but complete breach of thesystem,system when an adversary can access theframe keysframe-key generationinterface,interface but cannot reveal the master keys (e.g., when the master keys are stored inan HSM).a Hardware Security Module (HSM)). For example, an external parallel construction based on a KDF on aHashhash function with a mixed-in entropy can be described as follows: K^i = HKDF-Expand(K, label_i, k), where label_i is additional entropy that must be sent to the recipient (e.g.,besent jointly with an encrypted message). The entropy label_i and the corresponding key K^i must be generated directly before message processing. 6. Internal Re-keying Mechanisms This section presents an approach toincreaseincreasing the key lifetime by using a transformation of adata processingdata-processing key (section key) during each separate message processing. Each message is processed starting with the same key (the first sectionkey)key), and each section key is updated after processing N bits of the message (section). This section provides internal re-keying mechanisms called ACPKM (Advanced Cryptographic Prolongation of Key Material) and ACPKM- Master that do not use a master key and use a masterkeykey, respectively. Such mechanisms are integrated into the base modes of operation and actually form new modes ofoperation, thereforeoperation. Therefore, they are called "internal re-keying" mechanisms in this document. Internal re-keying mechanisms are recommended to be used in protocols that process large single messages (e.g., CMS messages), since the maximum gain in increasing the key lifetime is achieved by increasing the length of a message, while it provides almost no increase in the number of messages that can be processed with one initial key. Internal re-keying increases the key lifetime through the following approach. Suppose protocol P uses some base mode of operation. Let L1 and L2 be a side channel and combinatoriallimitations respectivelylimitations, respectively, and for some fixedamountnumber of messagesqq, let m1, m2 be the lengths ofmessages,messages that can be safely processed with a single initial key K according to these limitations. Thus,by analogy withtheSection 5approach without re-keyingthe(analogous to Section 5) yields a final key lifetimerestriction, as displayed in Figure 7, isrestriction equal toL1L1, and only q messages of the length m1 can be safelyprocessed.processed; see Figure 7. K | v ^ +----------------+------------------------------------+ | |==============L1| L2| | |================| | q |================| | | |================| | | |================| | v +----------------+------------------------------------+ <-------m1-------> <----------------------------m2-----------------------> Figure 7: BasicprinciplesPrinciples ofmessage processingMessage Processing withoutinternal re-keyingInternal Re- keying Suppose that the safety margin for the protocol P is fixed and the internal re-keying approach is applied to the base mode of operation. Suppose further that every message is processed with a section key, which is transformed after processing N bits of data, where N is a parameter. If q * N does not exceedL1L1, then theside channelside-channel limitation L1 goesoffoff, and the resulting key lifetime limitation of the initial key K can be calculated on the basis of a new combinatorial limitation L2'. The security of the mode of operation that uses internal re-keying increases when compared to the base mode of operation without re-keying (thus, L2 < L2'). Hence, as displayed in Figure 8, the resulting key lifetime limitationin case ofif using internal re-keying can be increased up to L2'. K-----> K^1-------------> K^2 -----------> . . . | | v v ^ +---------------+---------------+------------------+--...--+ | |=============L1|=============L1|====== L2| L2'| | |===============|===============|====== | | q |===============|===============|====== . . . | | | |===============|===============|====== | | | |===============|===============|====== | | v +---------------+---------------+------------------+--...--+ <-------N-------> Figure 8: BasicprinciplesPrinciples ofmessage processingMessage Processing withinternal re-keyingInternal Re- keying Note:theThe key transformation process is depicted in a simplified form. A specific approach (ACPKM and ACPKM-Master re-keying mechanisms) is described below. Since the performance of encryption can slightly decrease for rather small values of N, theparameter Nmaximum possible value should be selected for parameter N for a particular protocolas maximum possiblein order to provide the necessary key lifetime for the considered security models. Consider an example. Suppose L1 = 128 MB and L2 = 10 TB. Let the message size in the protocol be large/unlimited(may(which may exhaust the whole key lifetime L2). The most restrictive resulting key lifetime limitation is equal to 128 MB. Thus, there is a need to put a limit on the maximum message size m_max. For example, if m_max = 32 MB, it may happen that the renegotiation of initial key K would be required after processing only four messages. If an internal re-keying mechanism with section size N = 1 MB is used, more than L1 / N = 128 MB / 1 MB = 128 messages can be processed before the renegotiation of initial key K (instead of4four messagesin casewhen an internal re-keying mechanism is not used). Note that only one section of each message is processed with the section key K^i, and, consequently, the key lifetime limitation L1 goes off.HenceHence, the resulting key lifetime limitation L2' can be set to morethenthan 10 TB (inthe casecases when a single large message is processed using the initial key K). 6.1. Methods of Key Lifetime Control Suppose L is an amount of data that can be safely processed with one sectionkey,key and N is a section size (fixed parameter). Suppose M^{i}_1 is the first section of message M^{i}, i = 1, ... , q (seeFigureFigures 9 andFigure 10), then10); the parameter q can then be calculated in accordance with one of the following two approaches: o Explicit approach: q_i is such that |M^{1}_1| + ... + |M^{q}_1| <= L, |M^{1}_1| + ... + |M^{q+1}_1| > L This approach allowstouse of the section key K^i in an almost optimalwayway, but it can be applied onlyin casewhen messages cannot be lost or reordered (e.g., TLS records). o Implicit approach: q = L / N. The amount of data processed with one section key K^i is calculated under the assumption that the length of every message is equal to or greater than section size N andso itthus can be considerably less than the key lifetime limitation L. On the other hand, this approach can be appliedin casewhen messages may be lost or reordered (e.g., DTLS records). 6.2. Constructions that Do Not Require a Master Key This section describes the block cipher modes that use the ACPKM re- keying mechanism, which does not use a masterkey:key; an initial key is used directly for the data encryption. 6.2.1. ACPKM Re-keying Mechanisms This section defines a periodical key transformation without a master key, which is called the ACPKM re-keying mechanism. This mechanism can be applied to one of the base encryption modes (CTR and GCM block cipher modes)for gettingto get an extension of this encryption mode that uses periodical key transformation without a master key. This extension can be considered as a new encryption mode. An additional parameter that defines the functioning of base encryption modes with the ACPKM re-keying mechanism is the section size N. The value of N is measured in bits and is fixed within a specific protocol based on the requirements of the system capacity and the key lifetime. The section size N MUST be divisible by the block size n. The main idea behind internal re-keying without a master key is presented in Figure 9: Section size = const = N, maximum message size = m_max. ____________________________________________________________________ ACPKM ACPKM ACPKM K^1 = K ---> K^2 ---...