Given a subset of states $S$ deterministic finite automaton and word $w$, the preimage is all mapped to state in by action $w$. We study three natural problems concerning words giving certain preimages. The first problem whether, for given subset, there exists \emph{extending} (giving larger preimage). second whether \emph{totally extending} whole set as preimage)---equivalently, an \emph{avoid...

The classical design principle Merkle-Damg̊ard [13, 6] is scrutinized by many ways such as Joux’s multicollision attack, Kelsey-Schneier second preimage attack etc. In TCC’04, Maurer et al. introduced a strong security notion called as “indifferentiability” for a hash function based on a compression function. The classical design principle is also insecure against this strong security notion whe...

The Even-Mansour structure and the chopMD mode are two widely-used strategies in hash function designs. They are adopted by many hash functions including two SHA-3 finalists, the JH hash function and the Grøstl hash function. The Even-Mansour structure combining the chopMD mode is supposed to enhance the security of hash functions against collision and preimage attacks, while our results show t...

We provide two necessary conditions on hash functions for the Schnorr signature scheme to be secure, assuming compact group representations such as those which occur in elliptic curve groups. We also show, via an argument in the generic group model, that these conditions are sufficient. Our hash function security requirements are variants of the standard notions of preimage and second preimage ...

In this paper, we examine the resistance of the popular hash function SHA-1 and its predecessor SHA-0 against dedicated preimage attacks. In order to assess the security margin of these hash functions against these attacks, two new cryptanalytic techniques are developed: – Reversing the inversion problem: the idea is to start with an impossible expanded message that would lead to the required d...

The SATisfiability Problem is a core problem in mathematical logic and computing theory. The last decade progresses have led it to be a great and competitive approach to practically solve a wide range of industrial and academic problems. Thus, the current SAT solving capacity allows the propositional formalism to be an interesting alternative to tackle cryptanalysis problems. This paper deals w...

Symmetric key cryptographic algorithms provide confidentiality, integrity, and authentication in modern communication systems. Our confidence in these algorithms is largely based on the fact that intense cryptanalysis has been carried out over several years without revealing any weakness. This thesis makes three independent contributions to the cryptanalysis of symmetric key primitives and hash...

We revisit meet-in-the-middle attacks on block ciphers and recent developments in meet-in-the-middle preimage attacks on hash functions. Despite the presence of a secret key in the block cipher case, we identify techniques that can also be mounted on block ciphers, thus allowing us to improve the cryptanalysis of the block cipher KTANTAN family. The first and major contribution is that we spot ...

Many cryptographic applications of hash functions are analyzed in the random oracle model. Unfortunately, most concrete hash functions, including the SHA family, use the iterative (strengthened) Merkle-Damgård transform applied to a corresponding compression function. Moreover, it is well known that the resulting “structured” hash function cannot be generically used as a random oracle, even if ...

We consider the problem of determining robot manipulation plans when sensing and control uncertainties are specified as conditional probability densities. Traditional approaches are usually based on worst-case error analysis in a methodology known as preimage backchaining. We have developed a general framework for determining sensor-based robot plans by blending ideas from stocbastic optimal co...