Paper 2007/430

Cryptanalysis of LASH

Scott Contini, Krystian Matusiewicz, Josef Pieprzyk, Ron Steinfeld, Jian Guo, San Ling, and Huaxiong Wang

Abstract

We show that the LASH-$x$ hash function is vulnerable to attacks that trade time for memory, including collision attacks as fast as $2^{\frac{4}{11}x}$ and preimage attacks as fast as $2^{\frac47x}$. Moreover, we describe heuristic lattice based collision attacks that use small memory but require very long messages. Based upon experiments, the lattice attacks are expected to find collisions much faster than $2^{x/2}$. All of these attacks exploit the designers' choice of an all zero IV. We then consider whether LASH can be patched simply by changing the IV. In this case, we show that LASH is vulnerable to a $2^{\frac78x}$ preimage attack. We also show that LASH is trivially not a PRF when any subset of input bytes is used as a secret key. None of our attacks depend upon the particular contents of the LASH matrix -- we only assume that the distribution of elements is more or less uniform. Additionally, we show a generalized birthday attack on the final compression of LASH which requires $O\left(x2^{\frac{x}{2(1+\frac{107}{105})}}\right) \approx O(x2^{x/4})$ time and memory. Our method extends the Wagner algorithm to truncated sums, as is done in the final transform in LASH.