-> K^{l_max-1} ----> K^{l_max} | | | | | | | | v v v v M^{1} |==========|==========| ... |==========|=======: | M^{2} |==========|==========| ... |=== | : | . . . . . . : : : : : : : : M^{q} |==========|==========| ... |==========|===== : | section : <----------> m_max N bit ___________________________________________________________________ l_max = ceil(m_max/N). Figure 9: Internalre-keyingRe-keying without amaster keyMaster Key During the processing of the input message M with the length m in some encryption mode that uses the ACPKM key transformation of the initial keyKK, the message is divided into l = ceil(m / N) sections (denoted as M = M_1 | M_2 | ... | M_l, where M_i is in V_N for i in {1, 2, ... , l - 1} and M_l is in V_r, r <= N). The first section of each message is processed with the section key K^1 = K. To process the (i + 1)-th section of eachmessagemessage, the section key K^{i+1} is calculated using the ACPKM transformation as follows: K^{i+1} = ACPKM(K^i) = MSB_k(E_{K^i}(D_1) | ... | E_{K^i}(D_J)), where J = ceil(k/n) and D_1, D_2, ... , D_J are in V_n and are calculated as follows: D_1 | D_2 | ... | D_J = MSB_{J * n}(D), where D is the following constant in V_{1024}: D = ( 80 | 81 | 82 | 83 | 84 | 85 | 86 | 87 | 88 | 89 | 8a | 8b | 8c | 8d | 8e | 8f | 90 | 91 | 92 | 93 | 94 | 95 | 96 | 97 | 98 | 99 | 9a | 9b | 9c | 9d | 9e | 9f | a0 | a1 | a2 | a3 | a4 | a5 | a6 | a7 | a8 | a9 | aa | ab | ac | ad | ae | af | b0 | b1 | b2 | b3 | b4 | b5 | b6 | b7 | b8 | b9 | ba | bb | bc | bd | be | bf | c0 | c1 | c2 | c3 | c4 | c5 | c6 | c7 | c8 | c9 | ca | cb | cc | cd | ce | cf | d0 | d1 | d2 | d3 | d4 | d5 | d6 | d7 | d8 | d9 | da | db | dc | dd | de | df | e0 | e1 | e2 | e3 | e4 | e5 | e6 | e7 | e8 | e9 | ea | eb | ec | ed | ee | ef | f0 | f1 | f2 | f3 | f4 | f5 | f6 | f7 | f8 | f9 | fa | fb | fc | fd | fe | ff)N o t e :Note: The constant D is such that D_1, ... , D_J are pairwise different for any allowed n and k values.N o t e :Note: The highest bit of each octet of the constant D is equal to 1. This condition isimportant, asimportant as, in conjunction with a certain mode message lengthlimitationlimitation, it allowsto preventprevention of collisions of block cipher permutation inputs in casesofwith key transformation and message processing (for moredetailsdetails, see Section 4.4 of [AAOS2017]). 6.2.2. CTR-ACPKM Encryption Mode This section defines a CTR-ACPKM encryption mode that uses the ACPKM internal re-keying mechanism for the periodical key transformation. The CTR-ACPKM mode can be considered as the base encryption mode CTR (see [MODES]) extended by the ACPKM re-keying mechanism. The CTR-ACPKM encryption mode can be used with the following parameters: o 64 <= n <=512;512. o 128 <= k <=512;512. otheThe number c of bits in a specific part of the block to be incremented is such that 32 <= c <= 3 / 4 n, where c is a multiple of8;8. otheThe maximum message size m_max = n * 2^{c-1}. The CTR-ACPKM mode encryption and decryption procedures are defined as follows: +----------------------------------------------------------------+ | CTR-ACPKM-Encrypt(N, K, ICN, P) | |----------------------------------------------------------------| | Input: | | - section size N, | | - initial key K, | | - initial counter nonce ICN in V_{n-c}, | | - plaintext P = P_1 | ... | P_b, |P| <= m_max. | | Output: | | - ciphertext C. | |----------------------------------------------------------------| | 1. CTR_1 = ICN | 0^c | | 2. For j = 2, 3, ... , b do | | CTR_{j} = Inc_c(CTR_{j-1}) | | 3. K^1 = K | | 4. For i = 2, 3, ... , ceil(|P| / N) | | K^i = ACPKM(K^{i-1}) | | 5. For j = 1, 2, ... , b do | | i = ceil(j * n / N), | | G_j = E_{K^i}(CTR_j) | | 6. C = P (xor) MSB_{|P|}(G_1 | ... | G_b) | | 7. Return C | +----------------------------------------------------------------+ +----------------------------------------------------------------+ | CTR-ACPKM-Decrypt(N, K, ICN, C) | |----------------------------------------------------------------| | Input: | | - section size N, | | - initial key K, | | - initial counter nonce ICN in V_{n-c}, | | - ciphertext C = C_1 | ... | C_b, |C| <= m_max. | | Output: | | - plaintext P. | |----------------------------------------------------------------| | 1. P = CTR-ACPKM-Encrypt(N, K, ICN, C) | | 2. Return P | +----------------------------------------------------------------+ The initial counter nonceICN(ICN) value for each message that is encrypted under the given initial key K must be chosen in a unique manner. 6.2.3. GCM-ACPKM Authenticated Encryption Mode This section defines the GCM-ACPKM authenticated encryption mode that uses the ACPKM internal re-keying mechanism for the periodical key transformation. The GCM-ACPKM mode can be considered as the base authenticated encryption mode GCM (see [GCM]) extended by the ACPKM re-keying mechanism. The GCM-ACPKM authenticated encryption mode can be used with the following parameters: o n in {128,256};256}. o 128 <= k <=512;512. otheThe number c of bits in a specific part of the block to be incremented is such that 1 / 4 n <= c <= 1 / 2 n, c is a multiple of8;8. oauthenticationAuthentication tag lengtht;t. otheThe maximum message size m_max = min{n * (2^{c-1} - 2), 2^{n/2} - 1}. The GCM-ACPKM mode encryption and decryption procedures are defined as follows: +-------------------------------------------------------------------+ | GHASH(X, H) | |-------------------------------------------------------------------| | Input: | | - bit string X = X_1 | ... | X_m, X_1, ... , X_m in V_n. | | Output: | | - block GHASH(X, H) in V_n. | |-------------------------------------------------------------------| | 1. Y_0 = 0^n | | 2. For i = 1, ... , m do | | Y_i = (Y_{i-1} (xor) X_i) * H | | 3. Return Y_m | +-------------------------------------------------------------------+ +-------------------------------------------------------------------+ | GCTR(N, K, ICB, X) | |-------------------------------------------------------------------| | Input: | | - section size N, | | - initial key K, | | - initial counter block ICB, | | - X = X_1 | ... | X_b. | | Output: | | - Y in V_{|X|}. | |-------------------------------------------------------------------| | 1. If X inV_0V_0, then return Y, where Y in V_0 | | 2. GCTR_1 = ICB | | 3. For i = 2, ... , b do | | GCTR_i = Inc_c(GCTR_{i-1}) | | 4. K^1 = K | | 5. For j = 2, ... , ceil(|X| / N) | | K^j = ACPKM(K^{j-1}) | | 6. For i = 1, ... , b do | | j = ceil(i * n / N), | | G_i = E_{K_j}(GCTR_i) | | 7. Y = X (xor) MSB_{|X|}(G_1 | ... | G_b) | | 8. Return Y | +-------------------------------------------------------------------+ +-------------------------------------------------------------------+ | GCM-ACPKM-Encrypt(N, K, ICN, P, A) | |-------------------------------------------------------------------| | Input: | | - section size N, | | - initial key K, | | - initial counter nonce ICN in V_{n-c}, | | - plaintext P = P_1 | ... | P_b, |P| <= m_max, | | - additional authenticated data A. | | Output: | | - ciphertext C, | | - authentication tag T. | |-------------------------------------------------------------------| | 1. H = E_{K}(0^n) | | 2. ICB_0 = ICN | 0^{c-1} | 1 | | 3. C = GCTR(N, K, Inc_c(ICB_0), P) | | 4. u = n * ceil(|C| / n) - |C| | | v = n * ceil(|A| / n) - |A| | | 5. S = GHASH(A | 0^v | C | 0^u | Vec_{n/2}(|A|) | | | | Vec_{n/2}(|C|), H) | | 6. T = MSB_t(E_{K}(ICB_0) (xor) S) | | 7. Return C | T | +-------------------------------------------------------------------+ +-------------------------------------------------------------------+ | GCM-ACPKM-Decrypt(N, K, ICN, A, C, T) | |-------------------------------------------------------------------| | Input: | | - section size N, | | - initial key K, | | - initial counter block ICN, | | - additional authenticated data A, | | - ciphertext C = C_1 | ... | C_b, |C| <= m_max, | | - authentication tag T. | | Output: | | - plaintext P or FAIL. | |-------------------------------------------------------------------| | 1. H = E_{K}(0^n) | | 2. ICB_0 = ICN | 0^{c-1} | 1 | | 3. P = GCTR(N, K, Inc_c(ICB_0), C) | | 4. u = n * ceil(|C| / n) - |C| | | v = n * ceil(|A| / n) - |A| | | 5. S = GHASH(A | 0^v | C | 0^u | Vec_{n/2}(|A|) | | | | Vec_{n/2}(|C|), H) | | 6. T' = MSB_t(E_{K}(ICB_0) (xor) S) | | 7. If T =T'T', then return P; else return FAIL | +-------------------------------------------------------------------+ The * operation on (pairs of) the 2^n possible blocks corresponds to the multiplication operation for the binary Galois (finite) field of 2^n elements defined by the polynomial f as follows(by analogy with(analogous to [GCM]): n = 128: f = a^128 + a^7 + a^2 + a^1 + 1, n = 256: f = a^256 + a^10 + a^5 + a^2 + 1. The initial counter nonce ICN value for each message that is encrypted under the given initial key K must be chosen in a unique manner. The key for computing values E_{K}(ICB_0) and H is not updated and is equal to the initial key K. 6.3. Constructions that Require a Master Key This section describes the block cipher modes that use the ACPKM- Master re-keying mechanism, which use the initial key K as a master key, so K is never used directly for data processing but is used for key derivation. 6.3.1. ACPKM-Master Key Derivation from the Master Key This section defines periodical key transformation with a master key, which is called the ACPKM-Master re-keying mechanism. This mechanism can be applied to one of the base modes of operation (CTR, GCM, CBC, CFB, OMAC modes) for getting an extension that uses periodical key transformation with a master key. This extension can be considered as a new mode of operation. Additional parameters that define the functioning of modes of operation that use the ACPKM-Master re-keying mechanism are the section size N, the change frequency T* of the master keys K*_1, K*_2, ... (see Figure10)10), and the size d of the section key material. The values of N and T* are measured in bits and are fixed within a specificprotocol,protocol based on the requirements of the system capacity and the key lifetime. The section size N MUST be divisible by the block size n. The master key frequency T* MUST be divisible by d and by n. The main idea behind internal re-keying with a master key is presented in Figure 10: Master key frequency T*, section size N, maximum message size = m_max. _____________________________________________________________________ ACPKM ACPKM K*_1 = K----------> K*_2 ---------...