CFRG S. Smyshlyaev, Ed.
InternetDraft CryptoPro
Intended status: Informational R. Housley
Expires: August 31, 2017 Vigil Security, LLC
M. Bellare
University of California, San Diego
E. Alekseev
E. Smyshlyaeva
CryptoPro
February 27, 2017
Rekeying Mechanisms for Symmetric Keys
draftirtfcfrgrekeying00
Abstract
This specification contains a description of a variety of methods to
increase the lifetime of symmetric keys. It provides external and
internal rekeying mechanisms that can be used with such modes of
operations as CTR, GCM, CBC, CFB, OFB and OMAC.
Status of This Memo
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Table of Contents
1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . 3
2. Conventions Used in This Document . . . . . . . . . . . . . . 3
3. Basic Terms and Definitions . . . . . . . . . . . . . . . . . 3
4. External Rekeying Mechanisms . . . . . . . . . . . . . . . . 5
4.1. Parallel Constructions . . . . . . . . . . . . . . . . . 5
4.1.1. Parallel Construction Based on a KDF on a Block
Cipher . . . . . . . . . . . . . . . . . . . . . . . 6
4.1.2. Parallel Construction Based on HKDF . . . . . . . . . 6
4.2. Serial Constructions . . . . . . . . . . . . . . . . . . 7
4.2.1. Serial Construction Based on a KDF on a Block Cipher 7
4.2.2. Serial Construction Based on HKDF . . . . . . . . . . 8
5. Internal Rekeying Mechanisms . . . . . . . . . . . . . . . . 8
5.1. Constructions that Do Not Require Master Key . . . . . . 8
5.1.1. ACPKM Rekeying Mechanisms . . . . . . . . . . . . . 8
5.1.2. CTRACPKM Encryption Mode . . . . . . . . . . . . . . 10
5.1.3. GCMACPKM Encryption Mode . . . . . . . . . . . . . . 12
5.2. Constructions that Require Master Key . . . . . . . . . . 14
5.2.1. ACPKMMaster Key Generation from the Master Key . . . 15
5.2.2. CTR Mode Key Meshing . . . . . . . . . . . . . . . . 17
5.2.3. GCM Mode Key Meshing . . . . . . . . . . . . . . . . 19
5.2.4. CBC Mode Key Meshing . . . . . . . . . . . . . . . . 22
5.2.5. CFB Mode Key Meshing . . . . . . . . . . . . . . . . 24
5.2.6. OFB Mode Key Meshing . . . . . . . . . . . . . . . . 26
5.2.7. OMAC Mode Key Meshing . . . . . . . . . . . . . . . . 27
6. Joint Usage of External and Internal Rekeying . . . . . . . 29
7. Security Considerations . . . . . . . . . . . . . . . . . . . 29
7.1. Principles of Choice of Constructions and Security
Parameters . . . . . . . . . . . . . . . . . . . . . . . 29
7.2. Requirements For Base Primitives . . . . . . . . . . . . 30
8. References . . . . . . . . . . . . . . . . . . . . . . . . . 30
8.1. Normative References . . . . . . . . . . . . . . . . . . 30
8.2. Informative References . . . . . . . . . . . . . . . . . 31
Appendix A. Test examples . . . . . . . . . . . . . . . . . . . 31
Appendix B. Contributors . . . . . . . . . . . . . . . . . . . . 35
Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . . 35
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1. Introduction
Common attacks base their success on the ability to get many
encryptions under a single key. If encryption is performed under a
single key, there is a certain maximum threshold number of messages
that can be safely encrypted. These restrictions can come either
from combinatorial properties of the used cipher modes of operation
(for example, birthday attack [BDJR]) or from particular
cryptographic attacks on the used block cipher (for example, linear
cryptanalysis [Matsui]). Moreover, most strict restrictions here
follow from the need to resist sidechannel 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 practical
vulnerabilities (see [BL]). Therefore, when the total size of a
plaintext processed with a single key reaches threshold values, this
key cannot be used anymore and certain procedures with encryption
keys are needed.
The most simple and obvious way for overcoming the key lifetimes
limitations is a renegotiation of a regular session key. However,
this reduces the total performance since it usually entails the
frequent use of a public key cryptography.
Another way is to use a transformation of a previously negotiated
key. This specification presents the description of such mechanisms
and the description of the cases when these mechanisms should be
applied.
2. Conventions Used in This Document
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 [RFC2119].
3. Basic Terms and Definitions
This document uses the following terms and definitions for the sets
and operations on the elements of these sets:
(xor) exclusiveor of two binary vectors of the same length.
V* the set of all strings of a finite length (hereinafter
referred to as strings), including the empty string;
V_s 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;
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X the bit length of the bit string X;
AB 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;
Z_{2^n} ring of residues modulo 2^n;
Int_s: V_s > Z_{2^s} 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;
Vec_s: Z_{2^s} > V_s the transformation inverse to the mapping
Int_s;
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_{si+1}) in V_i;
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;
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;
a^s denotes 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 least integer that is not less than x;
k the key K size (in bits);
n the block size of the block cipher (in bits);
b the total number of data blocks in the plaintext (b = ceil(m/
n));
N the section size (the number of bits in a data section);
l the number of data sections in the plaintext;
m the message M size (in bits);
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phi_i: V_s > V_s 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}.
A plaintext message P and a ciphertext C are divided into b = ceil(m/
n) segments 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, ... , b1, and
P_b, C_b are in V_r, where r <= n if not otherwise stated.
4. External Rekeying Mechanisms
This section presents an approach to increase the lifetime of
negotiated keys after processing a limited number of integral
messages. It provides an external parallel and serial rekeying
mechanisms (see [AbBell]). These mechanisms use an initial
(negotiated) key as a master key, which is never used directly for
the data processing but is used for key generation. Such mechanisms
operate outside of the base modes of operations and do not change
them at all, therefore they are called "external rekeying" in this
document.
4.1. Parallel Constructions
The main idea behind external rekeying with parallel construction is
presented in Fig.1:
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Lifetime of a key = L,
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} ========== 
_____________________________________________________________
M_{i,1} + ... + M_{i,q_i} <= L, i = 1, ... , t.
Figure 1: External parallel rekeying mechanisms
4.1.1. Parallel Construction Based on a KDF on a Block Cipher
ExtParallelC rekeying mechanism is based 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*}(J1)),
where J = ceil(k/n).
4.1.2. Parallel Construction Based on HKDF
ExtParallelH rekeying mechanism is based on HMACbased key
derivation function HKDFExpand, described in [RFC5869], and is used
to generate t keys for t sections as follows:
K^1  K^2  ...  K^t = ExtParallelH(K*, t*k) = HKDFExpand(K*,
label, t*k),
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where label is a string (can be a zerolength string) that is defined
by a specific protocol.
4.2. Serial Constructions
The main idea behind external rekeying with serial construction is
presented in Fig.2:
Lifetime of a key = L,
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} ========== 
_____________________________________________________________
M_{i,1} + ... + M_{i,q_i} <= L, i = 1, ... , t.
Figure 2: External serial rekeying mechanisms
4.2.1. Serial Construction Based on a KDF on a Block Cipher
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}(J1)),
where J = ceil(k/n), i = 1, ... , t, K*_i is calculated as follows:
K*_1 = K*,
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K*_{j+1} = MSB_k(E_{K*_j}(J)  E_{K*_j}(J+1)  ...  E_{K*_j}(2J
1)),
where j = 1, ... , t1.
4.2.2. Serial Construction Based on HKDF
The key K^i is calculated using ExtSerialH transformation as follows:
K^i = ExtSerialH(K*, i) = HKDFExpand(K*_i, label1, k),
where i = 1, ... , t, HKDFExpand is an HMACbased key derivation
function, described in [RFC5869], K*_i is calculated as follows:
K*_1 = K*,
K*_{j+1} = HKDFExpand(K*_j, label2, k), where j = 1, ... , t1,
where label1 and label2 are different strings (can be a zerolength
strings) that are defined by a specific protocol (see, for example,
TLS 1.3 updating traffic keys algorithm [TLSDraft]).
5. Internal Rekeying Mechanisms
This section presents an approach to increase the lifetime of
negotiated key by rekeying during each separate message processing.
It provides an internal rekeying mechanisms called ACPKM and ACPKM
Master that do not use and use a master key respectively. Such
mechanisms are integrated into the base modes of operations and can
be considered as the base mode extensions, therefore they are called
"internal rekeying" in this document.
5.1. Constructions that Do Not Require Master Key
This section describes the block cipher modes that uses the ACPKM re
keying mechanism (described in Section 5.1.1), which does not use
master key: an initial key is used directly for the encryption of the
data.
5.1.1. ACPKM Rekeying Mechanisms
This section defines periodical key transformation with no master key
which is called ACPKM rekeying 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.
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An additional parameter that defines the functioning of basic
encryption modes with the ACPKM rekeying 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 choosing N will be provided
in Section 7). The section size N MUST be divisible by the block
size n.
The main idea behind internal rekeying with no master key is
presented in Fig.3:
Lifetime of a key = L,
section size = const = N,
maximum message size = m_max.
____________________________________________________________________
ACPKM ACPKM ACPKM
K^1 = K > K^2 ...> K^{l_max1} > K^{l_max}
   
