Description
Digital signatures were introduced to guarantee the authenticity and integrity of the underlying messages. However, and in situations where the signed data is commercially or personally sensitive, the universal verification of digital signatures is undesirable, and needs to be limited or controlled. Therefore, mechanisms which share most properties with digital signatures except the universal verification were invented to respond to the aforementioned need; we call such mechanisms ``opaque signatures''. In this talk, we study confirmer signatures where the verification cannot be achieved without the cooperation of a specific entity, i.e. the confirmer, via the so-called confirmation/denial protocols. Generic constructions of designated confirmer signatures follow one of the following two strategies; either produce a digital signature on the message to be signed, then encrypt the resulting signature, or produce a commitment on the message, encrypt the string used to generate the commitment, and finally sign the latter. In this talk, we revisit both methods and establish the minimal and sufficient assumptions on the building blocks in order to attain secure confirmer signatures. Our study concludes that both paradigms, when used in their basic form, cannot allow a class of encryption schemes which is vital for the efficiency of the confirmation/denial protocols. Next, we propose a variation of both paradigms which thrives on very cheap encryption and consequently leads to efficient confirmer signatures. Indeed, the resulting constructions do not only compete with the dedicated realizations of confirmer/undeniable signatures proposed recently, e.g. \citep{LeTrieuKurosawaOgata2009b,SchuldtMatsuura2010}, but also serve for analyzing the early schemes that have a speculative security.<br/> The contents of this talk are parts of the speaker's PhD thesis.
Next sessions
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Efficient zero-knowledge proofs and arguments in the CL framework
Speaker : Agathe Beaugrand - Institut de Mathématiques de Bordeaux
The CL encryption scheme, proposed in 2015 by Castagnos and Laguillaumie, is a linearly homomorphic encryption scheme, based on class groups of imaginary quadratic fields. The specificity of these groups is that their order is hard to compute, which means it can be considered unknown. This particularity, while being key in the security of the scheme, brings technical challenges in working with CL,[…] -
Constant-time lattice reduction for SQIsign
Speaker : Sina Schaeffler - IBM Research
SQIsign is an isogeny-based signature scheme which has recently advanced to round 2 of NIST's call for additional post-quantum signatures. A central operation in SQIsign is lattice reduction of special full-rank lattices in dimension 4. As these input lattices are secret, this computation must be protected against side-channel attacks. However, known lattice reduction algorithms like the famous[…] -
Circuit optimisation problems in the context of homomorphic encryption
Speaker : Sergiu Carpov - Arcium
Fully homomorphic encryption (FHE) is an encryption scheme that enables the direct execution of arbitrary computations on encrypted data. The first generation of FHE schemes began with Gentry's groundbreaking work in 2019. It relies on a technique called bootstrapping, which reduces noise in FHE ciphertexts. This construction theoretically enables the execution of any arithmetic circuit, but[…] -
Cycles of pairing-friendly abelian varieties
Speaker : Maria Corte-Real Santos - ENS Lyon
A promising avenue for realising scalable proof systems relies on the existence of 2-cycles of pairing-friendly elliptic curves. More specifically, such a cycle consists of two elliptic curves E/Fp and E’/Fq that both have a low embedding degree and also satisfy q = #E(Fp) and p = #E’(Fq). These constraints turn out to be rather restrictive; in the decade that has passed since 2-cycles were first[…]-
Cryptography
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