-----> K*_l_max ___|___ ___|___ ___|___ | | | | | | v ... v v ... v v ... v K[1] K[t] K[t+1] K[2*t] K[(l_max-1)t+1] K[l_max*t] | | | | | | | | | | | | v v v v v v M^{1}||======|...|======||======|...|======||...||======|...|== : || M^{2}||======|...|======||======|...|======||...||======|...|====: || ... || | | || | | || || | | : || M^{q}||======|...|======||==== |...| ||...|| |...| : || section : <------> : N bit m_max _____________________________________________________________________ |K[i]| = d, t = T* / d, l_max = ceil(m_max / (N * t)). Figure 10: Internalre-keyingRe-keying with amaster keyMaster Key During the processing of the input message M with the length m in some mode of operation that uses ACPKM-Master key transformation with the initial key K and the master key frequencyT*T*, the message M is divided into l = ceil(m / N) sections (denoted as M = M_1 | M_2 | ... | M_l, where M_i is in V_N for i in {1, 2, ... , l - 1} and M_l is in V_r, r <= N). The j-th section of each message is processed with the key material K[j], j in {1, ... , l}, |K[j]| = d,thatwhich is calculated with the ACPKM-Master algorithm as follows: K[1] | ... | K[l] = ACPKM-Master(T*, K, d, l) = CTR-ACPKM-Encrypt (T*, K, 1^{n/2}, 0^{d*l}). Note:theThe parameters d and l MUST be such that d * l <= n * 2^{n/2-1}. 6.3.2. CTR-ACPKM-Master Encryption Mode This section defines a CTR-ACPKM-Master encryption mode that uses the ACPKM-Master internal re-keying mechanism for the periodical key transformation. The CTR-ACPKM-Master encryption mode can be considered as the base encryption mode CTR (see [MODES]) extended by the ACPKM-Master re- keying mechanism. The CTR-ACPKM-Master encryption mode can be used with the following parameters: o 64 <= n <=512;512. o 128 <= k <=512;512. otheThe number c of bits in a specific part of the block to be incremented is such that 32 <= c <= 3 / 4 n, c is a multiple of8;8. otheThe maximum message size m_max = min{N * (n * 2^{n/2-1} / k), n * 2^c}. The key material K[j] that is used forone sectionone-section processing is equal to K^j, where |K^j| = k bits. The CTR-ACPKM-Master mode encryption and decryption procedures are defined as follows: +----------------------------------------------------------------+ | CTR-ACPKM-Master-Encrypt(N, K, T*, ICN, P) | |----------------------------------------------------------------| | Input: | | - section size N, | | - initial key K, | | - master key frequency T*, | | - initial counter nonce ICN in V_{n-c}, | | - plaintext P = P_1 | ... | P_b, |P| <= m_max. | | Output: | | - ciphertext C. | |----------------------------------------------------------------| | 1. CTR_1 = ICN | 0^c | | 2. For j = 2, 3, ... , b do | | CTR_{j} = Inc_c(CTR_{j-1}) | | 3. l = ceil(|P| / N) | | 4. K^1 | ... | K^l = ACPKM-Master(T*, K, k, l) | | 5. For j = 1, 2, ... , b do | | i = ceil(j * n / N), | | G_j = E_{K^i}(CTR_j) | | 6. C = P (xor) MSB_{|P|}(G_1 | ... |G_b) | | 7. Return C | |----------------------------------------------------------------+ +----------------------------------------------------------------+ | CTR-ACPKM-Master-Decrypt(N, K, T*, ICN, C) | |----------------------------------------------------------------| | Input: | | - section size N, | | - initial key K, | | - master key frequency T*, | | - initial counter nonce ICN in V_{n-c}, | | - ciphertext C = C_1 | ... | C_b, |C| <= m_max. | | Output: | | - plaintext P. | |----------------------------------------------------------------| | 1. P = CTR-ACPKM-Master-Encrypt(N, K, T*, ICN, C) | | 1. Return P | +----------------------------------------------------------------+ The initial counter nonce ICN value for each message that is encrypted under the given initial key must be chosen in a unique manner. 6.3.3. GCM-ACPKM-Master Authenticated Encryption Mode This section defines a GCM-ACPKM-Master authenticated encryption mode that uses the ACPKM-Master internal re-keying mechanism for the periodical key transformation. The GCM-ACPKM-Master authenticated encryption mode can be considered as the base authenticated encryption mode GCM (see [GCM]) extended by the ACPKM-Master re-keying mechanism. The GCM-ACPKM-Master authenticated encryption mode can be used with the following parameters: o n in {128,256};256}. o 128 <= k <=512;512. otheThe number c of bits in a specific part of the block to be incremented is such that 1 / 4 n <= c <= 1 / 2 n, c is a multiple of8;8. o authentication tag lengtht;t. o the maximum message size m_max = min{N * ( n * 2^{n/2-1} / k), n * (2^c - 2), 2^{n/2} - 1}. The key material K[j] that is used for the j-th section processing is equal to K^j, |K^j| = k bits. The GCM-ACPKM-Master mode encryption and decryption procedures are defined as follows: +-------------------------------------------------------------------+ | GHASH(X, H) | |-------------------------------------------------------------------| | Input: | | - bit string X = X_1 | ... | X_m, X_i in V_n for i in {1, ... ,m}| | Output: | | - block GHASH(X, H) in V_n | |-------------------------------------------------------------------| | 1. Y_0 = 0^n | | 2. For i = 1, ... , m do | | Y_i = (Y_{i-1} (xor) X_i) * H | | 3. Return Y_m | +-------------------------------------------------------------------+ +-------------------------------------------------------------------+ | GCTR(N, K, T*, ICB, X) | |-------------------------------------------------------------------| | Input: | | - section size N, | | - initial key K, | | - master key frequency T*, | | - initial counter block ICB, | | - X = X_1 | ... | X_b. | | Output: | | - Y in V_{|X|}. | |-------------------------------------------------------------------| | 1. If X inV_0V_0, then return Y, where Y in V_0 | | 2. GCTR_1 = ICB | | 3. For i = 2, ... , b do | | GCTR_i = Inc_c(GCTR_{i-1}) | | 4. l = ceil(|X| / N) | | 5. K^1 | ... | K^l = ACPKM-Master(T*, K, k, l) | | 6. For j = 1, ... , b do | | i = ceil(j * n / N), | | G_j = E_{K^i}(GCTR_j) | | 7. Y = X (xor) MSB_{|X|}(G_1 | ... | G_b) | | 8. Return Y | +-------------------------------------------------------------------+ +-------------------------------------------------------------------+ | GCM-ACPKM-Master-Encrypt(N, K, T*, ICN, P, A) | |-------------------------------------------------------------------| | Input: | | - section size N, | | - initial key K, | | - master key frequency T*, | | - initial counter nonce ICN in V_{n-c}, | | - plaintext P = P_1 | ... | P_b, |P| <= m_max. | | - additional authenticated data A. | | Output: | | - ciphertext C, | | - authentication tag T. | |-------------------------------------------------------------------| | 1. K^1 = ACPKM-Master(T*, K, k, 1) | | 2. H = E_{K^1}(0^n) | | 3. ICB_0 = ICN | 0^{c-1} | 1 | | 4. C = GCTR(N, K, T*, Inc_c(ICB_0), P) | | 5. u = n * ceil(|C| / n) - |C| | | v = n * ceil(|A| / n) - |A| | | 6. S = GHASH(A | 0^v | C | 0^u | Vec_{n/2}(|A|) | | | | Vec_{n/2}(|C|), H) | | 7. T = MSB_t(E_{K^1}(ICB_0) (xor) S) | | 8. Return C | T | +-------------------------------------------------------------------+ +-------------------------------------------------------------------+ | GCM-ACPKM-Master-Decrypt(N, K, T*, ICN, A, C, T) | |-------------------------------------------------------------------| | Input: | | - section size N, | | - initial key K, | | - master key frequency T*, | | - initial counter nonce ICN in V_{n-c}, | | - additional authenticated data A. | | - ciphertext C = C_1 | ... | C_b, |C| <= m_max, | | - authentication tag T. | | Output: | | - plaintext P or FAIL. | |-------------------------------------------------------------------| | 1. K^1 = ACPKM-Master(T*, K, k, 1) | | 2. H = E_{K^1}(0^n) | | 3. ICB_0 = ICN | 0^{c-1} | 1 | | 4. P = GCTR(N, K, T*, Inc_c(ICB_0), C) | | 5. u = n * ceil(|C| / n) - |C| | | v = n * ceil(|A| / n) - |A| | | 6. S = GHASH(A | 0^v | C | 0^u | Vec_{n/2}(|A|) | | | | Vec_{n/2}(|C|), H) | | 7. T' = MSB_t(E_{K^1}(ICB_0) (xor) S) | | 8.IFIf T =T'T', then return P; else return FAIL. | +-------------------------------------------------------------------+ The * operation on (pairs of) the 2^n possible blocks corresponds to the multiplication operation for the binary Galois (finite) field of 2^n elements defined by the polynomial f as follows (by analogy with [GCM]): n = 128: f = a^128 + a^7 + a^2 + a^1 + 1, n = 256: f = a^256 + a^10 + a^5 + a^2 + 1. The initial counter nonce ICN value for each message that is encrypted under the given initial key must be chosen in a unique manner. 