Rump session CRYPTO 2009

Hash Functions and Cayley Graphs:

the end of the story?

Christophe Petit

Jean-Jacques Quisquater

UCL Crypto Group

Rump session CRYPTO 2009

The dream

Rump session CRYPTO 2009

Recently

Rump session CRYPTO 2009

Hash functions (1990-...) designed by randomness?

Rump session CRYPTO 2009

Zemor-Tillich hash functions1994-2009

Rump session CRYPTO 2009

Rump session CRYPTO 2009

IACR eprint 2009-376

Rump session CRYPTO 2009

Rump session CRYPTO 2009

Rump session CRYPTO 2009

Rump session CRYPTO 2009

Conclusion I

Rump session CRYPTO 2009

Conclusion II

• Zemor-Tillich is completely broken• Preimage in few seconds with a

small program• Length of the preimage around

100.000 bits

Rump session CRYPTO 2009

End?

• No!• Changing the generators• More generators• Working in other algebra• A new field!