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PRO (Pseudorandom Oracle) is an important security of hash functions because it ensures that the PRO hash function inherits all properties of a random oracle in single stage games up to the PRO bound (e.g., collision resistant security, preimage resistant security and so on). In this paper, we propose new blockcipher-based double-length hash functions, which are PROs up to $\mathcal{O}(2^n)$ query complexity in the ideal cipher model. Our hash functions use a single blockcipher, which encrypts an n-bit string using a 2n-bit key, and maps an input of arbitrary length to an n-bit output. Since many blockciphers supports a 2n-bit key (e.g. AES supports a 256-bit key), the assumption to use the 2n-bit key length blockcipher is acceptable. To our knowledge, this is the first time double-length hash functions based on a single (practical size) blockcipher with birthday PRO security.

Blockcipher-Based Double-Length Hash Functions for Pseudorandom Oracles