Cryptology ePrint Archive: Report 2008/493

Secure Parameters for SWIFFT

Johannes Buchmann and Richard Lindner

Abstract: The SWIFFT compression functions, proposed by Lyubashevsky et al. at FSE 2008, are very efficient instantiations of generalized compact knapsacks for a specific set of parameters. They have the property that, asymptotically, finding collisions for a randomly chosen compression function implies being able to solve computationally hard ideal lattice problems in the worst-case.

We present three results. First, we present new average-case problems, which may be used for all lattice schemes whose security is proven with the worst-case to average-case reduction in either general or ideal lattices. The new average-case problems require less description bits, resulting in improved keysize and speed for these schemes. Second, we propose a parameter generation algorithm for SWIFFT where the main parameter n can be any integer in the image of Euler's totient function, and not necessarily a power of 2 as before. Third, we give experimental evidence that finding pseudo-collisions for SWIFFT is as hard as breaking a 68-bit symmetric cipher according to the well-known heuristic by Lenstra and Verheul. We also recommend conservative parameters corresponding to a 127-bit symmetric cipher.

Category / Keywords: post-quantum cryptography, hash functions, lattices

Date: received 25 Nov 2008, last revised 15 Jul 2009

Contact author: rlindner at cdc informatik tu-darmstadt de

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Note: Added section on new average-case problems

Version: 20090715:093026 (All versions of this report)

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