﻿ Re-keying Mechanisms for Symmetric Keys CryptoPro
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General CFRG re-keying, key, meshing If encryption is performed under a single key, there is a certain maximum threshold amount of data that can be safely encrypted. This amount is called key lifetime. This specification contains a description of a variety of methods to increase the lifetime of symmetric keys. It provides external and internal re-keying mechanisms based on hash functions and on block ciphers that can be used with such modes of operations as CTR, GCM, CCM, CBC, CFB, OFB and OMAC.
The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT", "SHOULD", "SHOULD NOT", "RECOMMENDED", "MAY", and "OPTIONAL" in this document are to be interpreted as described in .
This document uses the following terms and definitions for the sets and operations on the elements of these sets: exclusive-or of two binary vectors of the same length. the set of all strings of a finite length (hereinafter referred to as strings), including the empty string; the set of all binary strings of length s, where s is a non-negative integer; substrings and string components are enumerated from right to left starting from one; the bit length of the bit string X; 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 to A, and the right substring in V_|B| is equal to B; ring of residues modulo 2^n; the transformation that maps a string a = (a_s, ... , a_1), a in V_s, into the integer Int_s(a) = 2^{s-1}*a_s + ... + 2*a_2 + a_1; the transformation inverse to the mapping Int_s; 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; 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; 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; denotes the string in V_s that consists of s 'a' bits; the block cipher permutation under the key K in V_k; the least integer that is not less than x; the key K size (in bits), k is multiple of 8; the block size of the block cipher (in bits), n is multiple of 8; the total number of data blocks in the plaintext (b = ceil(m/n)); the section size (the number of bits in a data section); the number of data sections in the plaintext; the transformation that maps a string a = (a_s, ... , a_1) into the value phi_i(a) = a_i for all i in {1, ... , s}. A plaintext message P and a 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, where P_i and C_i are in V_n, for i = 1, 2, ... , b-1, and P_b, C_b are in V_r, where r <= n if not otherwise stated.
Suppose L is an amount of data that can be safely processed with one key (without re-keying). For i in {1, 2, ..., t} the key K^i (see Figure 1 and Figure 2) should be transformed after processing q_i integral messages, where q_i can be calculated in accordance with one of the following two approaches: Explicit approach: |M^{i,1}| + ... + |M^{i,q_i}| <= L, |M^{i,1}| + ... + |M^{i,q_i + 1}| > L. This approach allows to use the key K^i in almost optimal way but it cannot be applied in case when messages may be lost or reordered (e.g. DTLS packets). Implicit approach: q_i = L / m_max, i = 1, ... , t. The amount of data processed with one key K^i is calculated under the assumption that every message has the maximum length m_max. Hence this amount can be considerably less than the key lifetime limitation L. On the other hand this approach can be applied in case when messages may be lost or reordered (e.g. DTLS packets).
The main idea behind external re-keying with parallel construction is presented in Fig.1: The key K^i, i = 1, ... , t-1, is updated after processing a certain amount of data (see ).
ExtParallelC re-keying mechanism is based on key derivation function on a block cipher and is used to generate t keys for t sections as follows: K^1 | K^2 | ... | K^t = ExtParallelC(K, t*k) = MSB_{t*k}(E_{K}(0) | E_{K}(1) | ... | E_{K}(R-1)), where R = ceil(t*k/n).
ExtParallelH re-keying mechanism is based on HMAC key derivation function HKDF-Expand, described in , and is used to generate t keys for t sections as follows: K^1 | K^2 | ... | K^t = ExtParallelH(K, t*k) = HKDF-Expand(K, label, t*k), where label is a string (can be a zero-length string) that is defined by a specific protocol.
The main idea behind external re-keying with serial construction is presented in Fig.2: The key K^i, i = 1, ... , t-1, is updated after processing a certain amount of data (see ).