   
v v v v
Message(1) ==================== ... =================: 
Message(2) ==================== ... ===  : 
. . . . . . : .
: : : : : : : :
Message(q) ==================== ... =============== : 
section :
<> m_max
N bit
___________________________________________________________________
l_max = ceil(m_max/N),
q*N <= L.
Figure 3: Key meshing with no master key
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) parts (denoted as M = M_1 
M_2  ...  M_l, where M_i is in V_N for i = 1, 2, ... , l1 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 transformation as follows:
K^{i+1} = ACPKM(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:
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D_1  D_2  ...  D_J = MSB_{J*n}(D),
where D is the following constant in V_{1024}:
D = ( F3  74  E9  23  FE  AA  D6  DD
 98  B4  B6  3D  57  8B  35  AC
 A9  0F  D7  31  E4  1D  64  5E
 40  8C  87  87  28  CC  76  90
 37  76  49  9F  7D  F3  3B  06
 92  21  7B  06  37  BA  9F  B4
 F2  71  90  3F  3C  F6  FD  1D
 70  BB  BB  88  E7  F4  1B  76
 7E  44  F9  0E  46  91  5B  57
 00  BC  13  45  BE  0D  BD  C7
 61  38  19  3C  41  30  86  82
 1A  A0  45  79  23  4C  4C  F3
 64  F2  6A  CC  EA  48  CB  B4
 0C  B9  A9  28  C3  B9  65  CD
 9A  CA  60  FB  9C  A4  62  C7
 22  C0  6C  E2  4A  C7  FB  5B).
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.
N o t e : The constant D is such that D =
sha512(streebog512(0^1024))  sha512(streebog512(1^1024)), where
sha512 is a hash function with 512bit output corresponding to the
algorithm SHA512 [SHA512], streebog512 is a hash function with
512bit output, corresponding to the algorithm GOST R 34.112012
[GOST34112012], [RFC6986].
5.1.2. CTRACPKM Encryption Mode
This section defines a CTRACPKM encryption mode that uses internal
ACPKM rekeying mechanism for the periodical key transformation.
The CTRACPKM mode can be considered as the extended by the ACPKM re
keying mechanism basic encryption mode CTR (see [MODES]).
The CTRACPKM encryption mode can be used with the following
parameters:
o 64 <= n <= 512;
o 128 <= k <= 512;
o the number of bits c in a specific part of the block to be
incremented is such that 32 <= c <= 3/4 n.
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The CTRACPKM mode encryption and decryption procedures are defined
as follows:
++
 CTRACPKMEncrypt(N, K, ICN, P) 