6.3.4. CBC-ACPKM-Master Encryption Mode This section defines a CBC-ACPKM-Master encryption mode that uses the ACPKM-Master internal re-keying mechanism for the periodical key transformation. The CBC-ACPKM-Master encryption mode can be considered as the base encryption mode CBC (see [MODES]) extended by the ACPKM-Master re- keying mechanism. The CBC-ACPKM-Master encryption mode can be used with the following parameters: o 64 <= n <=512;512. o 128 <= k <=512;512. otheThe maximum message size m_max = N * (n * 2^{n/2-1} / k). In the specification of the CBC-ACPKM-Mastermodemode, the plaintext and ciphertext must be a sequence of one or more complete data blocks. If the data string to be encrypted does not initially satisfy this property, then it MUST be padded to form complete data blocks. The padding methods are out of the scope of this document. An example of a padding method can be found in Appendix A of [MODES]. The key material K[j] that is used for the j-th section processing is equal to K^j, |K^j| = k bits. Wewill denote byuse D_{K} to denote the decryption functionwhichthat is a permutation inverse to E_{K}. The CBC-ACPKM-Master mode encryption and decryption procedures are defined as follows: +----------------------------------------------------------------+ | CBC-ACPKM-Master-Encrypt(N, K, T*, IV, P) | |----------------------------------------------------------------| | Input: | | - section size N, | | - initial key K, | | - master key frequency T*, | | - initialization vector IV in V_n, | | - plaintext P = P_1 | ... | P_b, |P_b| = n, |P| <= m_max. | | Output: | | - ciphertext C. | |----------------------------------------------------------------| | 1. l = ceil(|P| / N) | | 2. K^1 | ... | K^l = ACPKM-Master(T*, K, k, l) | | 3. C_0 = IV | | 4. For j = 1, 2, ... , b do | | i = ceil(j * n / N), | | C_j = E_{K^i}(P_j (xor) C_{j-1}) | | 5. Return C = C_1 | ... | C_b | |----------------------------------------------------------------+ +----------------------------------------------------------------+ | CBC-ACPKM-Master-Decrypt(N, K, T*, IV, C) | |----------------------------------------------------------------| | Input: | | - section size N, | | - initial key K, | | - master key frequency T*, | | - initialization vector IV in V_n, | | - ciphertext C = C_1 | ... | C_b, |C_b| = n, |C| <= m_max. | | Output: | | - plaintext P. | |----------------------------------------------------------------| | 1. l = ceil(|C| / N) | | 2. K^1 | ... | K^l = ACPKM-Master(T*, K, k, l) | | 3. C_0 = IV | | 4. For j = 1, 2, ... , b do | | i = ceil(j * n / N) | | P_j = D_{K^i}(C_j) (xor) C_{j-1} | | 5. Return P = P_1 | ... | P_b | +----------------------------------------------------------------+ The initialization vector IV for any particular execution of the encryption process must be unpredictable. 6.3.5. CFB-ACPKM-Master Encryption Mode This section defines a CFB-ACPKM-Master encryption mode that uses the ACPKM-Master internal re-keying mechanism for the periodical key transformation. The CFB-ACPKM-Master encryption mode can be considered as the base encryption mode CFB (see [MODES]) extended by the ACPKM-Master re- keying mechanism. The CFB-ACPKM-Master encryption mode can be used with the following parameters: o 64 <= n <=512;512. o 128 <= k <=512;512. otheThe maximum message size m_max = N * (n * 2^{n/2-1} / k). The key material K[j] that is used for the j-th section processing is equal to K^j, |K^j| = k bits. The CFB-ACPKM-Master mode encryption and decryption procedures are defined as follows: +-------------------------------------------------------------+ | CFB-ACPKM-Master-Encrypt(N, K, T*, IV, P) | |-------------------------------------------------------------| | Input: | | - section size N, | | - initial key K, | | - master key frequency T*, | | - initialization vector IV in V_n, | | - plaintext P = P_1 | ... | P_b, |P| <= m_max. | | Output: | | - ciphertext C. | |-------------------------------------------------------------| | 1. l = ceil(|P| / N) | | 2. K^1 | ... | K^l = ACPKM-Master(T*, K, k, l) | | 3. C_0 = IV | | 4. For j = 1, 2, ... , b - 1 do | | i = ceil(j * n / N), | | C_j = E_{K^i}(C_{j-1}) (xor) P_j | | 5. C_b = MSB_{|P_b|}(E_{K^l}(C_{b-1})) (xor) P_b | | 6. Return C = C_1 | ... | C_b | |-------------------------------------------------------------+ +-------------------------------------------------------------+ | CFB-ACPKM-Master-Decrypt(N, K, T*, IV, C) | |-------------------------------------------------------------| | Input: | | - section size N, | | - initial key K, | | - master key frequency T*, | | - initialization vector IV in V_n, | | - ciphertext C = C_1 | ... | C_b, |C| <= m_max. | | Output: | | - plaintext P. | |-------------------------------------------------------------| | 1. l = ceil(|C| / N) | | 2. K^1 | ... | K^l = ACPKM-Master(T*, K, k, l) | | 3. C_0 = IV | | 4. For j = 1, 2, ... , b - 1 do | | i = ceil(j * n / N), | | P_j = E_{K^i}(C_{j-1}) (xor) C_j | | 5. P_b = MSB_{|C_b|}(E_{K^l}(C_{b-1})) (xor) C_b | | 6. Return P = P_1 | ... | P_b | +-------------------------------------------------------------+ The initialization vector IV for any particular execution of the encryption process must be unpredictable. 6.3.6. OMAC-ACPKM-Master Authentication Mode This section defines an OMAC-ACPKM-Master message authentication code calculation mode that uses the ACPKM-Master internal re-keying mechanism for the periodical key transformation. The OMAC-ACPKM-Master mode can be considered as the base message authentication code calculation modeOMAC,OMAC1, which is also known as CMAC (see [RFC4493]), extended by the ACPKM-Master re-keying mechanism. The OMAC-ACPKM-Master message authentication code calculation mode can be used with the following parameters: o n in {64, 128,256};256}. o 128 <= k <=512;512. otheThe maximum message size m_max = N * (n * 2^{n/2-1} / (k + n)). The key material K[j] that is used forone sectionone-section processing is equal to K^j | K^j_1, where |K^j| = k bits and |K^j_1| =n.n bits. The following is a specification of the subkey generation process of OMAC: +-------------------------------------------------------------------+ | Generate_Subkey(K1, r) | |-------------------------------------------------------------------| | Input: | | - key K1. | | Output: | | - key SK. | |-------------------------------------------------------------------| | 1. If r =nn, then return K1 | | 2. If r <nn, then | | if MSB_1(K1) = 0 | | return K1 << 1 | | else | | return (K1 << 1) (xor) R_n || |+-------------------------------------------------------------------+HereHere, R_n takes the following values: o n = 64: R_{64} = 0^{59} |11011;11011. o n = 128: R_{128} = 0^{120} |10000111;10000111. o n = 256: R_{256} = 0^{145} | 10000100101. The OMAC-ACPKM-Master message authentication code calculation mode is defined as follows: +-------------------------------------------------------------------+ | OMAC-ACPKM-Master(K, N, T*, M) | |-------------------------------------------------------------------| | Input: | | - section size N, | | - initial key K, | | - master key frequency T*, | | - plaintext M = M_1 | ... | M_b, |M| <= m_max. | | Output: | | - message authentication code T. | |-------------------------------------------------------------------| | 1. C_0 = 0^n | | 2. l = ceil(|M| / N) | | 3. K^1 | K^1_1 | ... | K^l | K^l_1 = | = ACPKM-Master(T*, K, (k + n), l) | | 4. For j = 1, 2, ... , b - 1 do | | i = ceil(j * n / N), | | C_j = E_{K^i}(M_j (xor) C_{j-1}) | | 5. SK = Generate_Subkey(K^l_1, |M_b|) | | 6. If |M_b| =nn, then M*_b = M_b | | else M*_b = M_b | 1 | 0^{n - 1 -|M_b|} | | 7. T = E_{K^l}(M*_b (xor) C_{b-1} (xor) SK) | | 8. Return T | +-------------------------------------------------------------------+ 7. Joint Usage of External and Internal Re-keying Both external re-keying and internal re-keying have their own advantages anddisadvantagesdisadvantages, which are discussed in Section 1. For instance, using external re-keying can essentially limit the message length, while in the case of internalre-keyingre-keying, the section size, which can be chosen as the maximal possible for operational properties, limits theamountnumber of separate messages. Therefore, the choice of re-keying mechanism (either external or internal) depends on particular protocol features. However, some protocols may have features that requireto takethe advantagesprovided byof both the external and internalre- keyingre-keying mechanisms: for example, the protocol mainly transmitsmessages of small length,short messages, but it must additionally support processing of very longmessages processing.messages. In suchsituationssituations, it is necessary to use external and internal re-keying jointly, since these techniques negate each other's disadvantages. For composition of external and internal re-keyingtechniquestechniques, any mechanism described in Section 5 can be used with any mechanism described in Section 6. For example, consider the GCM-ACPKM mode with external serial re- keying based on a KDF on aHashhash function. Denoteby a frame sizethe number of messages in each frame (in the case of the implicit approach to the key lifetime control) for externalre-keying.re-keying as a frame size. Let L be a key lifetime limitation. The section size N for internal re-keying and the frame size q for external re-keying must be chosen in such a way that q * N must not exceed L. Suppose that t messages (ICN_i, P_i, A_i), with initial counter nonce ICN_i, plaintextP_iP_i, and additional authenticated dataA_i,A_i will be processed before renegotiation. For authenticated encryption of each message (ICN_i, P_i, A_i), i = 1, ..., t, the following algorithm can be applied: 1. j = ceil(i / q), 2. K^j = ExtSerialH(K, j), 3. C_i | T_i = GCM-ACPKM-Encrypt(N, K^j, ICN_i, P_i, A_i). Note that noncesICN_i,ICN_i that are used under the same framekey,key must be unique for each message. 