International Association for Cryptologic Research

International Association
for Cryptologic Research


Guilhem Castagnos


Public Key Encryption with Flexible Pattern Matching 📺
Elie Bouscatié Guilhem Castagnos Olivier Sanders
Many interesting applications of pattern matching (e.g. deep-packet inspection or medical data analysis) target very sensitive data. In particular, spotting illegal behaviour in internet traffic conflicts with legitimate privacy requirements, which usually forces users (e.g. children, employees) to blindly trust an entity that fully decrypts their traffic in the name of security. The compromise between traffic analysis and privacy can be achieved through searchable encryption. However, as the traffic data is a stream and as the patterns to search are bound to evolve over time (e.g. new virus signatures), these applications require a kind of searchable encryption that provides more flexibility than the classical schemes. We indeed need to be able to search for patterns of variable sizes in an arbitrary long stream that has potentially been encrypted prior to pattern identification. To stress these specificities, we call such a scheme a stream encryption supporting pattern matching. Recent papers use bilinear groups to provide public key constructions supporting these features. These solutions are lighter than more generic ones (e.g. fully homomorphic encryption) while retaining the adequate expressivity to support pattern matching without harming privacy more than needed. However, all existing solutions in this family have weaknesses with respect to efficiency and security that need to be addressed. Regarding efficiency, their public key has a size linear in the size of the alphabet, which can be quite large, in particular for applications that naturally process data as bytestrings. Regarding security, they all rely on a very strong computational assumption that is both interactive and specially tailored for this kind of scheme. In this paper, we tackle these problems by providing two new constructions using bilinear groups to support pattern matching on encrypted streams. Our first construction shares the same strong assumption but dramatically reduces the size of the public key by removing the dependency on the size of the alphabet, while nearly halving the size of the ciphertext. On a typical application with large patterns, our public key is two order of magnitude smaller that the one of previous schemes, which demonstrates the practicality of our approach. Our second construction manages to retain most of the good features of the first one while exclusively relying on a simple (static) variant of DDH, which solves the security problem of previous works.
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.