The key K^i is calculated using ExtSerialC transformation as follows: K^i = ExtSerialC(K, i) = MSB_k(E_{K*_i}(0) | E_{K*_i}(1) | ... | E_{K*_i}(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}(J) | E_{K*_j}(J+1) | ... | E_{K*_j}(2J-1)), where j = 1, ... , t-1.
The key K^i is calculated using ExtSerialH transformation as follows: K^i = ExtSerialH(K, i) = HKDF-Expand(K*_i, label1, k), where i = 1, ... , t, HKDF-Expand is an HMAC-based key derivation function, described in , 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 (can be a zero-length strings) that are defined by a specific protocol (see, for example, TLS 1.3 updating traffic keys algorithm ).
Suppose L is an amount of data that can be safely processed with one key (without re-keying), N is a section size (fixed parameter). Suppose M^{i}_1 is the first section of message M^{i}, i = 1, ... , q (see Figure 3 and Figure 4), then the parameter q can be calculated in accordance with one of the following two approaches: Explicit approach: |M^{1}_1| + ... + |M^{q}_1| <= L, |M^{1}_1| + ... + |M^{q+1}_1| > L This approach allows to use the key K^i in an almost optimal way but it cannot be applied in case when messages may be lost or reordered (e.g. DTLS packets). Implicit approach: q = L / N. The amount of data processed with one key K^i is calculated under the assumption that the length of every message is equal or more then section size N and so it can be considerably less than the key lifetime limitation L. On the other hand this approach can be applied in case when messages may be lost or reordered (e.g. DTLS packets).
This section describes the block cipher modes that use the ACPKM re-keying mechanism, which does not use master key: an initial key is used directly for the encryption of the data.
This section defines periodical key transformation with no master key which is called ACPKM re-keying mechanism. This mechanism can be applied to one of the basic encryption modes (CTR and GCM block cipher modes) for getting an extension of this encryption mode that uses periodical key transformation with no 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 key lifetime (some recommendations on choice of N will be provided in ). The section size N MUST be divisible by the block size n. The main idea behind internal re-keying with no master key is presented in Fig.3: During the processing of the input message M with the length m in some encryption mode that uses ACPKM key transformation of the key K 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 = 1, 2, ... , l-1 and M_l is in V_r, r <= N). The first section of each message is processed with the initial key K^1 = K. To process the (i+1)-th section of each message the K^{i+1} key value is calculated using 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), parameter c is fixed by a specific encryption mode which uses ACPKM key transformation 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}: N o t e : The constant D is such that D_1, ... , D_J are pairwise different for any allowed n, k values. N o t e : The constant D is such that phi_c(D_t) = 1 for any allowed n, k, c and t in {1, ... , J}. This condition is important, as it allows to prevent collisions of blocks of transformed key and block cipher permutation inputs.
This section defines a CTR-ACPKM encryption mode that uses internal ACPKM re-keying mechanism for the periodical key transformation. The CTR-ACPKM mode can be considered as the extended by the ACPKM re-keying mechanism basic encryption mode CTR (see ). The CTR-ACPKM encryption mode can be used with the following parameters: 64 <= n <= 512; 128 <= k <= 512; the number of bits c in a specific part of the block to be incremented is such that 16 <= c <= 3/4 n, c is multiple of 8. The CTR-ACPKM mode encryption and decryption procedures are defined as follows: The initial counter nonce ICN value for each message that is encrypted under the given key must be chosen in a unique manner. The message size MUST NOT exceed n * 2^{c-1} bits.
This section defines GCM-ACPKM authenticated encryption mode that uses internal ACPKM re-keying mechanism for the periodical key transformation. The GCM-ACPKM mode can be considered as the basic authenticated encryption mode GCM (see ) extended by the ACPKM re-keying mechanism. The GCM-ACPKM authenticated encryption mode can be used with the following parameters: n in {128, 256}; 128 <= k <= 512; the number of bits c in a specific part of the block to be incremented is such that 32 <= c <= 3/4 n, c is multiple of 8.; authentication tag length t. The GCM-ACPKM mode encryption and decryption procedures are defined as follows: 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 ): f = a^128 + a^7 + a^2 + a^1 + 1. f = a^256 + a^10 + a^5 + a^2 + 1. The initial vector IV value for each message that is encrypted under the given key must be chosen in a unique manner. The plaintext size MUST NOT exceed n*(2^{c-1} - 2) bits. The key for computing values E_{K}(ICB_0) and H is not updated and is equal to the initial key K.