8. Security Considerations Re-keying should be used to increase"a priori"a priori security properties of ciphers in hostile environments (e.g., with side-channel adversaries). Ifsomeefficient attacksare known foron acipher, itcipher are known, the cipher must not be used.SoThus, re-keying cannot be used as a patch for vulnerable ciphers. Base cipher properties must be wellanalyzed,analyzed because the security of re-keying mechanisms is based on the security of a block cipher as a pseudorandom function. Re-keying is not intended to solve anypost-quantumpostquantum security issues for symmetric cryptography, since the reduction of security caused by Grover's algorithm is not connected with a size of plaintext transformed by a cipher--- only a negligible (sufficient for key uniqueness) material isneeded;needed -- and the aim of re-keying is to limitathe size of plaintext transformed under one initial key. Re-keying can provide backward security only if previous key material is securely deleted after usage by all parties. 9. IANA Considerations This documentdoes not require anyhas no IANA actions. 10. References 10.1. Normative References [CMS] Housley, R., "Cryptographic Message Syntax (CMS)", STD 70, RFC 5652, DOI 10.17487/RFC5652, September 2009,<http://www.rfc-editor.org/info/rfc5652>.<https://www.rfc-editor.org/info/rfc5652>. [DTLS] Rescorla, E. and N. Modadugu, "Datagram Transport Layer Security Version 1.2", RFC 6347, DOI 10.17487/RFC6347, January 2012,<http://www.rfc-editor.org/info/rfc6347>.<https://www.rfc-editor.org/info/rfc6347>. [ESP] Kent, S., "IP Encapsulating Security Payload (ESP)", RFC 4303, DOI 10.17487/RFC4303, December 2005,<http://www.rfc-editor.org/info/rfc4303>.<https://www.rfc-editor.org/info/rfc4303>. [GCM] Dworkin, M., "Recommendation for Block Cipher Modes of Operation: Galois/Counter Mode (GCM) and GMAC", NIST Special Publication800-38D http://nvlpubs.nist.gov/nistpubs/Legacy/SP/ nistspecialpublication800-38d.pdf,800-38D, DOI 10.6028/NIST.SP.800-38D, November2007.2007, <http://nvlpubs.nist.gov/nistpubs/Legacy/SP/ nistspecialpublication800-38d.pdf>. [MODES] Dworkin, M., "Recommendation for Block Cipher Modes of Operation: Methods and Techniques", NIST Special Publication 800-38A, DOI 10.6028/NIST.SP.800-38A, December 2001. [NISTSP800-108] National Institute of Standards and Technology, "Recommendation for Key Derivation Using Pseudorandom Functions", NIST Special Publication 800-108,November 2008,October 2009, <http://nvlpubs.nist.gov/nistpubs/Legacy/SP/ nistspecialpublication800-108.pdf>. [RFC2119] Bradner, S., "Key words for use in RFCs to Indicate Requirement Levels", BCP 14, RFC 2119, DOI 10.17487/RFC2119, March 1997, <https://www.rfc-editor.org/info/rfc2119>. [RFC4493] Song, JH., Poovendran, R., Lee, J., and T. Iwata, "The AES-CMAC Algorithm", RFC 4493, DOI 10.17487/RFC4493, June 2006, <https://www.rfc-editor.org/info/rfc4493>. [RFC5869] Krawczyk, H. and P. Eronen, "HMAC-based Extract-and-Expand Key Derivation Function (HKDF)", RFC 5869, DOI 10.17487/RFC5869, May 2010, <https://www.rfc-editor.org/info/rfc5869>. [RFC7836] Smyshlyaev, S., Ed., Alekseev, E., Oshkin, I., Popov, V., Leontiev, S., Podobaev, V., and D. Belyavsky, "Guidelines on the Cryptographic Algorithms to Accompany the Usage of Standards GOST R 34.10-2012 and GOST R 34.11-2012", RFC 7836, DOI 10.17487/RFC7836, March 2016, <https://www.rfc-editor.org/info/rfc7836>. [RFC8174] Leiba, B., "Ambiguity of Uppercase vs Lowercase in RFC 2119 Key Words", BCP 14, RFC 8174, DOI 10.17487/RFC8174, May 2017, <https://www.rfc-editor.org/info/rfc8174>. [SSH] Ylonen, T. and C. Lonvick, Ed., "The Secure Shell (SSH) Transport Layer Protocol", RFC 4253, DOI 10.17487/RFC4253, January 2006,<http://www.rfc-editor.org/info/rfc4253>.<https://www.rfc-editor.org/info/rfc4253>. [TLS] Rescorla, E., "The Transport Layer Security (TLS) Protocol Version 1.3", RFC 8446, DOI 10.17487/RFC8446, August 2018,<http://www.rfc-editor.org/info/rfc8446>.<https://www.rfc-editor.org/info/rfc8446>. 10.2. Informative References [AAOS2017] Ahmetzyanova, L., Alekseev, E., Oshkin, I., and S. Smyshlyaev, "Increasing the Lifetime of Symmetric Keys for the GCM Mode by Internal Re-keying", Cryptology ePrintArchiveArchive, Report 2017/697, 2017, <https://eprint.iacr.org/2017/697.pdf>. [AbBell]Michel AbdallaAbdalla, M. andMihirM. Bellare, "Increasing the Lifetime of a Key: A Comparative Analysis of the Security ofRe- keyingRe-keying Techniques",ASIACRYPT2000, LNCSASIACRYPT 2000, Lecture Notes in Computer Science, Volume 1976, pp. 546-559, DOI 10.1007/3-540-44448-3_42, October 2000. [AESDUKPT]ANSI,American National Standards Institute, "Retail Financial Services Symmetric Key Management - Part 3: Derived Unique Key Per Transaction", ANSI X9.24-3-2017, October 2017. [FKK2005] Fu, K., Kamara, S., and T. Kohno, "Key Regression: Enabling Efficient Key Distribution for Secure Distributed Storage", November 2005, <https://homes.cs.washington.edu/~yoshi/papers/KR/ NDSS06.pdf>. [FPS2012] Faust, S., Pietrzak, K., andj.J. Schipper, "Practical Leakage-Resilient Symmetric Cryptography",CHES2012 LNCS, vol.Cryptographic Hardware and Embedded Systems (CHES), Lecture Notes in Computer Science, Volume 7428, pp.213-232,,213-232, DOI 10.1007/978-3-642-33027-8_13, 2012, <https://link.springer.com/content/ pdf/10.1007%2F978-3-642-33027-8_13.pdf>. [FRESHREKEYING] Dziembowski, S., Faust, S., Herold, G., Journault, A., Masny, D., and F. Standaert, "Towards Sound Fresh Re- Keying with Hard (Physical) Learning Problems", Cryptology ePrintArchiveArchive, Report 2016/573, June 2016, <https://eprint.iacr.org/2016/573>. [GGM] Goldreich, O., Goldwasser, S., and S. Micali, "How to Construct Random Functions", Journal of the Association for ComputingMachinery Vol.33, No.4,Machinery, Volume 33, No. 4, pp. 792-807, DOI 10.1145/6490.6503, October 1986,<http://www.wisdom.weizmann.ac.il/~/oded/X/ggm.pdf>.<https://dl.acm.org/citation.cfm?doid=6490.6503>. [KMNT2003] Kim, Y., Maino, F., Narasimha, M., and G. Tsudik, "Secure Group Services for Storage Area Networks", IEEECommunicationCommunications Magazine 41, Number 8, pp. 92-99, DOI 10.1109/SISW.2002.1183514, August 2003,<http://www.ics.uci.edu/~gts/paps/kmnt02.pdf>.<https://ieeexplore.ieee.org/document/1183514>. [LDC]Howard M.Heys, H., "A Tutorial on Linear and Differential Cryptanalysis",2017, <http://www.cs.bc.edu/~straubin/crypto2017/heys.pdf>.2001, <https://citeseerx.ist.psu.edu/viewdoc/ citations?doi=10.1.1.2.2759>. [OWT] Joye, M. and S. Yen, "One-Way Cross-Trees and Their Applications", Public Key Cryptography (PKC), Lecture Notes in Computer Science, Volume 2274, DOI 10.1007/3-540-45664-3_25, February 2002, <https://link.springer.com/content/ pdf/10.1007%2F3-540-45664-3_25.pdf>. [P3]PeterAlexander,"DynamicP., "Subject: [Cfrg] Dynamic Key Changes on EncryptedSessions",Sessions. - Draft I-D Attached", message to the CFRGmail archive , Decembermailing list, 4 November 2017,<https://www.ietf.org/mail-archive/web/cfrg/current/ msg09401.html>.