Crypto Forum Research Group David A. McGrew
Internet Draft Cisco Systems, Inc.
Expires April, 2003 October, 2002
Integer Counter Mode
<draft-irtf-cfrg-icm-00.txt>
Status of this Memo
This document is an Internet Draft and is in full conformance with
all provisions of Section 10 of RFC-2026. Internet Drafts are working
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1. Abstract
This document specifies Integer Counter Mode (ICM), a mode of
operation of a block cipher which defines an indexed keystream
generator (which generates a keystream segment given an index).
This mode is efficient, parallelizable, and has been proven secure
given realistic assumptions about the block cipher. Test vectors
are provided for AES.
Counter Mode admits many variations. The variant specified in
this document is secure and flexible, yet it enables a single
implementation of a keystream generator to suffice in different
application domains.
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2. Notational Conventions
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 RFC-2119 [B97].
3. Introduction
Counter Mode is a way to define a pseudorandom keystream generator
using a block cipher [CTR]. The keystream can be used for additive
encryption, key derivation, or any other application requiring
pseudorandom data.
In ICM, the keystream is logically broken into segments. Each
segment is identified with a segment index, and the segments have
equal lengths. This segmentation makes ICM especially appropriate
for securing packet-based protocols.
4. ICM
In this section, ICM keystream generation and encryption are
defined.
4.1. ICM Parameters
The following parameters are used in ICM. These parameters MUST
remain fixed for any given use of a key.
Parameter Meaning
-----------------------------------------------------------------
BLOCK_LENGTH the number of octets in the cipher block
KEY_LENGTH the number of octets in the cipher key
OFFSET_LENGTH the number of octets in the offset
SEGMENT_INDEX_LENGTH the number of octets in the segment index
BLOCK_INDEX_LENGTH the number of octets in the block index
4.2. Keystream Segments
Conceptually, ICM is a keystream generator that takes a secret key
and a segment index as an input and then outputs a keystream
segment. The segmentation lends itself to packet encryption, as
each keystream segment can be used to encrypt a distinct packet.
A counter is a value containing BLOCK_LENGTH octets which is
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incremented using an increment function based on integer addition,
to produce a sequence of distinct values which are used as inputs to
the block cipher. (In the context of this specification, an integer
is an octet string, the most significant of which is the first.)
The output blocks of the cipher are concatenated to form the
keystream segment. The first octet of the segment is the first
octet of the first output block, and so on. A schematic of this
process is shown in Figure 1.
Figure 1. The generation of a keystream segment given a segment
index and a block cipher key K. Here C[i] and S[i] denote the ith
counter and keystream block, respectively.
segment
index
|
v
C[0] -----> C[1] -----> C[2] -----> ...
| | |
v v v
+---+ +---+ +---+
K->| E | K->| E | K->| E | ...
+---+ +---+ +---+
| | |
v v v
S[0] S[1] S[2] ...
The ith counter C[i] of the keystream segment with segment index s
is defined as
C[i] = (i + s * (256^BLOCK_INDEX_LENGTH)) (+) r
where r denotes the shifted Offset, which is defined as the Offset
times 256^(BLOCK_LENGTH - OFFSET_LENGTH). (This multiplication
left-shifts the Offset so that it is aligned with the leftmost
edge of the block.) Here ^ denotes exponentiation and (+) denotes
the bitwise exclusive-or operation.
The number of blocks in any segment MUST NOT exceed
256^BLOCK_INDEX_LENGTH. The number of segments MUST NOT exceed
256^SEGMENT_INDEX_LENGTH. These restrictions ensure the uniqueness
of each block cipher input. They also imply that each segment
contains no more than (256^BLOCK_INDEX_LENGTH)*BLOCK_LENGTH octets.
The sum of SEGMENT_INDEX_LENGTH and BLOCK_INDEX_LENGTH MUST NOT
exceed BLOCK_LENGTH / 2. This requirement protects the ICM
keystream generator from potentially failing to be pseudorandom (see
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the rationale).
Figure 2. An illustration of the structure of a counter with
BLOCK_LENGTH = 8, SEGMENT_INDEX_LENGTH = 2, and BLOCK_INDEX_LENGTH
= 2. The field marked `null' is not part of either the block
or segment indices.
0 1 2 3
0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| null |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| segment index | block index |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
4.3. ICM Encryption
Unless otherwise specified, ICM encryption consists of bitwise
exclusive-oring the keystream into the plaintext to produce
the ciphertext.
4.4 ICM KEY
An ICM key consists of the block cipher key and an Offset. The
Offset is an integer with OFFSET_LENGTH octets, which is used to
`randomize' the logical starting point of keystream. The Offset is
crucial to providing security; see the rationale. The value of
OFFSET_LENGTH SHOULD be at least half that of BLOCK_LENGTH.
For the purposes of transporting an ICM key, e.g. in a signaling
protocol, that key SHOULD be considered a sequence of octets in
which the block cipher key precedes the Offset.
5. Implementation Considerations
Implementation of the `add one modulo 2^m' operation is simple. For
example, with BLOCK_LENGTH = 8 (m=64), it can be implemented in C as
if (!++x) ++y;
where x and y are 32-bit unsigned integers in network byte order.
The implementation of general purpose addition modulo 2^m is
slightly more complicated.
The fact that the Offset is left-aligned enables an implementation
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to avoid propagating carry values outside of the block index and/or
the segment index. Choosing an OFFSET_LENGTH value equal to half
that of BLOCK_LENGTH avoids all of these carries, since the Offset
is then shifted so that it occupies the most significant octets of
the block, while the block and segment indices occupy the least
significant ones.