This section defines a CCM-ACPKM authenticated encryption block cipher mode that uses internal ACPKM re-keying mechanism for the periodical key transformation. The CCM-ACPKM mode can be considered as the extended by the ACPKM re-keying mechanism basic authenticated encryption mode CCM (see ). Since defines CCM authenticated encryption mode only for 128-bit block size, the CCM-ACPKM authenticated encryption mode can be used only with the parameter n = 128. However, the CCM-ACPKM design principles can easily be applied to other block sizes, but these modes will require their own specifications. The CCM-ACPKM authenticated encryption mode differs from CCM mode in keys that are used for encryption during CBC-MAC calculation (see Section 2.2 of ) and key stream blocks generation (see Section 2.3 of ). The CCM mode uses the same initial key K block cipher encryption operations, while the CCM-ACPKM mode uses the keys K^1, K^2, ..., which are generated from the key K as follows: K^1 = K, K^{i+1} = ACPKM( K^i ). The keys K^1, K^2, ..., which are used as follows. CBC-MAC calculation: under a separate message processing during the first N/n block cipher encryption operations the key K^1 is used, the key K^2 is used for the next N/n block cipher encryption operations and so on. For example, if N = 2n, then CBC-MAC calculation for a sequence of t blocks B_0, B_1, ..., B_t is as follows: X_1 = E( K^1, B_0 ), X_2 = E( K^1, X_1 XOR B_1 ), X_3 = E( K^2, X_2 XOR B_2 ), X_4 = E( K^2, X_3 XOR B_3 ), X_5 = E( K^3, X_4 XOR B_4 ), ... T = first-M-bytes( X_t+1 ) The key stream blocks generation: under a separate message processing during the first N/n block cipher encryption operations the key K^1 is used, the key K^2 is used for the next N/n block cipher encryption operations and so on. For example, if N = 2n, then the key stream blocks are generated as follows: S_0 = E( K^1, A_0 ), S_1 = E( K^1, A_1 ), S_2 = E( K^2, A_2 ), S_3 = E( K^2, A_3 ), S_4 = E( K^3, A_4 ), ...
This section describes the block cipher modes that uses the ACPKM-Master re-keying mechanism, which use the initial key K as a master key K, so K is never used directly for the data processing but is used for key derivation.
This section defines periodical key transformation with master key K which is called ACPKM-Master re-keying mechanism. This mechanism can be applied to one of the basic modes of operation (CTR, GCM, CBC, CFB, OFB, OMAC modes) for getting an extension of this modes of operations that uses periodical key transformation with master key. This extension can be considered as a new mode of operation . Additional parameters that defines the functioning of basic modes of operation with the ACPKM-Master re-keying mechanism are the section size N and change frequency T* of the key K. The values of N and T* are measured in bits and are fixed within a specific protocol based on the requirements of the system capacity and key lifetime (some recommendations on choosing N and T* will be provided in ). The section size N MUST be divisible by the block size n. The key frequency T* MUST be divisible by n. The main idea behind internal re-keying with master key is presented in Fig.4: 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 master key K and key frequency 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, that has been calculated with the ACPKM-Master algorithm as follows: K | ... | K[l] = ACPKM-Master(T*, K, d*l) = CTR-ACPKM-Encrypt (T*, K, 1^{n/2}, 0^{d*l}).