 Input: 
  Section size N, 
  key K, 
  initial counter nonce ICN in V_{nc}, 
  plaintext P = P_1  ...  P_b, P < n * 2^{c1}. 
 Output: 
  Ciphertext C. 

 1. CTR_1 = ICN  0^c 
 2. For j = 2, 3, ... , b do 
 CTR_{j} = Inc_c(CTR_{j1}) 
 3. K^1 = K 
 4. For i = 2, 3, ... , ceil(P/N) 
 K^i = ACPKM(K^{i1}) 
 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 
++
++
 CTRACPKMDecrypt(N, K, ICN, C) 

 Input: 
  Section size N, 
  key K, 
  initial counter nonce ICN in V_{nc}, 
  ciphertext C = C_1  ...  C_b, C < n * 2^{c1}. 
 Output: 
  Plaintext P. 

 1. Return CTRACPKMEncrypt(N, K, ICN, C) 
++
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 m MUST NOT exceed n * 2^{c1} bits.
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5.1.3. GCMACPKM Encryption Mode
This section defines a GCMACPKM encryption mode that uses internal
ACPKM rekeying mechanism for the periodical key transformation.
The GCMACPKM mode can be considered as the extended by the ACPKM re
keying mechanism basic encryption mode GCM (see [GCM]).
The GCMACPKM encryption mode can be used with the following
parameters:
o n in {128, 256};
o 128 <= k <= 512;
o the number of bits c in a specific part of the block to be
incremented is such that 32 <= c <= 3/4 n;
o authentication tag length t.
The GCMACPKM 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_{i1} (xor) X_i) * H 
 3. Return Y_m 
++
++
 GCTR(N, K, ICB, X) 

 Input: 
  Section size N, 
  key K, 
  initial counter block ICB, 
  X = X_1  ...  X_b, X_i in V_n for i = 1, ... , b1 and 
 X_b in V_r, where r <= n. 
 Output: 
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  Y in V_{X}. 

 1. If X in V_0 then return Y, where Y in V_0 
 2. GCTR_1 = ICB 
 3. For i = 2, ... , b do 
 GCTR_i = Inc_c(GCTR_{i1}) 
 4. K^1 = K 
 5. For j = 2, ... , ceil(l*n / N) 
 K^j = ACPKM(K^{j1}) 
 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. 
++
++
 GCMACPKMEncrypt(N, K, IV, P, A) 

 Input: 
  Section size N, 
  key K, 
  initial counter nonce ICN in V_{nc}, 
  plaintext P, P <= n*(2^{c1}  2), P = P_1  ...  P_b, 
  additional authenticated data A. 
 Output: 
  Ciphertext C, 
  authentication tag T. 

 1. H = E_{K}(0^n) 
 2. If c = 32, then ICB_0 = ICN  0^31  1 
 if c!= 32, then s = n * ceil(ICN / n)  ICN, 
 ICB_0 = GHASH(ICN  0^{s+n64}  Vec_64(ICN), H) 
 3. C = GCTR(N, K, Inc_32(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  0^{n128}  Vec_64(A)  
  Vec_64(C), H) 
 6. T = MSB_t(E_{K}(ICB_0) (xor) S) 
 7. Return C  T 
++
++
 GCMACPKMDecrypt(N, K, IV, A, C, T) 

 Input: 
  Section size N, 
  key K, 
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  initial counter block ICB, 
  additional authenticated data A. 
  ciphertext C, C <= n*(2^{c1}  2), C = C_1  ...  C_b, 
  authentication tag T 
 Output: 
  Plaintext P or FAIL. 