<https://mailarchive.ietf.org/arch/msg/cfrg/ ecTR3Hb-DFfrPCVmY0ghyYOEcxU>. [Pietrzak2009] Pietrzak, K., "A Leakage-Resilient Mode of Operation",EUROCRYPT2009 LNCS, vol.EUROCRYPT 2009, Lecture Notes in Computer Science, Volume 5479, pp.462-482,,462-482, DOI 10.1007/978-3-642-01001-9_27, April 2009, <https://iacr.org/archive/ eurocrypt2009/54790461/54790461.pdf>. [SIGNAL] Perrin, T., Ed. and M. Marlinspike, "The Double Ratchet Algorithm", November 2016, <https://signal.org/docs/specifications/doubleratchet/ doubleratchet.pdf>. [Sweet32]KarthikeyanBhargavan,GaetanK. and G. Leurent, "On the Practical (In-)Security of 64-bit Block Ciphers: Collision Attacks on HTTP over TLS and OpenVPN",Cryptology ePrint Archive Report 2016/798,Proceedings of the 2016 ACM SIGSAC Conference on Computer and Communications Security, pp. 456-467, DOI 10.1145/2976749.2978423, October 2016, <https://sweet32.info/SWEET32_CCS16.pdf>. [TAHA] Taha, M. and P. Schaumont, "Key Updating for Leakage Resiliency With Application to AES Modes of Operation", IEEE Transactions on Information Forensics and Security, DOI 10.1109/TIFS.2014.2383359, December 2014, <http://ieeexplore.ieee.org/document/6987331/>. [TEMPEST]By CraigRamsay,JasperC. and J. Lohuis, "TEMPEST attacks against AES. Covertly stealing keys for 200 euro", June 2017, <https://www.fox-it.com/en/wp-content/uploads/sites/11/ Tempest_attacks_against_AES.pdf>. [U2F] Chang, D., Mishra, S., Sanadhya, S., and A.Singhl,Singh, "On Making U2F Protocol Leakage-Resilient viaRe-keying.",Re-keying", Cryptology ePrintArchiveArchive, Report 2017/721, August 2017, <https://eprint.iacr.org/2017/721.pdf>. Appendix A. Test Examples A.1. Test Examples for External Re-keying A.1.1. External Re-keying with a Parallel Construction External re-keying with a parallel construction based on AES-256 **************************************************************** k = 256 t = 128 Initial key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xternal re-keying with a parallel construction based on SHA-256 **************************************************************** k = 256 t = 128 label: SHA2label Initial key: 00 01 02 03 04 05 06 07 08 09 0A 0B 0C 0D 0E 0F 0F 0E 0D 0C 0B 0A 09 08 07 06 05 04 03 02 01 00 K^1: C1 A1 4C A0 30 29 BE 43 9F 35 3C 79 1A 51 48 57 26 7A CD 5A E8 7D E7 D1 B2 E2 C7 AF A4 29 BD 35 K^2: 03 68 BB 74 41 2A 98 ED C4 7B 94 CC DF 9C F4 9E A9 B8 A9 5F 0E DC 3C 1E 3B D2 59 4D D1 75 82 D4 K^3: 2F D3 68 D3 A7 8F 91 E6 3B 68 DC 2B 41 1D AC 80 0A C3 14 1D 80 26 3E 61 C9 0D 24 45 2A BD B1 AE ... K^126: 55 AC 2B 25 00 78 3E D4 34 2B 65 0E 75 E5 8B 76 C8 04 E9 D3 B6 08 7D C0 70 2A 99 A4 B5 85 F1 A1 K^127: 77 4D 15 88 B0 40 90 E5 8C 6A D7 5D 0F CF 0A 4A 6C 23 F1 B3 91 B1 EF DF E5 77 64 CD 09 F5 BC AF K^128: E5 81 FF FB 0C 90 88 CD E5 F4 A5 57 B6 AB D2 2E 94 C3 42 06 41 AB C1 72 66 CC 2F 59 74 9C 86 B3 A.1.2. External Re-keying with a Serial Construction External re-keying with a serial construction based on AES-256 ************************************************************** AES 256 examples: k = 256 t = 128 Initial key: 00 01 02 03 04 05 06 07 08 09 0A 0B 0C 0D 0E 0F 0F 0E 0D 0C 0B 0A 09 08 07 06 05 04 03 02 01 00 K*_1: 00 01 02 03 04 05 06 07 08 09 0A 0B 0C 0D 0E 0F 0F 0E 0D 0C 0B 0A 09 08 07 06 05 04 03 02 01 00 K^1: 66 B8 BD E5 90 6C EC DF FA 8A B2 FD 92 84 EB F0 51 16 8A B6 C8 A8 38 65 54 85 31 A5 D2 BA C3 86 K*_2: 64 7D 5C D5 1C 3D 62 98 BC 09 B1 D8 64 EC D9 B1 6F ED F5 D3 77 57 48 75 35 2B 5F 4D B6 5B E0 15 K^2: 66 B8 BD E5 90 6C EC DF FA 8A B2 FD 92 84 EB F0 51 16 8A B6 C8 A8 38 65 54 85 31 A5 D2 BA C3 86 K*_3: 64 7D 5C D5 1C 3D 62 98 BC 09 B1 D8 64 EC D9 B1 6F ED F5 D3 77 57 48 75 35 2B 5F 4D B6 5B E0 15 K^3: 66 B8 BD E5 90 6C EC DF FA 8A B2 FD 92 84 EB F0 51 16 8A B6 C8 A8 38 65 54 85 31 A5 D2 BA C3 86 ... K*_126: 64 7D 5C D5 1C 3D 62 98 BC 09 B1 D8 64 EC D9 B1 6F ED F5 D3 77 57 48 75 35 2B 5F 4D B6 5B E0 15 K^126: 66 B8 BD E5 90 6C EC DF FA 8A B2 FD 92 84 EB F0 51 16 8A B6 C8 A8 38 65 54 85 31 A5 D2 BA C3 86 K*_127: 64 7D 5C D5 1C 3D 62 98 BC 09 B1 D8 64 EC D9 B1 6F ED F5 D3 77 57 48 75 35 2B 5F 4D B6 5B E0 15 K^127: 66 B8 BD E5 90 6C EC DF FA 8A B2 FD 92 84 EB F0 51 16 8A B6 C8 A8 38 65 54 85 31 A5 D2 BA C3 86 K*_128: 64 7D 5C D5 1C 3D 62 98 BC 09 B1 D8 64 EC D9 B1 6F ED F5 D3 77 57 48 75 35 2B 5F 4D B6 5B E0 15 K^128: 66 B8 BD E5 90 6C EC DF FA 8A B2 FD 92 84 EB F0 51 16 8A B6 C8 A8 38 65 54 85 31 A5 D2 BA C3 86 External re-keying with a serial construction based on SHA-256 ************************************************************** k = 256 t = 128 Initial key: 00 01 02 03 04 05 06 07 08 09 0A 0B 0C 0D 0E 0F 0F 0E 0D 0C 0B 0A 09 08 07 06 05 04 03 02 01 00 label1: SHA2label1 label2: SHA2label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est Examples for Internal Re-keying A.2.1. Internal Re-keying Mechanisms that Do Not Require a Master Key CTR-ACPKM mode with AES-256 *************************** k = 256 n = 128 c = 64 N = 256 Initial key K: 00000: 88 99 AA BB CC DD EE FF 00 11 22 33 44 55 66 77 00010: FE DC BA 98 76 54 32 10 01 23 45 67 89 AB CD EFPlain textPlaintext P: 00000: 11 22 33 44 55 66 77 00 FF EE DD CC BB AA 99 88 00010: 00 11 22 33 44 55 66 77 88 99 AA BB CC EE FF 0A 00020: 11 22 33 44 55 66 77 88 99 AA BB CC EE FF 0A 00 00030: 22 33 44 55 66 77 88 99 AA BB CC EE FF 0A 00 11 00040: 33 44 55 66 77 88 99 AA BB CC EE FF 0A 00 11 22 00050: 44 55 66 77 88 99 AA BB CC EE FF 0A 00 11 22 33 00060: 55 66 77 88 99 AA BB CC EE FF 0A 00 11 22 33 44 ICN: 12 34 56 78 90 AB CE F0 A1 B2 C3 D4 E5 F0 01 12 23 34 45 56 67 78 89 90 12 13 14 15 16 17 18 19 D_1: 00000: 80 81 82 83 84 85 86 87 88 89 8A 8B 8C 8D 8E 8F D_2: 00000: 90 91 92 93 94 95 96 97 98 99 9A 9B 9C 9D 9E 9F Section_1 Section key K^1: 00000: 88 99 AA BB CC DD EE FF 00 11 22 33 44 55 66 77 00010: FE DC BA 98 76 54 32 10 01 23 45 67 89 AB CD EF Input block CTR_1: 00000: 12 34 56 78 90 AB CE F0 00 00 00 00 00 00 00 00 Output block G_1: 00000: FD 7E F8 9A D9 7E A4 B8 8D B8 B5 1C 1C 9D 6D D0 Input block CTR_2: 00000: 12 34 56 78 90 AB CE F0 00 00 00 00 00 00 00 01 Output block G_2: 00000: 19 98 C5 71 76 37 FB 17 11 E4 48 F0 0C 0D 60 B2 Section_2 Section key K^2: 00000: F6 80 D1 21 2F A4 3D F4 EC 3A 91 DE 2A B1 6F 1B 00010: 36 B0 48 8A 4F C1 2E 09 98 D2 E4 A8 88 E8 4F 3D Input block CTR_3: 00000: 12 34 56 78 90 AB CE F0 00 00 00 00 00 00 00 02 Output block G_3: 00000: E4 88 89 4F B6 02 87 DB 77 5A 07 D9 2C 89 46 EA Input block CTR_4: 00000: 12 34 56 78 90 AB CE F0 00 00 00 00 00 00 00 03 Output block G_4: 00000: BC 4F 87 23 DB F0 91 50 DD B4 06 C3 1D A9 7C A4 Section_3 Section key K^3: 00000: 8E B9 7E 43 27 1A 42 F1 CA 8E E2 5F 5C C7 C8 3B 00010: 1A CE 9E 5E D0 6A A5 3B 57 B9 6A CF 36 5D 24 B8 Input block CTR_5: 00000: 12 34 56 78 90 AB CE F0 00 00 00 00 00 00 00 04 Output block G_5: 00000: 68 6F 22 7D 8F B2 9C BD 05 C8 C3 7D 22 FE 3B B7 Input block CTR_6: 00000: 12 34 56 78 90 AB CE F0 00 00 00 00 00 00 00 05 Output block G_6: 00000: C0 1B F9 7F 75 6E 12 2F 80 59 55 BD DE 2D 45 87 Section_4 Section key K^4: 00000: C5 71 6C C9 67 98 BC 2D 4A 17 87 B7 8A DF 94 AC 00010: E8 16 F8 0B DB BC AD 7D 60 78 12 9C 0C B4 02 F5 Block number 7: Input block CTR_7: 00000: 12 34 56 78 90 AB CE F0 00 00 00 00 00 00 00 06 Output block G_7: 00000: 03 DE 34 74 AB 9B 65 8A 3B 54 1E F8 BD 2B F4 7D The result G = G_1 | G_2 | G_3 | G_4 | G_5 | G_6 | G_7: 00000: FD 7E F8 9A D9 7E A4 B8 8D B8 B5 1C 1C 9D 6D D0 00010: 19 98 C5 71 76 37 FB 17 11 E4 48 F0 0C 0D 60 B2 00020: E4 88 89 4F B6 02 87 DB 77 5A 07 D9 2C 89 46 EA 00030: BC 4F 87 23 DB F0 91 50 DD B4 06 C3 1D A9 7C A4 00040: 68 6F 22 7D 8F B2 9C BD 05 C8 C3 7D 22 FE 3B B7 00050: C0 1B F9 7F 75 6E 12 2F 80 59 55 BD DE 2D 45 87 00060: 03 DE 34 74 AB 9B 65 8A 3B 54 1E F8 BD 2B F4 7D The result ciphertext C = P (xor) MSB_{|P|}(G): 00000: EC 5C CB DE 8C 18 D3 B8 72 56 68 D0 A7 37 F4 58 00010: 19 89 E7 42 32 62 9D 60 99 7D E2 4B C0 E3 9F B8 00020: F5 AA BA 0B E3 64 F0 53 EE F0 BC 15 C2 76 4C EA 00030: 9E 7C C3 76 BD 87 19 C9 77 0F CA 2D E2 A3 7C B5 00040: 5B 2B 77 1B F8 3A 05 17 BE 04 2D 82 28 FE 2A 95 00050: 84 4E 9F 08 FD F7 B8 94 4C B7 AA B7 DE 3C 67 B4 00060: 56 B8 43 FC 32 31 DE 46 D5 AB 14 F8 AC 09 C7 39 GCM-ACPKM mode with AES-128 *************************** k = 128 n = 128 c = 32 N = 256Initilal KeyInitial key K: 00000: 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 Additional data A: 00000: 11 22 33 Plaintext: 00000: 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00010: 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00020: 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 ICN: 00000: 00 00 00 00 00 00 00 00 00 00 00 00 Number of sections: 2 Section key K^1: 00000: 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 Section key K^2: 00000: 15 1A 9F B0 B6 AC C5 97 6A FB 50 31 D1 DE C8 41 Encrypted GCTR_1 | GCTR_2 | GCTR_3: 00000: 03 88 DA CE 60 B6 A3 92 F3 28 C2 B9 71 B2 FE 78 00010: F7 95 AA AB 49 4B 59 23 F7 FD 89 FF 94 8B C1 E0 00020: D6 B3 12 46 E9 CE 9F F1 3A B3 42 7E E8 91 96 AD Ciphertext C: 00000: 03 88 DA CE 60 B6 A3 92 F3 28 C2 B9 71 B2 FE 78 00010: F7 95 AA AB 49 4B 59 23 F7 FD 89 FF 94 8B C1 E0 00020: D6 B3 12 46 E9 CE 9F F1 3A B3 42 7E E8 91 96 AD GHASH input: 00000: 11 22 33 00 00 00 00 00 00 00 00 00 00 00 00 00 00010: 03 88 DA CE 60 B6 A3 92 F3 28 C2 B9 71 B2 FE 78 00020: F7 95 AA AB 49 4B 59 23 F7 FD 89 FF 94 8B C1 E0 00030: D6 B3 12 46 E9 CE 9F F1 3A B3 42 7E E8 91 96 AD 00040: 00 00 00 00 00 00 00 18 00 00 00 00 00 00 01 80 GHASH output S: 00000: E8 ED E9 94 9A DD 55 30 B0 F4 4E F5 00 FC 3E 3C Authentication tag T: 00000: B0 0F 15 5A 60 A3 65 51 86 8B 53 A2 A4 1B 7B 66 The result C | T: 00000: 03 88 DA CE 60 B6 A3 92 F3 28 C2 B9 71 B2 FE 78 00010: F7 95 AA AB 49 4B 59 23 