This section defines a CTR-ACPKM-Master encryption mode that uses internal ACPKM-Master re-keying mechanism for the periodical key transformation. The CTR-ACPKM-Master encryption mode can be considered as the extended by the ACPKM-Master re-keying mechanism basic encryption mode CTR (see ). The CTR-ACPKM-Master encryption mode can be used with the following parameters: 64 <= n <= 512; 128 <= k <= 512; the number of bits c in a specific part of the block to be incremented is such that 32 <= c <= 3/4 n, c is multiple of 8. The key material K[j] that is used for one section processing is equal to K^j, |K^j| = k bits. The CTR-ACPKM-Master mode encryption and decryption procedures are defined as follows: The initial counter nonce ICN value for each message that is encrypted under the given key must be chosen in a unique manner. The counter (CTR_{i+1}) value does not change during key transformation. The message size MUST NOT exceed (2^{n/2-1}*n*N / k) bits.
This section defines a GCM-ACPKM-Master encryption mode that uses internal ACPKM-Master re-keying mechanism for the periodical key transformation. The GCM-ACPKM-Master encryption mode can be considered as the extended by the ACPKM-Master re-keying mechanism basic encryption mode GCM (see ). The GCM-ACPKM-Master encryption mode can be used with the following parameters: n in {128, 256}; 128 <= k <= 512; the number of bits c in a specific part of the block to be incremented is such that 32 <= c <= 3/4 n, c is multiple of 8; authentication tag length t. The key material K[j] that is used for one section processing is equal to K^j, |K^j| = k bits, that is calculated as follows: K^1 | ... | K^j | ... | K^l = ACPKM-Master(T*, K, k*l). The GCM-ACPKM-Master mode encryption and decryption procedures are defined as follows: 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 ): f = a^128 + a^7 + a^2 + a^1 + 1. f = a^256 + a^10 + a^5 + a^2 + 1. The initial vector IV value for each message that is encrypted under the given key must be chosen in a unique manner. The plaintext size MUST NOT exceed (2^{n/2-1}*n*N / k) bits.
This section defines a CCM-ACPKM-Master authenticated encryption mode of operations that uses internal ACPKM-Master re-keying mechanism for the periodical key transformation. The CCM-ACPKM-Master authenticated encryption mode is differed from CCM-ACPKM mode in the way the keys K^1, K^2, ... are generated. For CCM-ACPKM-Master mode the keys are generated as follows: K^i = K[i], where |K^i|=k and K|K|...|K[l] = ACPKM-Master( T*, K, k*l ).
This section defines a CBC-ACPKM-Master encryption mode that uses internal ACPKM-Master re-keying mechanism for the periodical key transformation. The CBC-ACPKM-Master encryption mode can be considered as the extended by the ACPKM-Master re-keying mechanism basic encryption mode CBC (see ). The CBC-ACPKM-Master encryption mode can be used with the following parameters: 64 <= n <= 512; 128 <= k <= 512. In the specification of the CBC-ACPKM-Master mode 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 outside the scope of this document. An example of a padding method can be found in Appendix A of . The key material K[j] that is used for one section processing is equal to K^j, |K^j| = k bits. We will denote by D_{K} the decryption function which is a permutation inverse to the E_{K}. The CBC-ACPKM-Master mode encryption and decryption procedures are defined as follows: The initialization vector IV for each message that is encrypted under the given key need not to be secret, but must be unpredictable. The message size MUST NOT exceed (2^{n/2-1}*n*N / k) bits.
This section defines a CFB-ACPKM-Master encryption mode that uses internal ACPKM-Master re-keying mechanism for the periodical key transformation. The CFB-ACPKM-Master encryption mode can be considered as the extended by the ACPKM-Master re-keying mechanism basic encryption mode CFB (see ). The CFB-ACPKM-Master encryption mode can be used with the following parameters: 64 <= n <= 512; 128 <= k <= 512. The key material K[j] that is used for one section processing is equal to K^j, |K^j| = k bits. The CFB-ACPKM-Master mode encryption and decryption procedures are defined as follows: The initialization vector IV for each message that is encrypted under the given key need not to be secret, but must be unpredictable. The message size MUST NOT exceed 2^{n/2-1}*n*N/k bits.
