Network Working Group S. Smyshlyaev, Ed.
Internet-Draft E. Alekseev
Intended status: Informational I. Oshkin
Expires: April 24, 2017 L. Ahmetzyanova
E. Smyshlyaeva
CryptoPro
October 21, 2016
The ACPKM internal re-keying mechanism for block cipher modes of
operation
draft-smyshlyaev-re-keying-00
Abstract
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.
Status of This Memo
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Table of Contents
1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . 2
2. Conventions Used in This Document . . . . . . . . . . . . . . 3
3. Basic Terms and Definitions . . . . . . . . . . . . . . . . . 3
4. CTR and GCM Block Cipher Modes . . . . . . . . . . . . . . . 4
4.1. CTR Block Cipher Mode . . . . . . . . . . . . . . . . . . 5
4.2. GCM Block Cipher Mode . . . . . . . . . . . . . . . . . . 6
5. ACPKM re-keying mechanisms . . . . . . . . . . . . . . . . . 9
5.1. ACPKM internal re-keying mechanism for CTR encryption
mode . . . . . . . . . . . . . . . . . . . . . . . . . . 10
5.2. ACPKM internal re-keying mechanism for GCM encryption
mode . . . . . . . . . . . . . . . . . . . . . . . . . . 10
6. Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . 11
7. Security Considerations . . . . . . . . . . . . . . . . . . . 11
8. References . . . . . . . . . . . . . . . . . . . . . . . . . 11
8.1. Normative References . . . . . . . . . . . . . . . . . . 11
8.2. Informative References . . . . . . . . . . . . . . . . . 11
Appendix A. Test examples . . . . . . . . . . . . . . . . . . . 12
Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . . 12
1. Introduction
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 [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 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 [BL]).
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.
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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.
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) exclusive-or 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;
|X| the bit length of the bit string X;
A|B 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;
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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_{s-i+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;
0^s denotes the string a in V_s that consists of s '0' bits;
E_K: V_n -> V_n the block cipher permutation under the key K in V_k;
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;
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);
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};
ceil(x) the least integer that is not less than x.
4. CTR and GCM Block Cipher Modes
This section describes the families of block cipher modes of
operations that are extended by the ACPKM re-keying mechanisms as
described in Section 5.
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).
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4.1. CTR Block Cipher Mode
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 [NIST-CTR].
The ACPKM-CTR re-keying mechanisms described in Section 5.1 can be
used with the following block cipher and CTR mode 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.
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:
Input:
Initial counter nonce ICN in V_{n-c},
plaintext P, |P| < n*2^c.
Output:
Ciphertext C.
___________________________________________________________________
CTR Encryption:
1. CTR_1 = ICN | 0^c.
2. For j = 1, 2, ..., b-1 do
CTR_{j+1} = Inc_c(CTR_j).
3. For j = 1, 2, ..., b do
G_j = E_K(CTR_j).
4. C = P (xor) MSB_{|P|}(G_1 |...|G_b).
5. Return C.
The CTR decryption mode is defined as follows:
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Input:
Initial counter nonce ICN in V_{n-c},
ciphertext C, |C| < n*2^c.
Output:
Plaintext P.
___________________________________________________________________
CTR Decryption:
1. CTR_1 = ICN | 0^c.
2. For j = 1, 2,..., b-1 do
CTR_{j+1} = Inc_c(CTR_j).
3. For j = 1, 2, ..., b do
G_j = E_K(CTR_j)
4. P = C (xor) MSB_{|C|}(G_1 |...|G_b).
5. Return P.
The initial counter nonce ICN value for each message that is
encrypted under the given key must be chosen in a unique manner.
4.2. GCM Block Cipher Mode
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 [NIST-GCM].
The ACPKM-GCM re-keying mechanisms described in Section 5.2 can be
used with the following GCM block cipher mode parameters:
o 128 <= 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.
4.2.1. GCM Subprocedures
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
Section 4.2.2 below.
4.2.1.1. Multiplication Operation on Blocks
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.
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4.2.1.2. GHASH Function
Algorithm 2: GHASH_H(X)
=======================
Input:
Bit string X = X_1 |...| X_m, where X_i in V_n for i in 1,...,m.
Output:
Block GHASHH (X) 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.
4.2.1.3. GCTR Function
Algorithm 3: GCTR_K(ICB, X)
===========================
Input:
Initial counter block ICB;
X = X_1 |...| X_t, X_i in V_n for i = 1,...,n-1 and X_n 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. t = ceil(|X|/n).
3. GCTR_1 = ICB.
4. For i = 2,...,t do
GCTR_i = Inc_c(GCTR_{i-1}).
5. For i = 1,...,t do
G_i = E_K(GCTR_i).
6. Y = X (xor) MSB_{|X|}(G_1 |...| G_t).
7. Return Y.
4.2.2. GCM Mode Description
The GCM encryption mode is defined as follows:
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Input:
Initialization vector IV in V_{n-c},
plaintext P, |P| < n*(2^c - 2).
additional authenticated data A.
Output:
Ciphertext C,
authentication tag T.