F7 FD 89 FF 94 8B C1 E0 00020: D6 B3 12 46 E9 CE 9F F1 3A B3 42 7E E8 91 96 AD 00030: B0 0F 15 5A 60 A3 65 51 86 8B 53 A2 A4 1B 7B 66 A.2.2. Internal Re-keying Mechanisms with a Master Key CTR-ACPKM-Master mode with AES-256 ********************************** k = 256 n = 128 c for CTR-ACPKM mode = 64 c for CTR-ACPKM-Master mode = 64 N = 256 T* = 512 Initial key K: 00000: 88 99 AA BB CC DD EE FF 00 11 22 33 44 55 66 77 00010: FE DC BA 98 76 54 32 10 01 23 45 67 89 AB CD EF Initial vector ICN: 00000: 12 34 56 78 90 AB CE F0 A1 B2 C3 D4 E5 F0 01 12 Plaintext P: 00000: 11 22 33 44 55 66 77 00 FF EE DD CC BB AA 99 88 00010: 00 11 22 33 44 55 66 77 88 99 AA BB CC EE FF 0A 00020: 11 22 33 44 55 66 77 88 99 AA BB CC EE FF 0A 00 00030: 22 33 44 55 66 77 88 99 AA BB CC EE FF 0A 00 11 00040: 33 44 55 66 77 88 99 AA BB CC EE FF 0A 00 11 22 00050: 44 55 66 77 88 99 AA BB CC EE FF 0A 00 11 22 33 00060: 55 66 77 88 99 AA BB CC EE FF 0A 00 11 22 33 44 K^1 | K^2 | K^3 | K^4: 00000: 9F 10 BB F1 3A 79 FB BD 4A 4C A8 64 C4 90 74 64 00010: 39 FE 50 6D 4B 86 9B 21 03 A3 B6 A4 79 28 3C 60 00020: 77 91 17 50 E0 D1 77 E5 9A 13 78 2B F1 89 08 D0 00030: AB 6B 59 EE 92 49 05 B3 AB C7 A4 E3 69 65 76 C3 00040: E8 76 2B 30 8B 08 EB CE 3E 93 9A C2 C0 3E 76 D4 00050: 60 9A AB D9 15 33 13 D3 CF D3 94 E7 75 DF 3A 94 00060: F2 EE 91 45 6B DC 3D E4 91 2C 87 C3 29 CF 31 A9 00070: 2F 20 2E 5A C4 9A 2A 65 31 33 D6 74 8C 4F F9 12 Section_1 K^1: 00000: 9F 10 BB F1 3A 79 FB BD 4A 4C A8 64 C4 90 74 64 00010: 39 FE 50 6D 4B 86 9B 21 03 A3 B6 A4 79 28 3C 60 Input block CTR_1: 00000: 12 34 56 78 90 AB CE F0 00 00 00 00 00 00 00 00 Output block G_1: 00000: 8C A2 B6 82 A7 50 65 3F 8E BF 08 E7 9F 99 4D 5C Input block CTR_2: 00000: 12 34 56 78 90 AB CE F0 00 00 00 00 00 00 00 01 Output block G_2: 00000: F6 A6 A5 BA 58 14 1E ED 23 DC 31 68 D2 35 89 A1 Section_2 K^2: 00000: 77 91 17 50 E0 D1 77 E5 9A 13 78 2B F1 89 08 D0 00010: AB 6B 59 EE 92 49 05 B3 AB C7 A4 E3 69 65 76 C3 Input block CTR_3: 00000: 12 34 56 78 90 AB CE F0 00 00 00 00 00 00 00 02 Output block G_3: 00000: 4A 07 5F 86 05 87 72 94 1D 8E 7D F8 32 F4 23 71 Input block CTR_4: 00000: 12 34 56 78 90 AB CE F0 00 00 00 00 00 00 00 03 Output block G_4: 00000: 23 35 66 AF 61 DD FE A7 B1 68 3F BA B0 52 4A D7 Section_3 K^3: 00000: E8 76 2B 30 8B 08 EB CE 3E 93 9A C2 C0 3E 76 D4 00010: 60 9A AB D9 15 33 13 D3 CF D3 94 E7 75 DF 3A 94 Input block CTR_5: 00000: 12 34 56 78 90 AB CE F0 00 00 00 00 00 00 00 04 Output block G_5: 00000: A8 09 6D BC E8 BB 52 FC DE 6E 03 70 C1 66 95 E8 Input block CTR_6: 00000: 12 34 56 78 90 AB CE F0 00 00 00 00 00 00 00 05 Output block G_6: 00000: C6 E3 6E 8E 5B 82 AA C4 A6 6C 14 8D B1 F6 9B EF Section_4 K^4: 00000: F2 EE 91 45 6B DC 3D E4 91 2C 87 C3 29 CF 31 A9 00010: 2F 20 2E 5A C4 9A 2A 65 31 33 D6 74 8C 4F F9 12 Input block CTR_7: 00000: 12 34 56 78 90 AB CE F0 00 00 00 00 00 00 00 06 Output block G_7: 00000: 82 2B E9 07 96 37 44 95 75 36 3F A7 07 F8 40 22 The result G = G_1 | G_2 | G_3 | G_4 | G_5 | G_6 | G_7: 00000: 8C A2 B6 82 A7 50 65 3F 8E BF 08 E7 9F 99 4D 5C 00010: F6 A6 A5 BA 58 14 1E ED 23 DC 31 68 D2 35 89 A1 00020: 4A 07 5F 86 05 87 72 94 1D 8E 7D F8 32 F4 23 71 00030: 23 35 66 AF 61 DD FE A7 B1 68 3F BA B0 52 4A D7 00040: A8 09 6D BC E8 BB 52 FC DE 6E 03 70 C1 66 95 E8 00050: C6 E3 6E 8E 5B 82 AA C4 A6 6C 14 8D B1 F6 9B EF 00060: 82 2B E9 07 96 37 44 95 75 36 3F A7 07 F8 40 22 The result ciphertext C = P (xor) MSB_{|P|}(G): 00000: 9D 80 85 C6 F2 36 12 3F 71 51 D5 2B 24 33 D4 D4 00010: F6 B7 87 89 1C 41 78 9A AB 45 9B D3 1E DB 76 AB 00020: 5B 25 6C C2 50 E1 05 1C 84 24 C6 34 DC 0B 29 71 00030: 01 06 22 FA 07 AA 76 3E 1B D3 F3 54 4F 58 4A C6 00040: 9B 4D 38 DA 9F 33 CB 56 65 A2 ED 8F CB 66 84 CA 00050: 82 B6 08 F9 D3 1B 00 7F 6A 82 EB 87 B1 E7 B9 DC 00060: D7 4D 9E 8F 0F 9D FF 59 9B C9 35 A7 16 DA 73 66 GCM-ACPKM-Master mode with AES-256 ********************************** k = 192 n = 128 c for the CTR-ACPKM mode = 64 c for the GCM-ACPKM-Master mode = 32 T* = 384 N = 256Initila KeyInitial key K: 00000: 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00010: 00 00 00 00 00 00 00 00 Additional data A: 00000: 11 22 33 Plaintext: 00000: 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00010: 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00020: 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00030: 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00040: 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 ICN: 00000: 00 00 00 00 00 00 00 00 00 00 00 00 Number of sections: 3 K^1 | K^2 | K^3: 00000: 93 BA AF FB 35 FB E7 39 C1 7C 6A C2 2E EC F1 8F 00010: 7B 89 F0 BF 8B 18 07 05 96 48 68 9F 36 A7 65 CC 00020: CD 5D AC E2 0D 47 D9 18 D7 86 D0 41 A8 3B AB 99 00030: F5 F8 B1 06 D2 71 78 B1 B0 08 C9 99 0B 72 E2 87 00040: 5A 2D 3C BE F1 6E 67 3C Encrypted GCTR_1 | ... | GCTR_5 00000: 43 FA 71 81 64 B1 E3 D7 1E 7B 65 39 A7 02 1D 52 00010: 69 9B 9E 1B 43 24 B7 52 95 74 E7 90 F2 BE 60 E8 00020: 11 62 C9 90 2A 2B 77 7F D9 6A D6 1A 99 E0 C6 DE 00030: 4B 91 D4 29 E3 1A 8C 11 AF F0 BC 47 F6 80 AF 14 00040: 40 1C C1 18 14 63 8E 76 24 83 37 75 16 34 70 08 Ciphertext C: 00000: 43 FA 71 81 64 B1 E3 D7 1E 7B 65 39 A7 02 1D 52 00010: 69 9B 9E 1B 43 24 B7 52 95 74 E7 90 F2 BE 60 E8 00020: 11 62 C9 90 2A 2B 77 7F D9 6A D6 1A 99 E0 C6 DE 00030: 4B 91 D4 29 E3 1A 8C 11 AF F0 BC 47 F6 80 AF 14 00040: 40 1C C1 18 14 63 8E 76 24 83 37 75 16 34 70 08 GHASH input: 00000: 11 22 33 00 00 00 00 00 00 00 00 00 00 00 00 00 00010: 43 FA 71 81 64 B1 E3 D7 1E 7B 65 39 A7 02 1D 52 00020: 69 9B 9E 1B 43 24 B7 52 95 74 E7 90 F2 BE 60 E8 00030: 11 62 C9 90 2A 2B 77 7F D9 6A D6 1A 99 E0 C6 DE 00040: 4B 91 D4 29 E3 1A 8C 11 AF F0 BC 47 F6 80 AF 14 00050: 40 1C C1 18 14 63 8E 76 24 83 37 75 16 34 70 08 00060: 00 00 00 00 00 00 00 18 00 00 00 00 00 00 02 80 GHASH output S: 00000: 6E A3 4B D5 6A C5 40 B7 3E 55 D5 86 D1 CC 09 7D Authentication tag T: 00050: CC 3A BA 11 8C E7 85 FD 77 78 94 D4 B5 20 69 F8 The result C | T: 00000: 43 FA 71 81 64 B1 E3 D7 1E 7B 65 39 A7 02 1D 52 00010: 69 9B 9E 1B 43 24 B7 52 95 74 E7 90 F2 BE 60 E8 00020: 11 62 C9 90 2A 2B 77 7F D9 6A D6 1A 99 E0 C6 DE 00030: 4B 91 D4 29 E3 1A 8C 11 AF F0 BC 47 F6 80 AF 14 00040: 40 1C C1 18 14 63 8E 76 24 83 37 75 16 34 70 08 00050: CC 3A BA 11 8C E7 85 FD 77 78 94 D4 B5 20 69 F8 CBC-ACPKM-Master mode with AES-256 ********************************** k = 256 n = 128 c for the CTR-ACPKM mode = 64 N = 256 T* = 512 Initial key K: 00000: 88 99 AA BB CC DD EE FF 00 11 22 33 44 55 66 77 00010: FE DC BA 98 76 54 32 10 01 23 45 67 89 AB CD EF Initial vector IV: 00000: 12 34 56 78 90 AB CE F0 A1 B2 C3 D4 E5 F0 01 12 Plaintext P: 00000: 11 22 33 44 55 66 77 00 FF EE DD CC BB AA 99 88 00010: 00 11 22 33 44 55 66 77 88 99 AA BB CC EE FF 0A 00020: 11 22 33 44 55 66 77 88 99 AA BB CC EE FF 0A 00 00030: 22 33 44 55 66 77 88 99 AA BB CC EE FF 0A 00 11 00040: 33 44 55 66 77 88 99 AA BB CC EE FF 0A 00 11 22 00050: 44 55 66 77 88 99 AA BB CC EE FF 0A 00 11 22 33 00060: 55 66 77 88 99 AA BB CC EE FF 0A 00 11 22 33 44 K^1 | K^2 | K^3 | K^4: 00000: 9F 10 BB F1 3A 79 FB BD 4A 4C A8 64 C4 90 74 64 00010: 39 FE 50 6D 4B 86 9B 21 03 A3 B6 A4 79 28 3C 60 00020: 77 91 17 50 E0 D1 77 E5 9A 13 78 2B F1 89 08 D0 00030: AB 6B 59 EE 92 49 05 B3 AB C7 A4 E3 69 65 76 C3 00040: E8 76 2B 30 8B 08 EB CE 3E 93 9A C2 C0 3E 76 D4 00050: 60 9A AB D9 15 33 13 D3 CF D3 94 E7 75 DF 3A 94 00060: F2 EE 91 45 6B DC 3D E4 91 2C 87 C3 29 CF 31 A9 00070: 2F 20 2E 5A C4 9A 2A 65 31 33 D6 74 8C 4F F9 12 Section_1 K^1: 00000: 9F 10 BB F1 3A 79 FB BD 4A 4C A8 64 C4 90 74 64 00010: 39 FE 50 6D 4B 86 9B 21 03 A3 B6 A4 79 28 3C 60 Plaintext block P_1: 00000: 11 22 33 44 55 66 77 00 FF EE DD CC BB AA 99 88 Input block P_1 (xor) C_0: 00000: 03 16 65 3C C5 CD B9 F0 5E 5C 1E 18 5E 5A 98 9A Output block C_1: 00000: 59 CB 5B CA C2 69 2C 60 0D 46 03 A0 C7 40 C9 7C Plaintext block P_2: 00000: 00 11 22 33 44 55 66 77 88 99 AA BB CC EE FF 0A Input block P_2 (xor) C_1: 00000: 59 DA 79 F9 86 3C 4A 17 85 DF A9 1B 0B AE 36 76 Output block C_2: 00000: 80 B6 02 74 54 8B F7 C9 78 1F A1 05 8B F6 8B 42 Section_2 K^2: 00000: 77 91 17 50 E0 D1 77 E5 9A 13 78 2B F1 89 08 D0 00010: AB 6B 59 EE 92 49 05 B3 AB C7 A4 E3 69 65 76 C3 Plaintext block P_3: 00000: 11 22 33 44 55 66 77 88 99 AA BB CC EE FF 0A 00 Input block P_3 (xor) C_2: 00000: 91 94 31 30 01 ED 80 41 E1 B5 1A C9 65 09 81 42 Output block C_3: 00000: 8C 24 FB CF 68 15 B1 AF 65 FE 47 75 95 B4 97 59 Plaintext block P_4: 00000: 22 33 44 55 66 77 88 99 AA BB CC EE FF 0A 00 11 Input block P_4 (xor) C_3: 00000: AE 17 BF 9A 0E 62 39 36 CF 45 8B 9B 6A BE 97 48 Output block C_4: 00000: 19 65 A5 00 58 0D 50 23 72 1B E9 90 E1 83 30 E9 Section_3 K^3: 00000: E8 76 2B 30 8B 08 EB CE 3E 93 9A C2 C0 3E 76 D4 00010: 60 9A AB D9 15 33 13 D3 CF D3 94 E7 75 DF 3A 94 Plaintext block P_5: 00000: 33 44 55 66 77 88 99 AA BB CC EE FF 0A 00 11 22 Input block P_5 (xor) C_4: 00000: 2A 21 F0 66 2F 85 C9 89 C9 D7 07 6F EB 83 21 CB