Speeding Up the Wide-Pipe: Secure and Fast Hashing

In this paper we propose a new sequential mode of operation – the Fast wide pipe or FWP for short – to hash messages of arbitrary length. The mode is shown to be (1) preimage-resistance preserving, (2) collision-resistance-preserving and, most importantly, (3) indifferentiable from a random oracle up to \(\mathcal{O}(2^{n/2})\) compression function invocations. In addition, our rigorous investigation suggests that any variants of Joux’s multi-collision, Kelsey-Schneier 2nd preimage and Herding attack are also ineffective on this mode. This fact leads us to conjecture that the indifferentiability security bound of FWP can be extended beyond the birthday barrier. From the point of view of efficiency, this new mode, for example, is always faster than the Wide-pipe mode when both modes use an identical compression function. In particular, it is nearly twice as fast as the Wide-pipe for a reasonable selection of the input and output size of the compression function. We also compare the FWP with several other modes of operation.

[1]  Nigel P. Smart,et al.  Advances in Cryptology - EUROCRYPT 2008, 27th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Istanbul, Turkey, April 13-17, 2008. Proceedings , 2008, EUROCRYPT.

[2]  Mihir Bellare,et al.  Multi-Property-Preserving Hash Domain Extension and the EMD Transform , 2006, ASIACRYPT.

[3]  John Kelsey,et al.  Herding Hash Functions and the Nostradamus Attack , 2006, EUROCRYPT.

[4]  Michael Wiener,et al.  Advances in Cryptology — CRYPTO’ 99 , 1999 .

[5]  Bruce Schneier,et al.  Second Preimages on n-bit Hash Functions for Much Less than 2n Work , 2005, IACR Cryptol. ePrint Arch..

[6]  Guido Bertoni,et al.  On the Indifferentiability of the Sponge Construction , 2008, EUROCRYPT.

[7]  Matthew Franklin,et al.  Advances in Cryptology – CRYPTO 2004 , 2004, Lecture Notes in Computer Science.

[8]  Ralph C. Merkle,et al.  One Way Hash Functions and DES , 1989, CRYPTO.

[9]  Stefan Lucks,et al.  A Failure-Friendly Design Principle for Hash Functions , 2005, ASIACRYPT.

[10]  Ivan Damgård,et al.  A Design Principle for Hash Functions , 1989, CRYPTO.

[11]  Mridul Nandi,et al.  Security Analysis of the Mode of JH Hash Function , 2010, FSE.

[12]  Kaoru Kurosawa,et al.  Advances in Cryptology - ASIACRYPT 2007, 13th International Conference on the Theory and Application of Cryptology and Information Security, Kuching, Malaysia, December 2-6, 2007, Proceedings , 2007, International Conference on the Theory and Application of Cryptology and Information Security.

[13]  Carl Pomerance,et al.  Advances in Cryptology — CRYPTO ’87 , 2000, Lecture Notes in Computer Science.

[14]  Eli Biham,et al.  A Framework for Iterative Hash Functions - HAIFA , 2007, IACR Cryptol. ePrint Arch..

[15]  Bimal Roy,et al.  Progress in Cryptology - INDOCRYPT 2009, 10th International Conference on Cryptology in India, New Delhi, India, December 13-16, 2009. Proceedings , 2009, INDOCRYPT.

[16]  Antoine Joux,et al.  Multicollisions in Iterated Hash Functions. Application to Cascaded Constructions , 2004, CRYPTO.

[17]  Ueli Maurer,et al.  Indifferentiability, Impossibility Results on Reductions, and Applications to the Random Oracle Methodology , 2004, TCC.

[18]  Mridul Nandi,et al.  Indifferentiability Characterization of Hash Functions and Optimal Bounds of Popular Domain Extensions , 2009, INDOCRYPT.

[19]  Jean-Sébastien Coron,et al.  Merkle-Damgård Revisited: How to Construct a Hash Function , 2005, CRYPTO.

[20]  Moti Yung,et al.  Advances in Cryptology — CRYPTO 2002 , 2002, Lecture Notes in Computer Science.

[21]  Ronald L. Rivest,et al.  The MD5 Message-Digest Algorithm , 1992, RFC.

[22]  Adi Shamir,et al.  New Cryptographic Primitives Based on Multiword T-Functions , 2004, FSE.

[23]  A. Maximov,et al.  Fast computation of large distributions and its cryptographic applications , 2005 .

[24]  Serge Vaudenay,et al.  Advances in Cryptology - EUROCRYPT 2006 , 2006, Lecture Notes in Computer Science.

[25]  Ronald L. Rivest,et al.  The MD4 Message-Digest Algorithm , 1990, RFC.

[26]  James H. Burrows,et al.  Secure Hash Standard , 1995 .

[27]  David A. Wagner,et al.  A Generalized Birthday Problem , 2002, CRYPTO.

[28]  Shoichi Hirose,et al.  A Simple Variant of the Merkle–Damgård Scheme with a Permutation , 2007, Journal of Cryptology.

[29]  Gerhard Goos,et al.  Fast Software Encryption , 2001, Lecture Notes in Computer Science.

[30]  Ronald Cramer,et al.  Advances in Cryptology - EUROCRYPT 2005, 24th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Aarhus, Denmark, May 22-26, 2005, Proceedings , 2005, EUROCRYPT.

[31]  Victor Shoup.  Advances in Cryptology - CRYPTO 2005: 25th Annual International Cryptology Conference, Santa Barbara, California, USA, August 14-18, 2005, Proceedings , 2005, CRYPTO.

[32]  Kefei Chen,et al.  Advances in Cryptology - ASIACRYPT 2006, 12th International Conference on the Theory and Application of Cryptology and Information Security, Shanghai, China, December 3-7, 2006, Proceedings , 2006, ASIACRYPT.