Description
A {\em black-box} secret sharing scheme (BBSSS) for a given access structure works in exactly the same way over any finite Abelian group, as it only requires black-box access to group operations and to random group elements. In particular, there is no dependence on e.g.\ the structure of the group or its order. The expansion factor of a BBSSS is the length of a vector of shares (the number of group elements in it) divided by the number of players $n$.<br/> In 2002 Cramer and Fehr proposed a threshold BBSSS with an asymptotically minimal expansion factor $\Theta(\log n)$. We present a BBSSS that is based on a new paradigm, namely, {\em primitive sets in algebraic number fields}. This leads to a new BBSSS with an expansion factor that is absolutely minimal up to an additive term of at most~2, which is an improvement by a constant additive factor. The construction uses techniques from algebraic number theory as well as algebraic geometry.<br/> We provide good evidence that our scheme is considerably more efficient in terms of the computational resources it requires. Indeed, the number of group operations to be performed is $\tilde{O}(n^2)$ instead of $\tilde{O}(n^3)$ for sharing and $\tilde{O}(n^{1.6})$ instead of $\tilde{O}(n^{2.6})$ for reconstruction. Finally, we show that our scheme, as well as that of Cramer and Fehr, has asymptotically optimal randomness efficiency.<br/> This is talk is based on joint work with Serge Fehr, Hendrik Lenstra, and Martijn Stam. An article with these results appears in the Proceedings of the 25th Annual IACR CRYPTO Conference, 2005.
Prochains exposés
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Wagner’s Algorithm Provably Runs in Subexponential Time for SIS^∞
Orateur : Johanna Loyer - Inria Saclay
At CRYPTO 2015, Kirchner and Fouque claimed that a carefully tuned variant of the Blum-Kalai-Wasserman (BKW) algorithm (JACM 2003) should solve the Learning with Errors problem (LWE) in slightly subexponential time for modulus q = poly(n) and narrow error distribution, when given enough LWE samples. Taking a modular view, one may regard BKW as a combination of Wagner’s algorithm (CRYPTO 2002), run[…]-
Cryptography
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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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Structured-Seed Local Pseudorandom Generators and their Applications
Orateur : Nikolas Melissaris - IRIF
We introduce structured‑seed local pseudorandom generators (SSL-PRGs), pseudorandom generators whose seed is drawn from an efficiently sampleable, structured distribution rather than uniformly. This seemingly modest relaxation turns out to capture many known applications of local PRGs, yet it can be realized from a broader family of hardness assumptions. Our main technical contribution is a[…]-
Cryptography
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Post-Quantum Public-Key Pseudorandom Correlation Functions for OT
Orateur : Mahshid Riahinia - ENS, CNRS
Public-Key Pseudorandom Correlation Functions (PK-PCF) are an exciting recent primitive introduced to enable fast secure computation. Despite significant advances in the group-based setting, success in the post-quantum regime has been much more limited. In this talk, I will introduce an efficient lattice-based PK-PCF for the string OT correlation. At the heart of our result lie several technical[…] -
Predicting Module-Lattice Reduction
Orateur : Paola de Perthuis - CWI
Is module-lattice reduction better than unstructured lattice reduction? This question was highlighted as `Q8' in the Kyber NIST standardization submission (Avanzi et al., 2021), as potentially affecting the concrete security of Kyber and other module-lattice-based schemes. Foundational works on module-lattice reduction (Lee, Pellet-Mary, Stehlé, and Wallet, ASIACRYPT 2019; Mukherjee and Stephens[…]-
Cryptography
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