 1. H = E_{K}(0^n) 
 2. If c = 32, then ICB_0 = ICN  0^31  1 
 if c!= 32, then s = n*ceil(ICN/n)ICN, 
 ICB_0 = GHASH(ICN  0^{s+n64}  Vec_64(ICN), H) 
 3. P = GCTR(N, K, Inc_32(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  0^{n128}  Vec_64(A)  
  Vec_64(C), H) 
 6. T' = MSB_t(E_{K}(ICB_0) (xor) S) 
 7. If 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 vector IV value for each message that is encrypted under
the given key must be chosen in a unique manner.
The message size m MUST NOT exceed n*(2^{c1}  2) bits.
The key for computing values E_{K}(ICB_0) and H is not updated and is
equal to the initial key K.
5.2. Constructions that Require Master Key
This section describes the block cipher modes that uses the ACPKM
Master rekeying mechanism (described in Section 5.2.1), 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.
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5.2.1. ACPKMMaster Key Generation from the Master Key
This section defines periodical key transformation with master key K*
which is called ACPKMMaster rekeying mechanism. This mechanism can
be applied to one of the basic encryption modes (CTR, GCM, CBC, CFB,
OFB, OMAC encryption modes) for getting an extension of this
encryption mode that uses periodical key transformation with master
key. This extension can be considered as a new encryption mode.
Additional parameters that defines the functioning of basic
encryption modes with the ACPKMMaster rekeying 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 Section 7). 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 rekeying with master key is presented
in Fig.4:
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Lifetime of a key = L,
change 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[2t] K[(l_max1)t+1] K[l_max*t]
     
     
v v v v v v
Message(1)========...================...========...========...== : 
Message(2)========...================...========...========...======: 
...           : 
Message(q)========...============ ... ... ... : 
section :
<> :
N bit m_max
_______________________________________________________________________________________
K[i] = d,
t = T*/d,
l_max = ceil(m_max/N),
q*N <= L.
Figure 4: Key meshing with master key
During the processing of the input message M with the length m in
some encryption mode that uses ACPKMMaster key transformation with
the master key K* and key frequency T* the message M 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 in {1, 2, ... , l1} and M_l is in V_r, r <= N). The
jth section is processed with the key material K[j], j in {1, ...
,l}, K[j] = d, that has been calculated with the ACPKMMaster
algorithm as follows:
IV = 1^{n/2},
K[1]  ...  K[l] = ACPKMMaster(T*, K*, d*l) = CTRACPKMEncrypt
(T*, K*, IV, 0^{d*l}).
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5.2.2. CTR Mode Key Meshing
This section defines a CTRACPKMMaster encryption mode that uses
internal ACPKMMaster rekeying mechanism for the periodical key
transformation.
The CTRACPKMMaster encryption mode can be considered as the
extended by the ACPKMMaster rekeying mechanism basic encryption
mode CTR (see [MODES]).
The CTRACPKMMaster encryption mode can be used with the following
parameters:
o 64 <= n <= 512;
o 128 <= k <= 512;
o the number of bits c in a specific part of the block to be
incremented is such that 32 <= c <= 3/4 n.
The key material K[j] that is used for one section processing is
equal to K^j, K^j = k bits.
The CTRACPKMMaster mode encryption and decryption procedures are
defined as follows:
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++
 CTRACPKMMasterEncrypt(N, K*, T*, ICN, P) 

 Input: 
  Section size N, 
  master key K*, 
  change frequency T*, 
  initial counter nonce ICN in V_{nc}, 
  plaintext P = P_1  ...  P_b, P <= 2^{n/21}*n*N / k. 
 Output: 
  Ciphertext C. 

 1. CTR_1 = ICN  0^c 
 2. For j = 2, 3, ... , b do 
 CTR_{j} = Inc_c(CTR_{j1}) 
 3. l = ceil(b*n / N) 
 4. K^1  ...  K^l = ACPKMMaster(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 
+
++
 CTRACPKMMasterDecrypt(N, K*, T*, ICN, C) 

 Input: 
  Section size N, 
  master key K*, 
  change frequency T*, 
  initial counter nonce ICN in V_{nc}, 
  ciphertext C = C_1  ...  C_b, C <= 2^{n/21}*n*N / k. 
 Output: 
  Plaintext P. 

 1. Return CTRACPKMMasterEncrypt(N, K*, T*, ICN, C) 
++
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 m MUST NOT exceed (2^{n/21}*n*N / k) bits.
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5.2.3. GCM Mode Key Meshing
This section defines a GCMACPKMMaster encryption mode that uses
internal ACPKMMaster rekeying mechanism for the periodical key
transformation.
The GCMACPKMMaster encryption mode can be considered as the
extended by the ACPKMMaster rekeying mechanism basic encryption
mode GCM (see [GCM]).
The GCMACPKMMaster encryption mode can be used with the following
parameters:
o n in {128, 256};
o 128 <= k <= 512;
o the number of bits c in a specific part of the block to be
incremented is such that 32 <= c <= 3/4 n;
o 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 = ACPKMMaster(T*, K*, k*l).
The GCMACPKMMaster 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_{i1} (xor) X_i)*H 
 3. Return Y_m 
++
++
 GCTR(N, K*, T*, ICB, X) 

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 Input: 
  Section size N, 
  master key K*, 
  change frequency T*, 
  initial counter block ICB, 
  X = X_1  ...  X_b, X_i in V_n for i = 1, ... , b1 and 
 X_b in V_r, where r <= n. 
 Output: 
  Y in V_{X}. 

