On Related-Secret Pseudorandomness

Related-key attacks are attacks against constructions which use a secret key (such as a blockcipher) in which an attacker attempts to exploit known or chosen relationships among keys to circumvent security properties. Security against related-key attacks has been a subject of study in numerous recent cryptographic papers. However, most of these results are attacks on specific constructions, while there has been little positive progress on constructing related-key secure primitives.

In this paper, we attempt to address the question of whether related-key secure blockciphers can be built from traditional cryptographic primitives. We develop a theoretical framework of “related-secret secure” cryptographic primitives, a class of primitives which includes related-key secure blockciphers and PRFs. We show that while a single related-secret pseduorandom bit is sufficient and necessary to create related-key secure blockciphers, hard-core bits with typical proofs are

not

related-secret psuedorandom. Since the pseudorandomness of hard-core bits is the essential technique known to make pseudorandomness from assumptions of simple hardness, this presents a very strong barrier to the development of provably related-key secure blockciphers based on standard hardness assumptions.