The ACPKM internal re-keying mechanism for block cipher modes of operation
CryptoPro18, Suschevsky val Moscow127018Russian Federation+7 (495) 995-48-20svs@cryptopro.ruCryptoPro18, Suschevsky val Moscow127018Russian Federation+7 (495) 995-48-20alekseev@cryptopro.ruCryptoPro18, Suschevsky val Moscow127018Russian Federation+7 (495) 995-48-20oshkin@cryptopro.ruCryptoPro18, Suschevsky val Moscow127018Russian Federation+7 (495) 995-48-20lah@cryptopro.ruCryptoPro18, Suschevsky val Moscow127018Russian Federation+7 (495) 995-48-20ess@cryptopro.ru
General
Network Working Groupre-keying, key, meshing
This specification presents an approach to increase the security
of block cipher operation modes based on re-keying (with no additional
keys needed) during each separate message processing. It provides an
internal re-keying mechanism called ACPKM.
This mechanism doesn’t require additional secret parameters
or complicated transforms - for key update only the base encryption
function is used.
An important problem related to secure functioning of any cryptographic system
is the control of key lifetimes. Regarding symmetric keys, the main concern is
constraining the key exposure. It could be done by limiting the maximal amount
of data processed with one key. The restrictions can come either from combinatorial
properties of the used cipher modes of operation (for example, birthday attack
) or from particular cryptographic attacks on the used
block cipher (for example, linear cryptanalysis ). Moreover,
most strict restrictions here follow from the need to resist side-channel attacks. The adversary’s opportunity
to obtain an essential amount of data processed with a single key leads not only to
theoretic but also to real vulnerabilities (see ). Therefore, when the total size of a plaintext
processed with the same key reaches threshold values, this key cannot be used
anymore and certain procedures on encryption keys are needed. It leads to several operating
limitations, e.g. the impossibility to process long messages and processing overhead
caused by derivation of additional keys.
This specification presents a mechanism to increase the key lifetime, which
is called ACPKM. This solution ("key meshing") transforms
the key value each time when the given amount of data, precisely the amount of
plaintext section (not the total amount of separate messages), is processed and
proceeds with a new transformed key value for a new plaintext section. Such a
transformation does not require any additional secret values. It is integrated into
the base mode of operation and can be considered as it's extension, therefore
it is called "internal re-keying" in this document.
This approach seems to be mostly useful in the case when the total
amount of data for an established key is not known beforehand:
the performance on useless operations won’t be lost if the data size is rather small,
and the security won't be lacked when it occurs to be large. The transformed
keys are computed only when they are needed.
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*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 a in V_s that consists of s '0' bits;
the block cipher permutation under the key K in V_k;
the key K size (in bits);
the block size of the block cipher (in bits);
the total number of data blocks in the plaintext;
the section size (the number of bits in a data section);
the number of data sections in the plaintext;
the message M size (in bits);
the transformation that maps a string a = (a_s, ...,a_1)
into the string phi_i(a) = a' = (a'_s, ...,a'_1), 1 <= i <= s,
such that a'_i = 1 and a'_j = a_j for all j in {1,...,s}/{i};
the least integer that is not less than x. This section describes the families of block cipher modes of operations that are extended by the ACPKM
re-keying mechanisms as described in . A plaintext message P and a ciphertext C are divided into b = ceil(m/n) parts
(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). The Counter (CTR) mode is a block cipher mode of operation that applies the block
cipher transformation E_K to a sequence of input blocks, called counters,
to produce a sequence of output blocks that are XORed with a plaintext
to produce a ciphertext, and vice versa. It is defined similar to the one specified in . The ACPKM-CTR re-keying mechanisms described in
can be used with the following block cipher and CTR mode 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. In the current document, the counters for a given message are denoted as
CTR_1, CTR_2, ..., CTR_b. The CTR encryption mode is defined as follows: The CTR decryption mode is 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. TODO: This section describes the family of block cipher modes of operation with both encryption and authentication.