 1. If X in V_0 then return Y, where Y in V_0 
 2. GCTR_1 = ICB 
 3. For i = 2, ... , b do 
 GCTR_i = Inc_c(GCTR_{i1}) 
 4. l = ceil(b*n / N) 
 5. K^1  ...  K^l = ACPKMMaster(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 
++
++
 GCMACPKMMasterEncrypt(N, K*, T*, IV, P, A) 

 Input: 
  Section size N, 
  master key K*, 
  change frequency T*, 
  initial counter nonce ICN in V_{nc}, 
  plaintext P, P <= n*(2^{c1}  2). 
  additional authenticated data A. 
 Output: 
  Ciphertext C, 
  authentication tag T. 

 1. K^1 = ACPKMMaster(T*, K*, k) 
 2. H = E_{K^1}(0^n) 
 3. If c = 32, then ICB_0 = ICN  0^31  1 
 if c!= 32, then s = n*ceil(ICN/n)  ICN, 
 ICB_0 = GHASH(ICN  0^{s+n64}  Vec_64(ICN), H) 
 4. C = GCTR(N, K*, T*, Inc_32(J_0), P) 
 5. u = n*ceil(C / n)  C 
 v = n*ceil(A / n)  A 
 6. S = GHASH(A  0^v  C  0^u  0^{n128}  Vec_64(A)  
  Vec_64(C), H) 
 7. T = MSB_t(E_{K^1}(J_0) (xor) S) 
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 8. Return C  T 
++
++
 GCMACPKMMasterDecrypt(N, K*, T*, IV, A, C, T) 

 Input: 
  Section size N, 
  master key K*, 
  change frequency T*, 
  initial counter nonce ICN in V_{nc}, 
  additional authenticated data A. 
  ciphertext C, C <= n*(2^{c1}  2), 
  authentication tag T, 
 Output: 
  Plaintext P or FAIL. 

 1. K^1 = ACPKMMaster(T*, K*, k) 
 2. H = E_{K^1}(0^n) 
 3. If c = 32, then ICB_0 = ICN  0^31  1 
 if c!= 32, then s = n*ceil(ICN / n)  ICN, 
 ICB_0 = GHASH(ICN  0^{s+n64}  Vec_64(ICN), H) 
 4. P = GCTR(N, K*, T*, Inc_32(J_0), C) 
 5. u = n*ceil(C / n)  C 
 v = n*ceil(A / n)  A 
 6. S = GHASH(A  0^v  C  0^u  0^{n128}  Vec_64(A)  
  Vec_64(C), H) 
 7. T' = MSB_t(E_{K^1}(ICB_0) (xor) S) 
 8. IF 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 vector IV value for each message that is encrypted under
the given key must be chosen in a unique manner.
The message size m MUST NOT exceed (2^{n/21}*n*N / k) bits.
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5.2.4. CBC Mode Key Meshing
This section defines a CBCACPKMMaster encryption mode that uses
internal ACPKMMaster rekeying mechanism for the periodical key
transformation.
The CBCACPKMMaster encryption mode can be considered as the
extended by the ACPKMMaster rekeying mechanism basic encryption
mode CBC (see [MODES]).
The CBCACPKMMaster encryption mode can be used with the following
parameters:
o 64 <= n <= 512;
o 128 <= k <= 512.
In the specification of the CBCACPKMMaster 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 [MODES].
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 CBCACPKMMaster mode encryption and decryption procedures are
defined as follows:
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++
 CBCACPKMMasterEncrypt(N, K*, T*, IV, P) 

 Input: 
  Section size N, 
  master key K*, 
  change frequency T*, 
  initialization vector IV in V_n, 
  plaintext P = P_1  ...  P_b, P <= 2^{n/21}*n*N / k, 
 P_b = n. 
 Output: 
  Ciphertext C. 

 1. l = ceil(b*n/N) 
 2. K^1  ...  K^l = ACPKMMaster(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_{j1}) 
 5. Return C = C_1  ...  C_b 
+
++
 CBCACPKMMasterDecrypt(N, K*, T*, IV, C) 

 Input: 
  Section size N, 
  master key K*, 
  change frequency T*, 
  initialization vector IV in V_n, 
  ciphertext C = C_1  ...  C_b, C <= 2^{n/21}*n*N/k, 
 C_b = n. 
 Output: 
  Plaintext P. 

 1. l = ceil(b*n / N) 
 2. K^1  ...  K^l = ACPKMMaster(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_{j1} 
 5. Return P = P_1  ...  P_b 
++
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 m MUST NOT exceed (2^{n/21}*n*N / k) bits.
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5.2.5. CFB Mode Key Meshing
This section defines a CFBACPKMMaster encryption mode that uses
internal ACPKMMaster rekeying mechanism for the periodical key
transformation.
The CFBACPKMMaster encryption mode can be considered as the
extended by the ACPKMMaster rekeying mechanism basic encryption
mode CFB (see [MODES]).
The CFBACPKMMaster encryption mode can be used with the following
parameters:
o 64 <= n <= 512;
o 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 CFBACPKMMaster mode encryption and decryption procedures are
defined as follows:
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++
 CFBACPKMMasterEncrypt(N, K*, T*, IV, P) 

 Input: 
  Section size N, 
  master key K*, 
  change frequency T*, 
  initialization vector IV in V_n, 
  plaintext P = P_1  ...  P_b, P <= 2^{n/21}*n*N / k. 
 Output: 
  Ciphertext C. 