___________________________________________________________________
GCM Encryption:
1. H = E_K(0^n).
2. if c = 32, then J_0 = IV | 0^31 | 1;
if c!= 32, then s = n*ceil(|IV|/n)-|IV|,
J_0 = GHASH_H(IV | 0^{s+n-64} | Vec_64(|IV|)).
3. C = GCTR_K(Inc_32(J_0),P).
4. u = n*ceil(|C|/n)-|C|,
v = n*ceil(|A|/n)-|A|.
5. S = GHASH_H(A | 0^v | C | 0^u | 0^{n-128} |
|Vec_64(|A|) | Vec_64(|C|)).
6. T = MSB_t(E_K(J_0) (xor) S).
7. Return C | T.
The GCM decryption mode is defined as follows:
Input:
Initialization vector IV in V_{n-c},
ciphertext C, |C| < n*(2^c - 2),
authentication tag T,
additional authenticated data A.
Output:
Plaintext P or FAIL.
___________________________________________________________________
GCM decryption:
1. H = E_K(0^n).
2. if c = 32, then J_0 = IV | 0^31 | 1;
if c!= 32, then s = n*ceil(|IV|/n)-|IV|,
J_0 = GHASH_H(IV | 0^{s+n-64} | Vec_64(|IV|)).
3. P = GCTR_K(Inc_32(J_0),C).
4. u = n*ceil(|C|/n)-|C|,
v = n*ceil(|A|/n)-|A|.
5. S = GHASH_H(A | 0^v | C | 0^u | 0^{n-128}|
|Vec_64(|A|) | Vec_64(|C|)).
6. T' = MSB_t(E_K(J_0) (xor) S).
7. IF T=T' then return P; else return FAIL.
The initial vector IV value for each message that is encrypted under
the given key must be chosen in a unique manner.
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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.
5. ACPKM re-keying mechanisms
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 Section 7).
The section size N MUST be divisible by the block size n.
The main idea behind internal re-keying is presented in Fig.1:
Lifetime of a key = L,
section size = const = N,
maximum message size = m_max.
____________________________________________________________________
ACPKM ACPKM ACPKM
K_1 = K ----> K_2 -----...-> K_{l_max-1} ----> K_{l_max}
Message(1) |==========|==========|======|=== | : |
| | | ... | | : |
Message(2) |==========|==========|======|==========|=======: |
. . . | | | ... | | : |
| | | | | : |
Message(q) |==========|==========|======|==========|===== : |
| | section | ... | | : |
<----------> :
N bit m_max
____________________________________________________________________
l_max = ceil(m_max/N),
q*N <= L.
Figure 1: Key meshing approach
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:
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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.
5.1. ACPKM internal re-keying mechanism for CTR encryption mode
This section defines a ACPKM-CTR internal re-keying mechanism for the
CTR encryption mode that was described in Section 4.1.
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.
5.2. ACPKM internal re-keying mechanism for GCM encryption mode
This section defines a ACPKM-GCM internal re-keying mechanism for the
GCM encryption mode that was described in Section 4.2.
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,
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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.
6. Acknowledgments
TODO
7. Security Considerations
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.
8. References
8.1. Normative References
[RFC2119] Bradner, S., "Key words for use in RFCs to Indicate
Requirement Levels", BCP 14, RFC 2119,
DOI 10.17487/RFC2119, March 1997,
<http://www.rfc-editor.org/info/rfc2119>.
8.2. Informative References
[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 394-403. 97, 1997.
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[BL] Bhargavan K., Leurent G., "On the Practical (In-)Security
of 64-bit 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. 386-397, 1994.
[NIST-CTR]
Dworkin, M., "Recommendation for Block Cipher Modes of
Operation: Methods and Techniques", NIST Special
Publication 800-38A, December 2001.
[NIST-GCM]
McGrew, D. and J. Viega, "The Galois/Counter Mode of
Operation (GCM)", Submission to NIST
http://csrc.nist.gov/CryptoToolkit/modes/proposedmodes/
gcm/gcm-spec.pdf, January 2004.
Appendix A. Test examples
TODO
Authors' Addresses
Stanislav Smyshlyaev (editor)
CryptoPro
18, Suschevsky val
Moscow 127018
Russian Federation
Phone: +7 (495) 995-48-20
Email: svs@cryptopro.ru
Evgeny Alekseev
CryptoPro
18, Suschevsky val
Moscow 127018
Russian Federation
Phone: +7 (495) 995-48-20
Email: alekseev@cryptopro.ru
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Igor Oshkin
CryptoPro
18, Suschevsky val
Moscow 127018
Russian Federation
Phone: +7 (495) 995-48-20
Email: oshkin@cryptopro.ru
Lilia Ahmetzyanova
CryptoPro
18, Suschevsky val
Moscow 127018
Russian Federation
Phone: +7 (495) 995-48-20
Email: lah@cryptopro.ru
Ekaterina Smyshlyaeva
CryptoPro
18, Suschevsky val
Moscow 127018
Russian Federation
Phone: +7 (495) 995-48-20
Email: ess@cryptopro.ru
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