Practical (Second) Preimage Attacks on TCS_SHA-3

TCS\_SHA-3 is a family of four cryptographic hash functions that are covered by an US patent (US 2009/0262925). The digest sizes are 224, 256, 384 and 512 bits. The hash functions use bijective functions in place of the standard, compression functions. In this paper we describe first and second preimage attacks on the full hash functions. The second preimage attack requires negligible time and the first preimage attack requires $O(2^{36})$ time. In addition to these attacks, we also present a negligible-time second preimage attack on a strengthened variant of the TCS\_SHA-3. All the attacks have negligible memory requirements