 1. l = ceil(b*n / N) 
 2. K^1  ...  K^l = ACPKMMaster(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}(C_{j1}) (xor) P_j 
 5. Return C = C_1  ...  C_b. 
+
++
 CFBACPKMMasterDecrypt(N, K*, T*, IV, C#) 

 Input: 
  Section size N, 
  master key K*, 
  change frequency T*, 
  initialization vector IV in V_n, 
  ciphertext C = C_1  ...  C_b, C <= 2^{n/21}*n*N / k. 
 Output: 
  Plaintext P. 

 1. l = ceil(b*n / N) 
 2. K^1  ...  K^l = ACPKMMaster(T*, K*, k*l) 
 3. C_0 = IV 
 4. For j = 1, 2, ... , b do 
 i = ceil(j*n / N), 
 P_j = E_{K^i}(C_{j1}) (xor) С_j 
 5. Return P = P_1  ...  P_b 
++
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 m MUST NOT exceed 2^{n/21}*n*N/k bits.
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5.2.6. OFB Mode Key Meshing
This section defines an OFBACPKMMaster encryption mode that uses
internal ACPKMMaster rekeying mechanism for the periodical key
transformation.
The OFBACPKMMaster encryption mode can be considered as the
extended by the ACPKMMaster rekeying mechanism basic encryption
mode OFB (see [MODES]).
The OFBACPKMMaster encryption mode can be used with the following
parameters:
o 64 <= n <= 512;
o 128 <= k <= 512.
The key material K[j] used for one section processing is equal to
K^j, K^j = k bits.
The OFBACPKMMaster mode encryption and decryption procedures are
defined as follows:
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++
 OFBACPKMMasterEncrypt(N, K*, T*, IV, P) 

 Input: 
  Section size N, 
  master key K*, 
  change frequency T*, 
  initialization vector IV in V_n, 
  plaintext P = P_1  ...  P_b, P <= 2^{n/21}*n*N / k. 
 Output: 
  Ciphertext C. 

 1. l = ceil(b*n / N) 
 2. K^1  ...  K^l = ACPKMMaster(T*, K*, k*l) 
 3. G_0 = IV 
 4. For j = 1, 2, ... , b do 
 i = ceil(j*n / N), 
 G_j = E_{K_i}(G_{j1}) 
 5. Return C = P (xor) MSB_{P}(G_1  ...  G_b) 
+
++
 OFBACPKMMasterDecrypt(N, K*, T*, IV, C) 

 Input: 
  Section size N, 
  master key K*, 
  change frequency T*, 
  initialization vector IV in V_n, 
  ciphertext C = C_1  ...  C_b, C <= 2^{n/21}*n*N / k. 
 Output: 
  Plaintext P. 

 1. Return OFBACPKMMasterEncrypt(N, K*, T*, IV, C) 
++
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 m MUST NOT exceed 2^{n/21}*n*N / k bits.
5.2.7. OMAC Mode Key Meshing
This section defines an OMACACPKMMaster message authentication code
calculation mode that uses internal ACPKMMaster rekeying mechanism
for the periodical key transformation.
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The OMACACPKMMaster encryption mode can be considered as the
extended by the ACPKMMaster rekeying mechanism basic message
authentication code calculation mode OMAC (see [RFC4493]).
The OMACACPKMMaster message authentication code calculation mode
can be used with the following parameters:
o n in {64, 128, 256};
o 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:
++
 Generate_Subkey(K, r) 

 Input: 
  Key K, 
 Output: 
  Key [K]. 

 1. If r = n then return K 
 2. If r < n then 
 if MSB_1(K1) = 0 
 return K1 << 1 
 else 
 return (K1 << 1) (xor) R_n 
 
++
Where R_n takes the following values:
o n = 64: R_{64} = 0^{59}  11011;
o n = 128: R_{128} = 0^{120}  10000111;
o n = 256: R_{256} = 0^{145}  10000100101.
The OMACACPKMMaster message authentication code calculation mode is
defined as follows:
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++
 OMACACPKMMaster(K*, N, T*, M) 

 Input: 
  Section size N, 
  master key K*, 
  key frequency T*, 
  plaintext M = M_1  ...  M_b, M <= 2^{n/2}*n^2*N / (k + n). 
 Output: 
  message authentication code T. 