It is defined similar to the one specified in . The ACPKM-GCM re-keying mechanisms described in
can be used with the following GCM block cipher mode parameters: 128 <= 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. This section presents three mathematical algorithms that appear in the specification of the
authenticated encryption and authenticated decryption functions of the GCM cipher mode
described in below. 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 and is defined by a particular GCM mode. The GCM encryption mode is defined as follows: The GCM decryption mode is defined as follows: The initial vector IV value for each message that is encrypted under the given key must be
chosen in a unique manner. N o t e : The encryption part in the GCM-ACPKM mode is the encryption
in the CTR-ACPKM mode with several differences: in the CTR mode the counter
for the plaintext encryption starts with the first CTR_1 value and in the GCM mode the counter
starts with the second GCTR_2 value. This section defines periodical key transformations for long message
processing that are considered as extensions of the basic CTR and GCM encryption
modes and are called ACPKM-CTR and ACPKM-GCM re-keying mechanisms. An additional parameter that defines the functioning of CTR and GCM block cipher
modes with the ACPKM key transformation algorithm is the section size N.
The value of N is fixed within a specific protocol based on the
requirements of the system capacity and key lifetime (some recommendations on choosing N will be provided in ). The section size
N MUST be divisible by the block size n. The main idea behind internal re-keying is presented in Fig.1: For the {i+1}-th section the K_{i+1} value is calculated as follows: K_{i+1} = ACPKM-CTR(K_i) = MSB_k(E_{K_i}(W_1)|...|E_{K_i}(W_J)), where J = ceil(k/n), W_t = phi_c(D_t) for any t in {1,...,J} 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 phi_c(D_1),..., phi_c(D_J) are pairwise different for any allowed n, k, c values. This section defines a ACPKM-CTR internal re-keying mechanism for the CTR encryption
mode that was described in . During the processing of the input message M with the length m using ACPKM-CTR
internal re-keying algorithm and the key K the message is divided into
l = ceil(m*N) parts (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 is processed
with the initial key K_1 = K. To process the (i+1)-th section the K_{i+1} key value
is calculated using ACPKM-CTR transformation of the key K_i.
The counter value (CTR_{i+1}) is not changed during this process. The message size m MUST NOT exceed n*2^{c-1} bits. This section defines a ACPKM-GCM internal re-keying mechanism for the GCM encryption
mode that was described in . During the processing of the input message M with the length m using ACPKM-GCM
internal re-keying algorithm and the key K the message is divided into
l = ceil(m/N) parts (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 is processed
with the initial key K_1 = K. To process the (i+1)-th section the K_{i+1} key value
is calculated using ACPKM-GCM transformation of the key K_i. The message size m MUST NOT exceed n*(2^{c-1}-2) bits. The key for computing values E_K(J_0) and H is not updated and is
equal to the initial key.
TODO
The ACPKM re-keying mechanisms provide the CTR and GCM encryption modes extensions that
have the following property: a compromise of a key of some section does not
lead to a compromise of previous keys but leads to a compromise of next keys. The ACPKM mechanism allows to increase the CTR and GCM encryption modes security
in proportion to the frequency of key changing, which is inversely related to the section size N.
Thus, the key lifetime can be noticeably increased: an amount of material that
is processed with the key K increases quadratically, divided by N. Since the performance of encryption can slightly decrease for rather small values of N,
the parameter of N SHOULD be selected for a particular protocol as maximum possible to provide
necessary key lifetime for the adversary models that are considered.
Linear Cryptanalysis Method for DES Cipher
Matsui M.
A concrete security treatment of symmetric encryption
Bellare M., Desai A., Jokipii E., Rogaway P.
On the Practical (In-)Security of 64-bit Block Ciphers: Collision Attacks on HTTP over TLS and OpenVPN
Bhargavan K., Leurent G.
The Galois/Counter Mode of Operation (GCM)
McGrew, D. and J. Viega
Recommendation for Block Cipher Modes of Operation: Methods and Techniques
Dworkin, M.