International Association for Cryptologic Research

International Association
for Cryptologic Research


Guilhem Castagnos

Affiliation: LFANT/IMB, Univ. Bordeaux, INRIA


Bandwidth-Efficient Threshold EC-DSA 📺
Threshold Signatures allow n parties to share the power of issuing digital signatures so that any coalition of size at least $$t+1$$ can sign, whereas groups of t or less players cannot. Over the last few years many schemes addressed the question of realizing efficient threshold variants for the specific case of EC-DSA signatures. In this paper we present new solutions to the problem that aim at reducing the overall bandwidth consumption. Our main contribution is a new variant of the Gennaro and Goldfeder protocol from ACM CCS 2018 that avoids all the required range proofs, while retaining provable security against malicious adversaries in the dishonest majority setting. Our experiments show that – for all levels of security – our signing protocol reduces the bandwidth consumption of best previously known secure protocols for factors varying between 4.4 and 9, while key generation is consistently two times less expensive. Furthermore compared to these same protocols, our signature generation is faster for 192-bits of security and beyond.
Two-Party ECDSA from Hash Proof Systems and Efficient Instantiations 📺
ECDSA is a widely adopted digital signature standard. Unfortunately, efficient distributed variants of this primitive are notoriously hard to achieve and known solutions often require expensive zero knowledge proofs to deal with malicious adversaries. For the two party case, Lindell [Lin17] recently managed to get an efficient solution which, to achieve simulation-based security, relies on an interactive, non standard, assumption on Paillier’s cryptosystem. In this paper we generalize Lindell’s solution using hash proof systems. The main advantage of our generic method is that it results in a simulation-based security proof without resorting to non-standard interactive assumptions.Moving to concrete constructions, we show how to instantiate our framework using class groups of imaginary quadratic fields. Our implementations show that the practical impact of dropping such interactive assumptions is minimal. Indeed, while for 128-bit security our scheme is marginally slower than Lindell’s, for 256-bit security it turns out to be better both in key generation and signing time. Moreover, in terms of communication cost, our implementation significantly reduces both the number of rounds and the transmitted bits without exception.
Practical Fully Secure Unrestricted Inner Product Functional Encryption Modulo p
Guilhem Castagnos Fabien Laguillaumie Ida Tucker
Functional encryption (FE) is a modern public-key cryptographic primitive allowing an encryptor to finely control the information revealed to recipients from a given ciphertext. Abdalla, Bourse, De Caro, and Pointcheval (PKC 2015) were the first to consider FE restricted to the class of linear functions, i.e. inner products. Though their schemes are only secure in the selective model, Agrawal, Libert, and Stehlé (CRYPTO 16) soon provided adaptively secure schemes for the same functionality. These constructions, which rely on standard assumptions such as the Decision Diffie-Hellman ( $$\mathsf {DDH}$$ ), the Learning-with-Errors ( $$\mathsf {LWE}$$ ), and Paillier’s Decision Composite Residuosity (DCR) problems, do however suffer of various practical drawbacks. Namely, the DCR based scheme only computes inner products modulo an RSA integer which is oversized for many practical applications, while the computation of inner products modulo a prime p either requires, for their $$\mathsf {DDH}$$ based scheme, that the inner product be contained in a sufficiently small interval for decryption to be efficient, or, as in the $$\mathsf {LWE}$$ based scheme, suffers of poor efficiency due to impractical parameters.In this paper, we provide adaptively secure FE schemes for the inner product functionality which are both efficient and allow for the evaluation of unbounded inner products modulo a prime p. Our constructions rely on new natural cryptographic assumptions in a cyclic group containing a subgroup where the discrete logarithm ( $$\mathsf {DL}$$ ) problem is easy which extend Castagnos and Laguillaumie’s assumption (RSA 2015) of a $$\mathsf {DDH}$$ group with an easy $$\mathsf {DL}$$ subgroup. Instantiating our generic constructions using class groups of imaginary quadratic fields gives rise to the most efficient FE for inner products modulo an arbitrary large prime p. One of our schemes outperforms the DCR variant of Agrawal et al.’s protocols in terms of size of keys and ciphertexts by factors varying between 2 and 20 for a 112-bit security.
What do DES S-boxes Say to Each Other ?
Nicolas T. Courtois Guilhem Castagnos Louis Goubin
DES is not only very widely implemented and used today, but triple DES and other derived schemes will probably still be around in ten or twenty years from now. We suggest that, if an algorithm is so widely used, its security should still be under scrutiny, and not taken for granted. In this paper we study the S-boxes of DES. Many properties of these are already known, yet usually they concern one particular S-box. This comes from the known design criteria on DES, that strongly suggest that S-boxes have been chosen independently of each other. On the contrary, we are interested in properties of DES S-boxes that concern a subset of two or more DES S-boxes. For example we study the properties related to Davies-Murphy attacks on DES, recall the known uniformity criteria to resist this attack, and discuss a stronger criterion. More generally we study many different properties, in particular related to linear cryptanalysis and algebraic attacks. The interesting question is to know if there are any interesting properties that hold for subsets of S-boxes bigger than 2. Such a property has already been shown by Shamir at Crypto'85 (and independently discovered by Franklin), but Coppersmith et al. explained that it was rather due to the known S-box design criteria. Our simulations confirm this, but not totally. We also present several new properties of similar flavour. These properties come from a new type of algebraic attack on block ciphers that we introduce. What we find is not easily explained by the known S-box design criteria, and the question should be asked if the S-boxes of DES are related to each other, or if they follow some yet unknown criteria. Similarly, we also found that the s5DES S-boxes have an unexpected common structure that can be exploited in a certain type of generalised linear attack. This fact substantially decreases the credibility of s5DES as a DES replacement. This paper has probably no implications whatsoever on the security of DES.