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.
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Buchmann, J., Lindner, R. (2009). Secure Parameters for SWIFFT. In: Roy, B., Sendrier, N. (eds) Progress in Cryptology - INDOCRYPT 2009. INDOCRYPT 2009. Lecture Notes in Computer Science, vol 5922. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-10628-6_1
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DOI: https://doi.org/10.1007/978-3-642-10628-6_1
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