 1. C_0 = 0^n 
 2. l = ceil(b*n / N) 
 3. K^1  K^1_1  ...  K^l  K^l_1 = ACPKMMaster(T*, K*, (k+n)*l) 
 4. For j = 1, 2, ... , b1 do 
 i = ceil(j*n / N), 
 C_j = E_{K^i}(M_j (xor) C_{j1}) 
 5. [K] = Generate_Subkey(K^l_1, M_b) 
 6. If M_b = n 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_{b1} (xor) [K]) 
 8. Return T 
++
The message size m MUST NOT exceed 2^{n/2}*n^2*N / (k + n) bits.
6. Joint Usage of External and Internal Rekeying
Any mechanism described in Section 4 can be used with any mechanism
described in Section 5.
7. Security Considerations
7.1. Principles of Choice of Constructions and Security Parameters
External rekeying mechanism is RECOMMENDED to be used in protocols
that process pretty small messages (e.g. TLS).
Internal rekeying mechanism is RECOMMENDED to be used in protocols
that can process large messages (e.g. IPSec).
For the protocols that process messages of different lengths it is
RECOMMENDED to use joint methods described in Section 6.
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7.2. Requirements For Base Primitives
Rekeying should be used to increase "a priori" security properties
of ciphers in hoslile environments (e.g. with sidechannel
adversaries). If some nonnegligible attacks are known for a cipher,
it MUST NOT be used. So rekeying can not be used as a patch for
vulnerable ciphers. Base cipher properties must be well analyzed,
because security of rekeying mechanisms is based on security of a
block cipher as a pseudorandom function.
8. References
8.1. Normative References
[GCM] McGrew, D. and J. Viega, "The Galois/Counter Mode of
Operation (GCM)", Submission to NIST
http://csrc.nist.gov/CryptoToolkit/modes/proposedmodes/
gcm/gcmspec.pdf, January 2004.
[GOST34112012]
Federal Agency on Technical Regulating and Metrology (In
Russian), "Information technology. Cryptographic Data
Security. Hashing function", GOST R 34.112012, 2012.
[MODES] Dworkin, M., "Recommendation for Block Cipher Modes of
Operation: Methods and Techniques", NIST Special
Publication 80038A, December 2001.
[RFC2119] Bradner, S., "Key words for use in RFCs to Indicate
Requirement Levels", BCP 14, RFC 2119,
DOI 10.17487/RFC2119, March 1997,
.
[RFC4493] Song, JH., Poovendran, R., Lee, J., and T. Iwata, "The
AESCMAC Algorithm", RFC 4493, DOI 10.17487/RFC4493, June
2006, .
[RFC5869] Krawczyk, H. and P. Eronen, "HMACbased ExtractandExpand
Key Derivation Function (HKDF)", RFC 5869,
DOI 10.17487/RFC5869, May 2010,
.
[SHA512] National Institute of Standards and Technology., "Secure
Hash Standard", FIPS 1802, August, with Change Notice 1
dated February 2004 2002.
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[TLSDraft]
Rescorla, E., "The Transport Layer Security (TLS) Protocol
Version 1.3", 2017, .
8.2. Informative References
[AbBell] Michel Abdalla and Mihir Bellare, "Increasing the Lifetime
of a Key: A Comparative Analysis of the Security of Re
keying Techniques", ASIACRYPT2000, LNCS 1976, pp. 546559,
2000.
[BDJR] Bellare M., Desai A., Jokipii E., Rogaway P., "A concrete
security treatment of symmetric encryption", In
Proceedings of 38th Annual Symposium on Foundations of
Computer Science (FOCS '97), pages 394403. 97, 1997.
[BL] Bhargavan K., Leurent G., "On the Practical (In)Security
of 64bit Block Ciphers: Collision Attacks on HTTP over
TLS and OpenVPN", Cryptology ePrint Archive Report 798,
2016.
[Matsui] Matsui M., "Linear Cryptanalysis Method for DES Cipher",
Advanced in Cryptology EUROCRYPT'93. Lect. Notes in Comp.
Sci., Springer. V.765.P. 386397, 1994.
[RFC6986] Dolmatov, V., Ed. and A. Degtyarev, "GOST R 34.112012:
Hash Function", RFC 6986, DOI 10.17487/RFC6986, August
2013, .
Appendix A. Test examples
CTRACPKM mode with AES256
*********
c = 64
k = 256
N = 256
n = 128
W_0:
F3 74 E9 23 FE AA D6 DD 98 B4 B6 3D 57 8B 35 AC
W_1:
A9 0F D7 31 E4 1D 64 5E C0 8C 87 87 28 CC 76 90
Key K:
88 99 AA BB CC DD EE FF 00 11 22 33 44 55 66 77
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FE DC BA 98 76 54 32 10 01 23 45 67 89 AB CD EF
Plain text P:
11 22 33 44 55 66 77 00 FF EE DD CC BB AA 99 88
00 11 22 33 44 55 66 77 88 99 AA BB CC EE FF 0A
11 22 33 44 55 66 77 88 99 AA BB CC EE FF 0A 00
