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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 documents of the Internet Engineering Task Force (IETF), its areas, and working groups. Note that other groups may also distribute working documents as Internet Drafts. Internet Drafts are draft documents valid for a maximum of six months and may be updated, replaced, or obsoleted by other documents at any time. It is inappropriate to use Internet Drafts as reference material or to cite them other than as "work in progress." The list of current Internet-Drafts can be accessed at The list of Internet-Draft Shadow Directories can be accessed at 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. McGrew [Page 1] Internet Draft Integer Counter Mode October, 2002 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 McGrew [Page 2] Internet Draft Integer Counter Mode October, 2002 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 McGrew [Page 3] Internet Draft Integer Counter Mode October, 2002 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 McGrew [Page 4] Internet Draft Integer Counter Mode October, 2002 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. McGrew [Page 5] Internet Draft Integer Counter Mode October, 2002 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 McGrew [Page 6] Internet Draft Integer Counter Mode October, 2002 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. and copied to the Crypto Forum Research Group at: 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), [CTR] M. Dworkin, NIST Special Publication 800-38A, "Recommendation for Block Cipher Modes of Operation: Methods and Techniques", 2001. Online at McGrew [Page 7] Internet Draft Integer Counter Mode October, 2002 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. McGrew [Page 8]