Over the past few decades, there has been great progress in cryptography towards provable security. Security properties for many cryptographic techniques are based, provably, on simple computational assumptions (such as the hardness of factoring), with strong proofs. Symmetric cryptography algorithms such as blockciphers and hash functions are typically designed without the benefit of strong proofs of security. There is good reason for this: for these algorithms especially, speed is an essential concern, and provable security tends to be attached to heavy computational methods such as modular exponentiation. Nonetheless, symmetric cryptographic algorithms do seem to be secure, able to resist all known attacks. This project seeks to expand on our theoretical understanding of the structural design principles underlying popular symmetric algorithms, with a particular focus on how these structures are able to strengthen simple building blocks into secure algorithms.
The research is driven by four central principles: (1) Focus on structures -- by considering the structures used in practice that connect simple components, rather than the lowest-level constructions themselves, results will apply to a wide range of potential designs. (2) Minimize assumptions -- the research must be aggressive in modeling underlying components as weak, so as to understand how they are strengthened by the structures that use them. (3) Avoid asymptotics -- in practice, a security parameter must be chosen and fixed, and asymptotic guarantees of security are of little comfort. Favor precise analysis and avoid inherently asymptotic scenarios like assuming computational limitations. (4) Focus on positive results -- while negative results (that is, attacks) inform the development of positive solutions, this is an area in which negative results are already far more advanced than positive ones. The research focuses mainly on blockcipher design and hash function design and connections between them.