This section defines an OFB-ACPKM-Master encryption mode that uses internal ACPKM-Master re-keying mechanism for the periodical key transformation. The OFB-ACPKM-Master encryption mode can be considered as the extended by the ACPKM-Master re-keying mechanism basic encryption mode OFB (see ). The OFB-ACPKM-Master encryption mode can be used with the following parameters: 64 <= n <= 512; 128 <= k <= 512. The key material K[j] used for one section processing is equal to K^j, |K^j| = k bits. The OFB-ACPKM-Master mode encryption and decryption procedures are defined as follows: The initialization vector IV for each message that is encrypted under the given key need not be unpredictable, but it must be a nonce that is unique to each execution of the encryption operation. The message size MUST NOT exceed 2^{n/2-1}*n*N / k bits.
This section defines an OMAC-ACPKM-Master message authentication code calculation mode that uses internal ACPKM-Master re-keying mechanism for the periodical key transformation. The OMAC-ACPKM-Master mode can be considered as the extended by the ACPKM-Master re-keying mechanism basic message authentication code calculation mode OMAC, which is also known as CMAC (see ). The OMAC-ACPKM-Master message authentication code calculation mode can be used with the following parameters: n in {64, 128, 256}; 128 <= k <= 512. The key material K[j] that is used for one section processing is equal to K^j | K^j_1, where |K^j| = k and |K^j_1| = n. The following is a specification of the subkey generation process of OMAC: Where R_n takes the following values: n = 64: R_{64} = 0^{59} | 11011; n = 128: R_{128} = 0^{120} | 10000111; n = 256: R_{256} = 0^{145} | 10000100101. The OMAC-ACPKM-Master message authentication code calculation mode is defined as follows: The message size MUST NOT exceed 2^{n/2}*n^2*N / (k + n) bits.
Any mechanism described in can be used with any mechanism described in .
Re-keying should be used to increase "a priori" security properties of ciphers in hostile environments (e.g. with side-channel adversaries). If some non-negligible attacks are known for a cipher, it must not be used. So re-keying cannot be used as a patch for vulnerable ciphers. Base cipher properties must be well analyzed, because security of re-keying mechanisms is based on security of a block cipher as a pseudorandom function. Re-keying is not intended to solve any post-quantum security issues for symmetric crypto 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 is needed and the aim of re-keying is to limit a size of plaintext transformed on one key.
The Transport Layer Security (TLS) Protocol Version 1.3 The Galois/Counter Mode of Operation (GCM) McGrew, D. and J. Viega Recommendation for Block Cipher Modes of Operation: Methods and Techniques Dworkin, M. Increasing the Lifetime of a Key: A Comparative Analysis of the Security of Re-keying Techniques Michel Abdalla and Mihir Bellare On the Practical (In-)Security of 64-bit Block Ciphers. Collision Attacks on HTTP over TLS and OpenVPN Karthikeyan Bhargavan, Gaëtan Leurent A Tutorial on Linear and Differential Cryptanalysis Howard M. Heys
Russ Housley Vigil Security, LLC housley@vigilsec.com Mihir Bellare University of California mihir@eng.ucsd.edu Evgeny Alekseev CryptoPro alekseev@cryptopro.ru Ekaterina Smyshlyaeva CryptoPro ess@cryptopro.ru Daniel Fox Franke Akamai Technologies dfoxfranke@gmail.com Lilia Ahmetzyanova CryptoPro lah@cryptopro.ru Ruth Ng University of California, San Diego ring@eng.ucsd.edu Shay Gueron University of Haifa, Israel Intel Corporation, Israel Development Center, Israel shay.gueron@gmail.com
We thank Scott Fluhrer, Dorothy Cooley, Yoav Nir, Jim Schaad and Paul Hoffman for their useful comments.