6. Parameters and Test Vectors for AES
This section provides ICM parameters and test vectors for AES
with a 128 bit block size and 128 bit key (that is, with a
BLOCK_LENGTH and KEY_LENGTH of 16).
All integers are expressed in hexadecimal. Each consecutive pair of
hex digits corresponds to an octet, so that the integer
000102030405060708090A0B0C0D0E0F corresponds to the octet sequence
{ 00, 01, 02, 02 ... }.
BLOCK_LENGTH 16
KEY_LENGTH 16
OFFSET_LENGTH 14
SEGMENT_INDEX_LENGTH 6
BLOCK_INDEX_LENGTH 2
Block Cipher Key: 2b7e151628aed2a6abf7158809cf4f3c
Offset: f0f1f2f3f4f5f6f7f8f9fafbfcfd
Segment Index: 000000000000
Keystream: e03ead0935c95e80e166b16dd92b4eb4
d23513162b02d0f72a43a2fe4a5f97ab
...
The counter values that correspond to the keystream blocks are
outlined below.
Counter Keystream
f0f1f2f3f4f5f6f7f8f9fafbfcfd0000 e03ead0935c95e80e166b16dd92b4eb4
f0f1f2f3f4f5f6f7f8f9fafbfcfd0001 d23513162b02d0f72a43a2fe4a5f97ab
f0f1f2f3f4f5f6f7f8f9fafbfcfd0002 41e95b3bb0a2e8dd477901e4fca894c0
... ...
7. Security Considerations
Each block cipher input is distinct for any segment and any block
index. To see this fact, subtract any two counter values with
distinct segment or block indices; the result is non-zero.
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The limitation on the number of segments which can be generated
ensures that the probability with which an adversary can distinguish
the keystream generator from random is negligible. For a
theoretical justification of this fact, see Bellare et. al. [BR98].
Their analysis shows that if the block cipher cannot be
distinguished from a random permutation, then the keystream
generated by ICM cannot be distinguished from keystream generated by
a truly random process, as long as the length of keystream which is
generated is kept below some threshold. The threshold defined in
Section 4.2 is sufficient for most uses of ICM for encryption. This
specification refrains from dictating a lower threshold in order to
refrain from dictating a particular policy, and to avoid a
complicated digression.
The use of the Offset, a key-dependent value which randomizes the
starting position of the keystream, is essential for security. The
omission of this mechanism leaves the door open for practical
attacks, such as the key collision attack and Hellman's time-memory
tradeoff attack; see McGrew and Fluhrer [MF00] for a description of
these attacks which is applicable to ICM. Several counter mode
proposals do not include an offset, and are thus vulnerable to these
attacks.
8. Rationale
This speficiation includes input from implementation experience with
several counter mode variants. The goals of ICM are to provide:
o a secure keystream generator and cipher, and
o a definition flexible enough that a single implementation can be
used for a variety of applications (e.g., Secure RTP [SRTP],
IPsec ESP [KA96]).
The Offset slightly increases the key management overhead, but this
minor disadvantage is well outweighed by other savings. The Offset
is no larger than a CBC mode IV, and ICM enables the use of an
explicit IV (as is commonly used with CBC [MD98]) to be avoided.
9. History
This draft is based on draft-mcgrew-saag-icm-00.txt, which was
submitted to SAAG on November, 2001 and which expired in May, 2002.
The current definition of ICM has changed from the earlier one; the
counter formation is different and the specifications are
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unfortunately not interoperable. This change was motivated by a
considerable amount of feedback on the desirability of admitting
optimizations of the sort described in Section 5, in which the carry
operations of counter addition need not be propagated across a large
register.
The current definition of ICM is interoperable with that defined in
Secure RTP [SRTP].
10. Acknowledgements
Thanks are due to Helger Lipmaa, Jerome Etienne, Scott Fluhrer and
Mats Naslund for their helpful discussion and comments.
11. Contact Information
Questions and comments on this draft SHOULD be sent to:
David A. McGrew
Cisco Systems, Inc.
mcgrew@cisco.com
and copied to the Crypto Forum Research Group at:
cfrg@ietf.org.
12. References
[BR98] M. Bellare, A. Desai, E. Lokipii and P. Rogaway, A
Concrete Security Treatment of Symmetric Encryption:
Analysis of DES Modes of Operation, Proceedings of
the 38th Symposium on Foundations of Computer
Science, IEEE, 1997.
[B97] S. Bradner, Key words for use in RFCs to Indicate
Requirement Levels, RFC 2119, March 1997.
[AES] The Advanced Encryption Standard, United States
National Institute for Standards and Technology (NIST),
http://www.nist.gov/aes/.
[CTR] M. Dworkin, NIST Special Publication 800-38A,
"Recommendation for Block Cipher Modes of Operation: Methods
and Techniques", 2001. Online at
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http://csrc.nist.gov/publications/nistpubs/800-38a/sp800-
38a.pdf.
[MD98] Madson, C., and Doraswamy, N., "The ESP DES-CBC Cipher
Algorithm With Explicit IV", RFC 2405, November 1998.
[MF00] D. McGrew and S. Fluhrer, Attacks on Additive Encryption and
Implications on Internet Security, Selected Areas in
Cryptography 2000.
[SRTP] The Secure Real-time Transport Protocol, Baugher et. al.,
Internet Draft, draft-ietf-avt-srtp-05.txt.
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