**Cryptanalysis of LASH**

*Scott Contini and Krystian Matusiewicz and Josef Pieprzyk and Ron Steinfeld and Jian Guo and 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.

**Category / Keywords: **secret-key cryptography / LASH, hash function, collision attack, preimage attack

**Publication Info: **Extended version of FSE 2008 submission

**Date: **received 18 Nov 2007

**Contact author: **scontini at ics mq edu au

**Available format(s): **PDF | BibTeX Citation

**Version: **20071124:103756 (All versions of this report)

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