22 33 44 55 66 77 88 99 AA BB CC EE FF 0A 00 11
33 44 55 66 77 88 99 AA BB CC EE FF 0A 00 11 22
44 55 66 77 88 99 AA BB CC EE FF 0A 00 11 22 33
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
ACPKM's iteration 1
Process block 1
Input block (ctr)
12 34 56 78 90 AB CE F0 00 00 00 00 00 00 00 00
Output block (ctr)
FD 7E F8 9A D9 7E A4 B8 8D B8 B5 1C 1C 9D 6D D0
Plain text
11 22 33 44 55 66 77 00 FF EE DD CC BB AA 99 88
Cipher text
EC 5C CB DE 8C 18 D3 B8 72 56 68 D0 A7 37 F4 58
Process block 2
Input block (ctr)
12 34 56 78 90 AB CE F0 00 00 00 00 00 00 00 01
Output block (ctr)
19 98 C5 71 76 37 FB 17 11 E4 48 F0 0C 0D 60 B2
Plain text
00 11 22 33 44 55 66 77 88 99 AA BB CC EE FF 0A
Cipher text
19 89 E7 42 32 62 9D 60 99 7D E2 4B C0 E3 9F B8
Updated key
C6 C1 AF 82 3F 52 22 F8 97 CF F1 94 5D F7 21 9E
21 6F 29 0C EF C4 C7 E6 DC C8 B7 DD 83 E0 AE 60
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ACPKM's iteration 2
Process block 3
Input block (ctr)
12 34 56 78 90 AB CE F0 00 00 00 00 00 00 00 02
Output block (ctr)
92 B4 85 B5 B7 AD 3C 19 7E 53 92 32 13 9C 8E 7A
Plain text
11 22 33 44 55 66 77 88 99 AA BB CC EE FF 0A 00
Cipher text
83 96 B6 F1 E2 CB 4B 91 E7 F9 29 FE FD 63 84 7A
Process block 4
Input block (ctr)
12 34 56 78 90 AB CE F0 00 00 00 00 00 00 00 03
Output block (ctr)
59 3A AA 96 7C E3 58 FB 1B 7E 41 A1 77 34 B1 4A
Plain text
22 33 44 55 66 77 88 99 AA BB CC EE FF 0A 00 11
Cipher text
7B 09 EE C3 1A 94 D0 62 B1 C5 8D 4F 88 3E B1 5B
Updated key
65 3E FA 18 0B 0E 68 01 6F 56 54 A5 F3 EE BC D5
04 F1 1F E3 F1 7A 92 07 57 A8 82 BE A5 9E CA 16
ACPKM's iteration 3
Process block 5
Input block (ctr)
12 34 56 78 90 AB CE F0 00 00 00 00 00 00 00 04
Output block (ctr)
CE E5 51 54 12 2F 3F E7 8D 8E 86 21 C5 E5 47 12
Plain text
33 44 55 66 77 88 99 AA BB CC EE FF 0A 00 11 22
Cipher text
FD A1 04 32 65 A7 A6 4D 36 42 68 DE CF E5 56 30
Process block 6
Input block (ctr)
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12 34 56 78 90 AB CE F0 00 00 00 00 00 00 00 05
Output block (ctr)
DE D6 8F 03 FA C5 C5 B6 16 11 A3 78 2C 0D C1 EB
Plain text
44 55 66 77 88 99 AA BB CC EE FF 0A 00 11 22 33
Cipher text
9A 83 E9 74 72 5C 6F 0D DA FF 5C 72 2C 1C E3 D8
Updated key
C0 D5 50 26 4F DA CE 59 EF 80 9A 50 24 72 06 7D
29 83 74 25 78 C9 60 4F E3 B8 88 4F F8 F5 E2 BD
ACPKM's iteration 4
Process block 7
Input block (ctr)
12 34 56 78 90 AB CE F0 00 00 00 00 00 00 00 06
Output block (ctr)
D9 23 A6 CD 8A 00 A1 55 90 09 EC 87 40 B9 D6 AB
Plain text
55 66 77 88 99 AA BB CC EE FF 0A 00 11 22 33 44
Cipher text
8C 45 D1 45 13 AA 1A 99 7E F6 E6 87 51 9B E5 EF
Updated key
6A A0 92 07 73 31 63 50 46 FA 48 1C 9C 98 7B 6B
FC 99 48 DC BC AE AB C2 6D 46 E9 DD 43 F6 CA 56
Encrypted src
EC 5C CB DE 8C 18 D3 B8 72 56 68 D0 A7 37 F4 58
19 89 E7 42 32 62 9D 60 99 7D E2 4B C0 E3 9F B8
83 96 B6 F1 E2 CB 4B 91 E7 F9 29 FE FD 63 84 7A
7B 09 EE C3 1A 94 D0 62 B1 C5 8D 4F 88 3E B1 5B
FD A1 04 32 65 A7 A6 4D 36 42 68 DE CF E5 56 30
9A 83 E9 74 72 5C 6F 0D DA FF 5C 72 2C 1C E3 D8
8C 45 D1 45 13 AA 1A 99 7E F6 E6 87 51 9B E5 EF
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Appendix B. Contributors
o Daniel Fox Franke
Akamai Technologies
dfoxfranke@gmail.com
o Lilia Ahmetzyanova
CryptoPro
lah@cryptopro.ru
o Ruth Ng
University of California, San Diego
ring@eng.ucsd.edu
o Shay Gueron
University of Haifa, Israel
Intel Corporation, Israel Development Center, Israel
shay.gueron@gmail.com
Authors' Addresses
Stanislav Smyshlyaev (editor)
CryptoPro
18, Suschevsky val
Moscow 127018
Russian Federation
Phone: +7 (495) 9954820
Email: svs@cryptopro.ru
Russ Housley
Vigil Security, LLC
918 Spring Knoll Drive
Herndon VA 20170
USA
Email: housley@vigilsec.com
Mihir Bellare
University of California, San Diego
9500 Gilman Drive
La Jolla California 920930404
USA
Phone: (858) 5344544
Email: mihir@eng.ucsd.edu
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Evgeny Alekseev
CryptoPro
18, Suschevsky val
Moscow 127018
Russian Federation
Phone: +7 (495) 9954820
Email: alekseev@cryptopro.ru
Ekaterina Smyshlyaeva
CryptoPro
18, Suschevsky val
Moscow 127018
Russian Federation
Phone: +7 (495) 9954820
Email: ess@cryptopro.ru
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