Description
Cryptographic hash functions are efficiently computable functions that shrink a long input into a shorter output while achieving some of the useful security properties of a random function. The most common type of such hash functions is collision resistant hash functions (CRH), which prevent an efficient attacker from finding a pair of inputs on which the function has the same output.<br/> Despite the ubiquitous role of hash functions in cryptography, several of the most basic questions regarding their computational and algebraic complexity remained open. In this work we settle most of these questions under new, but arguably quite conservative, cryptographic assumptions, whose study may be of independent interest. Concretely, we obtain the following results: * Low-complexity CRH. Assuming the intractability of finding short codewords in natural families of linear error-correcting codes, there are CRH that shrink the input by a constant factor and have a constant algebraic degree over Z_2 (as low as 3), or even constant output locality and input locality and thus computable by linear-size circuits. Such CRH are potentially MPC- and FHE-friendly.<br/> * Win-win results. If low-degree CRH with good shrinkage do not exist, this has useful consequences for learning algorithms and data structures. * Degree-2 hash functions. Assuming the conjectured intractability of solving a random system of quadratic equations over Z_2, a uniformly random degree-2 mapping is a universal one-way hash function (UOWHF). UOWHF relaxes CRH by forcing the attacker to find a collision with a random input picked by a challenger. On the other hand, a uniformly random degree-2 mapping is not a CRH. We leave the existence of degree-2 CRH open, and relate it to open questions on the existence of degree-2 randomized encodings of functions. An important research direction is to understand the security of our assumptions from the cryptanalysis standpoint. Joint Work with Benny Applebaum, Naama Haramaty, Yuval Ishai and Eyal Kushilevitz, to appear in ITCS 2017.
Prochains exposés
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Présentations des nouveaux doctorants Capsule
Orateur : Alisée Lafontaine et Mathias Boucher - INRIA Rennes
2 nouveaux doctorants arrivent dans l'équipe Capsule et présenteront leurs thématiques de recherche. Alisée Lafontaine, encadrée par André Schrottenloher, présentera son stage de M2: "Quantum rebound attacks on double-block length hash functions" Mathias Boucher, encadré par Yixin Shen, parlera des algorithmes quantiques et des réseaux euclidiens. -
Design of fast AES-based Universal Hash Functions and MACs
Orateur : Augustin Bariant - ANSSI
Ultra-fast AES round-based software cryptographic authentication/encryption primitives have recently seen important developments, fuelled by the authenticated encryption competition CAESAR and the prospect of future high-profile applications such as post-5G telecommunication technology security standards. In particular, Universal Hash Functions (UHF) are crucial primitives used as core components[…]-
Cryptography
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Lie algebras and the security of cryptosystems based on classical varieties in disguise
Orateur : Mingjie Chen - KU Leuven
In 2006, de Graaf et al. proposed a strategy based on Lie algebras for finding a linear transformation in the projective linear group that connects two linearly equivalent projective varieties defined over the rational numbers. Their method succeeds for several families of “classical” varieties, such as Veronese varieties, which are known to have large automorphism groups. In this talk, we[…]-
Cryptography
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Some applications of linear programming to Dilithium
Orateur : Paco AZEVEDO OLIVEIRA - Thales & UVSQ
Dilithium is a signature algorithm, considered post-quantum, and recently standardized under the name ML-DSA by NIST. Due to its security and performance, it is recommended in most use cases. During this presentation, I will outline the main ideas behind two studies, conducted in collaboration with Andersson Calle-Vierra, Benoît Cogliati, and Louis Goubin, which provide a better understanding of[…] -
CryptoVerif: a computationally-sound security protocol verifier
Orateur : Bruno Blanchet - Inria
CryptoVerif is a security protocol verifier sound in the computational model of cryptography. It produces proofs by sequences of games, like those done manually by cryptographers. It has an automatic proof strategy and can also be guided by the user. It provides a generic method for specifying security assumptions on many cryptographic primitives, and can prove secrecy, authentication, and[…]-
Cryptography
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