Output block C_5: 00000: 56 D8 34 F4 6F 0F 4D E6 20 53 A9 5C B5 F6 3C 14 Plaintext block P_6: 00000: 44 55 66 77 88 99 AA BB CC EE FF 0A 00 11 22 33 Input block P_6 (xor) C_5: 00000: 12 8D 52 83 E7 96 E7 5D EC BD 56 56 B5 E7 1E 27 Output block C_6: 00000: 66 68 2B 8B DD 6E B2 7E DE C7 51 D6 2F 45 A5 45 Section_4 K^4: 00000: F2 EE 91 45 6B DC 3D E4 91 2C 87 C3 29 CF 31 A9 00010: 2F 20 2E 5A C4 9A 2A 65 31 33 D6 74 8C 4F F9 12 Plaintext block P_7: 00000: 55 66 77 88 99 AA BB CC EE FF 0A 00 11 22 33 44 Input block P_7 (xor) C_6: 00000: 33 0E 5C 03 44 C4 09 B2 30 38 5B D6 3E 67 96 01 Output block C_7: 00000: 7F 4D 87 F9 CA E9 56 09 79 C4 FA FE 34 0B 45 34Cipher textCiphertext C: 00000: 59 CB 5B CA C2 69 2C 60 0D 46 03 A0 C7 40 C9 7C 00010: 80 B6 02 74 54 8B F7 C9 78 1F A1 05 8B F6 8B 42 00020: 8C 24 FB CF 68 15 B1 AF 65 FE 47 75 95 B4 97 59 00030: 19 65 A5 00 58 0D 50 23 72 1B E9 90 E1 83 30 E9 00040: 56 D8 34 F4 6F 0F 4D E6 20 53 A9 5C B5 F6 3C 14 00050: 66 68 2B 8B DD 6E B2 7E DE C7 51 D6 2F 45 A5 45 00060: 7F 4D 87 F9 CA E9 56 09 79 C4 FA FE 34 0B 45 34 CFB-ACPKM-Master mode with AES-256 ********************************** k = 256 n = 128 c for the CTR-ACPKM mode = 64 N = 256 T* = 512 Initial key K: 00000: 88 99 AA BB CC DD EE FF 00 11 22 33 44 55 66 77 00010: FE DC BA 98 76 54 32 10 01 23 45 67 89 AB CD EF Initial vector IV: 00000: 12 34 56 78 90 AB CE F0 A1 B2 C3 D4 E5 F0 01 12 Plaintext P: 00000: 11 22 33 44 55 66 77 00 FF EE DD CC BB AA 99 88 00010: 00 11 22 33 44 55 66 77 88 99 AA BB CC EE FF 0A 00020: 11 22 33 44 55 66 77 88 99 AA BB CC EE FF 0A 00 00030: 22 33 44 55 66 77 88 99 AA BB CC EE FF 0A 00 11 00040: 33 44 55 66 77 88 99 AA BB CC EE FF 0A 00 11 22 00050: 44 55 66 77 88 99 AA BB CC EE FF 0A 00 11 22 33 00060: 55 66 77 88 99 AA BB CC K^1 | K^2 | K^3 | K^4 00000: 9F 10 BB F1 3A 79 FB BD 4A 4C A8 64 C4 90 74 64 00010: 39 FE 50 6D 4B 86 9B 21 03 A3 B6 A4 79 28 3C 60 00020: 77 91 17 50 E0 D1 77 E5 9A 13 78 2B F1 89 08 D0 00030: AB 6B 59 EE 92 49 05 B3 AB C7 A4 E3 69 65 76 C3 00040: E8 76 2B 30 8B 08 EB CE 3E 93 9A C2 C0 3E 76 D4 00050: 60 9A AB D9 15 33 13 D3 CF D3 94 E7 75 DF 3A 94 00060: F2 EE 91 45 6B DC 3D E4 91 2C 87 C3 29 CF 31 A9 00070: 2F 20 2E 5A C4 9A 2A 65 31 33 D6 74 8C 4F F9 12 Section_1 K^1: 00000: 9F 10 BB F1 3A 79 FB BD 4A 4C A8 64 C4 90 74 64 00010: 39 FE 50 6D 4B 86 9B 21 03 A3 B6 A4 79 28 3C 60 Plaintext block P_1: 00000: 11 22 33 44 55 66 77 00 FF EE DD CC BB AA 99 88 Encrypted block E_{K^1}(C_0): 00000: 1C 39 9D 59 F8 5D 91 91 A9 D2 12 9F 63 15 90 03 Output block C_1 = E_{K^1}(C_0) (xor) P_1: 00000: 0D 1B AE 1D AD 3B E6 91 56 3C CF 53 D8 BF 09 8B Plaintext block P_2: 00000: 00 11 22 33 44 55 66 77 88 99 AA BB CC EE FF 0A Encrypted block E_{K^1}(C_1): 00000: 6B A2 C5 42 52 69 C6 0B 15 14 06 87 90 46 F6 2E Output block C_2 = E_{K^1}(C_1) (xor) P_2: 00000: 6B B3 E7 71 16 3C A0 7C 9D 8D AC 3C 5C A8 09 24 Section_2 K^2: 00000: 77 91 17 50 E0 D1 77 E5 9A 13 78 2B F1 89 08 D0 00010: AB 6B 59 EE 92 49 05 B3 AB C7 A4 E3 69 65 76 C3 Plaintext block P_3: 00000: 11 22 33 44 55 66 77 88 99 AA BB CC EE FF 0A 00 Encrypted block E_{K^2}(C_2): 00000: 95 45 5F DB C3 9E 0A 13 9F CB 10 F5 BD 79 A3 88 Output block C_3 = E_{K^2}(C_2) (xor) P_3: 00000: 84 67 6C 9F 96 F8 7D 9B 06 61 AB 39 53 86 A9 88 Plaintext block P_4: 00000: 22 33 44 55 66 77 88 99 AA BB CC EE FF 0A 00 11 Encrypted block E_{K^2}(C_3): 00000: E0 AA 32 5D 80 A4 47 95 BA 42 BF 63 F8 4A C8 B2 Output block C_4 = E_{K^2}(C_3) (xor) P_4: 00000: C2 99 76 08 E6 D3 CF 0C 10 F9 73 8D 07 40 C8 A3 Section_3 K^3: 00000: E8 76 2B 30 8B 08 EB CE 3E 93 9A C2 C0 3E 76 D4 00010: 60 9A AB D9 15 33 13 D3 CF D3 94 E7 75 DF 3A 94 Plaintext block P_5: 00000: 33 44 55 66 77 88 99 AA BB CC EE FF 0A 00 11 22 Encrypted block E_{K^3}(C_4): 00000: FE 42 8C 70 C2 51 CE 13 36 C1 BF 44 F8 49 66 89 Output block C_5 = E_{K^3}(C_4) (xor) P_5: 00000: CD 06 D9 16 B5 D9 57 B9 8D 0D 51 BB F2 49 77 AB Plaintext block P_6: 00000: 44 55 66 77 88 99 AA BB CC EE FF 0A 00 11 22 33 Encrypted block E_{K^3}(C_5): 00000: 01 24 80 87 86 18 A5 43 11 0A CC B5 0A E5 02 A3 Output block C_6 = E_{K^3}(C_5) (xor) P_6: 00000: 45 71 E6 F0 0E 81 0F F8 DD E4 33 BF 0A F4 20 90 Section_4 K^4: 00000: F2 EE 91 45 6B DC 3D E4 91 2C 87 C3 29 CF 31 A9 00010: 2F 20 2E 5A C4 9A 2A 65 31 33 D6 74 8C 4F F9 12 Plaintext block P_7: 00000: 55 66 77 88 99 AA BB CC Encrypted block MSB_{|P_7|}(E_{K^4}(C_6)): 00000: 97 5C 96 37 55 1E 8C 7F Output block C_7 = MSB_{|P_7|}(E_{K^4}(C_6)) (xor) P_7 00000: C2 3A E1 BF CC B4 37 B3Cipher textCiphertext C: 00000: 0D 1B AE 1D AD 3B E6 91 56 3C CF 53 D8 BF 09 8B 00010: 6B B3 E7 71 16 3C A0 7C 9D 8D AC 3C 5C A8 09 24 00020: 84 67 6C 9F 96 F8 7D 9B 06 61 AB 39 53 86 A9 88 00030: C2 99 76 08 E6 D3 CF 0C 10 F9 73 8D 07 40 C8 A3 00040: CD 06 D9 16 B5 D9 57 B9 8D 0D 51 BB F2 49 77 AB 00050: 45 71 E6 F0 0E 81 0F F8 DD E4 33 BF 0A F4 20 90 00060: C2 3A E1 BF CC B4 37 B3 OMAC-ACPKM-Master mode with AES-256 *********************************** k = 256 n = 128 c for the CTR-ACPKM mode = 64 N = 256 T* = 768 Initial key K: 00000: 88 99 AA BB CC DD EE FF 00 11 22 33 44 55 66 77 00010: FE DC BA 98 76 54 32 10 01 23 45 67 89 AB CD EF Plaintext M: 00000: 11 22 33 44 55 66 77 00 FF EE DD CC BB AA 99 88 00010: 00 11 22 33 44 55 66 77 88 99 AA BB CC EE FF 0A 00020: 11 22 33 44 55 66 77 88 99 AA BB CC EE FF 0A 00 00030: 22 33 44 55 66 77 88 99 AA BB CC EE FF 0A 00 11 00040: 33 44 55 66 77 88 99 AA BB CC EE FF 0A 00 11 22 K^1 | K^1_1 | K^2 | K^2_1 | K^3 | K^3_1: 00000: 9F 10 BB F1 3A 79 FB BD 4A 4C A8 64 C4 90 74 64 00010: 39 FE 50 6D 4B 86 9B 21 03 A3 B6 A4 79 28 3C 60 00020: 77 91 17 50 E0 D1 77 E5 9A 13 78 2B F1 89 08 D0 00030: AB 6B 59 EE 92 49 05 B3 AB C7 A4 E3 69 65 76 C3 00040: 9D CC 66 42 0D FF 45 5B 21 F3 93 F0 D4 D6 6E 67 00050: BB 1B 06 0B 87 66 6D 08 7A 9D A7 49 55 C3 5B 48 00060: F2 EE 91 45 6B DC 3D E4 91 2C 87 C3 29 CF 31 A9 00070: 2F 20 2E 5A C4 9A 2A 65 31 33 D6 74 8C 4F F9 12 00080: 78 21 C7 C7 6C BD 79 63 56 AC F8 8E 69 6A 00 07 Section_1 K^1: 00000: 9F 10 BB F1 3A 79 FB BD 4A 4C A8 64 C4 90 74 64 00010: 39 FE 50 6D 4B 86 9B 21 03 A3 B6 A4 79 28 3C 60 K^1_1: 00000: 77 91 17 50 E0 D1 77 E5 9A 13 78 2B F1 89 08 D0 Plaintext block M_1: 00000: 11 22 33 44 55 66 77 00 FF EE DD CC BB AA 99 88 Input block M_1 (xor) C_0: 00000: 11 22 33 44 55 66 77 00 FF EE DD CC BB AA 99 88 Output block C_1: 00000: 0B A5 89 BF 55 C1 15 42 53 08 89 76 A0 FE 24 3E Plaintext block M_2: 00000: 00 11 22 33 44 55 66 77 88 99 AA BB CC EE FF 0A Input block M_2 (xor) C_1: 00000: 0B B4 AB 8C 11 94 73 35 DB 91 23 CD 6C 10 DB 34 Output block C_2: 00000: 1C 53 DD A3 6D DC E1 17 ED 1F 14 09 D8 6A F3 2C Section_2 K^2: 00000: AB 6B 59 EE 92 49 05 B3 AB C7 A4 E3 69 65 76 C3 00010: 9D CC 66 42 0D FF 45 5B 21 F3 93 F0 D4 D6 6E 67 K^2_1: 00000: BB 1B 06 0B 87 66 6D 08 7A 9D A7 49 55 C3 5B 48 Plaintext block M_3: 00000: 11 22 33 44 55 66 77 88 99 AA BB CC EE FF 0A 00 Input block M_3 (xor) C_2: 00000: 0D 71 EE E7 38 BA 96 9F 74 B5 AF C5 36 95 F9 2C Output block C_3: 00000: 4E D4 BC A6 CE 6D 6D 16 F8 63 85 13 E0 48 59 75 Plaintext block M_4: 00000: 22 33 44 55 66 77 88 99 AA BB CC EE FF 0A 00 11 Input block M_4 (xor) C_3: 00000: 6C E7 F8 F3 A8 1A E5 8F 52 D8 49 FD 1F 42 59 64 Output block C_4: 00000: B6 83 E3 96 FD 30 CD 46 79 C1 8B 24 03 82 1D 81 Section_3 K^3: 00000: F2 EE 91 45 6B DC 3D E4 91 2C 87 C3 29 CF 31 A9 00010: 2F 20 2E 5A C4 9A 2A 65 31 33 D6 74 8C 4F F9 12 K^3_1: 00000: 78 21 C7 C7 6C BD 79 63 56 AC F8 8E 69 6A 00 07 MSB1(K1) == 0 -> K2 = K1 << 1 K1: 00000: 78 21 C7 C7 6C BD 79 63 56 AC F8 8E 69 6A 00 07 K2: 00000: F0 43 8F 8E D9 7A F2 C6 AD 59 F1 1C D2 D4 00 0E Plaintext M_5: 00000: 33 44 55 66 77 88 99 AA BB CC EE FF 0A 00 11 22 Using K1, padding is not required Input block M_5 (xor) C_4: 00000: FD E6 71 37 E6 05 2D 8F 94 A1 9D 55 60 E8 0C A4 Output block C_5: 00000: B3 AD B8 92 18 32 05 4C 09 21 E7 B8 08 CF A0 B8 Message authentication code T: 00000: B3 AD B8 92 18 32 05 4C 09 21 E7 B8 08 CF A0 B8Appendix B.Acknowledgments We thank Mihir Bellare, Scott Fluhrer, Dorothy Cooley, Yoav Nir, Jim Schaad, Paul Hoffman, Dmitry Belyavsky, Yaron Sheffer, Alexey Melnikov, and Spencer Dawkins for their useful comments. Contributors o Russ Housley Vigil Security, LLC housley@vigilsec.com o Evgeny Alekseev CryptoPro alekseev@cryptopro.ru o Ekaterina Smyshlyaeva CryptoPro ess@cryptopro.ru o Shay Gueron University of Haifa, Israel Intel Corporation, Israel Development Center, Israel shay.gueron@gmail.com o Daniel Fox Franke Akamai Technologies dfoxfranke@gmail.com o Lilia Ahmetzyanova CryptoPro lah@cryptopro.ruAppendix C. Acknowledgments We thank Mihir Bellare, Scott Fluhrer, Dorothy Cooley, Yoav Nir, Jim Schaad, Paul Hoffman, Dmitry Belyavsky, Yaron Sheffer, Alexey Melnikov and Spencer Dawkins for their useful comments.Author's Address Stanislav Smyshlyaev (editor) CryptoPro 18, Suschevskiy val Moscow 127018 Russian Federation Phone: +7 (495) 995-48-20 Email: svs@cryptopro.ru