Fonction de dérivation de clé

En cryptographie, une fonction de dérivation de clé (en anglais, key derivation function ou KDF) est une fonction qui dérive une ou plusieurs clés secrètes d'une valeur secrète comme un mot de passe ou une phrase secrète en utilisant une fonction pseudo-aléatoire. Les fonctions de dérivation de clé peuvent être utilisées pour renforcer des clés en les étirant ou pour obtenir des clés d'un certain format. Utilisation des fonctions de dérivation de clé Les fonctions de dérivation de clé sont souvent utilisées conjointement avec des paramètres non secrets (appelés sels cryptographiques) pour dériver une ou plusieurs clés à partir d'une valeur secrète. Une telle utilisation peut empêcher un attaquant qui obtient une clé dérivée d'apprendre des informations utiles sur la valeur de clé originale ou sur l'une quelconque des autres clés dérivées. Les fonctions de dérivation de clé peuvent également être utilisées pour s'assurer que les clés dérivées ont d'autres propriétés sou

Mutual Authentication in RFID: Security and Privacy

Radu-Ioan Paise, Serge Vaudenay

In RFID protocols, tags identify and authenticate themselves to readers. At Asiacrypt 2007, Vaudenay studied security and privacy models for these protocols. We extend this model to protocols which offer reader authentication to tags. Whenever corruption is allowed, we prove that secure protocols cannot protect privacy unless we assume tags have a temporary memory which vanishes by itself. Under this assumption, we study several protocols. We enrich a few basic protocols to get secure mutual authentication RFID protocols which achieve weak privacy based on pseudorandom functions only, narrow- destructive privacy based on random oracles, and narrow-strong and forward privacy based on public-key cryptography.

ACM Press2008

Efficient Non-malleable Codes and Key-Derivation for Poly-size Tampering Circuits

Sebastian Faust

Non-malleable codes, defined by Dziembowski, Pietrzak and Wichs (ICS ’10), provide roughly the following guarantee: if a codeword c encoding some message x is tampered to c' = f(c) such that c c, then the tampered message x contained in c reveals no information about x. Non-malleable codes have applications to immunizing cryptosystems against tampering attacks and related-key attacks. One cannot have an efficient non-malleable code that protects against all efficient tampering functions f. However, in this work we show “the next best thing”: for any polynomial bound s given a-priori, there is an efficient non-malleable code that protects against all tampering functions f computable by a circuit of size s. More generally, for any family of tampering functions F of size |F| ≤ 2s, there is an efficient nonmalleable code that protects against all f ∈ F. The rate of our codes, defined as the ratio of message to codeword size, approaches 1. Our results are information-theoretic and our main proof technique relies on a careful probabilistic method argument using limited independence. As a result, we get an efficiently samplable family of efficient codes, such that a random member of the family is non-malleable with overwhelming probability. Alternatively, we can view the result as providing an efficient non-malleable code in the “common reference string” (CRS) model. We also introduce a new notion of non-malleable key derivation, which uses randomness x to derive a secret key y = h(x) in such a way that, even if x is tampered to a different value x = f(x), the derived key y = h(x) does not reveal any information about y. Our results for non-malleable key derivation are analogous to those for non-malleable codes. As a useful tool in our analysis, we rely on the notion of “leakage-resilient storage” of Davı, Dziembowski and Venturi (SCN ’10) and, as a result of independent interest, we also significantly improve on the parameters of such schemes.

Springer2014

Cryptographic Hash Functions in Groups and Provable Properties

Juraj Sarinay

We consider several "provably secure" hash functions that compute simple sums in a well chosen group (G,*). Security properties of such functions provably translate in a natural way to computational problems in G that are simple to define and possibly also hard to solve. Given k disjoint lists Li of group elements, the k-sum problem asks for gi ∊ Li such that g1 * g2 ... gk = 1G. Hardness of the problem in the respective groups follows from some "standard" assumptions used in public-key cryptology such as hardness of integer factoring, discrete logarithms, lattice reduction and syndrome decoding. We point out evidence that the k-sum problem may even be harder than the above problems. Two hash functions based on the group k-sum problem, SWIFFTX and FSB, were submitted to NIST as candidates for the future SHA-3 standard. Both submissions were supported by some sort of a security proof. We show that the assessment of security levels provided in the proposals is not related to the proofs included. The main claims on security are supported exclusively by considerations about available attacks. By introducing "second-order" bounds on bounds on security, we expose the limits of such an approach to provable security. A problem with the way security is quantified does not necessarily mean a problem with security itself. Although FSB does have a history of failures, recent versions of the two above functions have resisted cryptanalytic efforts well. This evidence, as well as the several connections to more standard problems, suggests that the k-sum problem in some groups may be considered hard on its own, and possibly lead to provable bounds on security. Complexity of the non-trivial tree algorithm is becoming a standard tool for measuring the associated hardness. We propose modifications to the multiplicative Very Smooth Hash and derive security from multiplicative k-sums in contrast to the original reductions that related to factoring or discrete logarithms. Although the original reductions remain valid, we measure security in a new, more aggressive way. This allows us to relax the parameters and hash faster. We obtain a function that is only three times slower compared to SHA-256 and is estimated to offer at least equivalent collision resistance. The speed can be doubled by the use of a special modulus, such a modified function is supported exclusively by the hardness of multiplicative k-sums modulo a power of two. Our efforts culminate in a new multiplicative k-sum function in finite fields that further generalizes the design of Very Smooth Hash. In contrast to the previous variants, the memory requirements of the new function are negligible. The fastest instance of the function expected to offer 128-bit collision resistance runs at 24 cycles per byte on an Intel Core i7 processor and approaches the 17.4 figure of SHA-256. The new functions proposed in this thesis do not provably achieve a usual security property such as preimage or collision resistance from a well-established assumption. They do however enjoy unconditional provable separation of inputs that collide. Changes in input that are small with respect to a well defined measure never lead to identical output in the compression function.