Description
We present new classical and quantum algorithms for solving random hard instances of the subset-sum problem, in which we are given n integers on n bits and try to find a subset of them that sums to a given target. This classical NP-complete problem has several applications in cryptography and underlies the security of some proposed post-quantum cryptosystems.<br/> At EUROCRYPT 2010, Howgrave-Graham and Joux (HGJ) introduced the representation technique and presented an algorithm running in time $\bigOt{2^{0.337 n}}$. This asymptotic time was improved by Becker, Coron, Joux (BCJ) at EUROCRYPT 2011. We show how to improve this further.<br/> We then move to the context of quantum algorithms. The two previous quantum speedups in the literature are given by Bernstein, Jeffery, Lange and Meurer (PQCRYPTO 2013) and Helm and May (TQC 2018), which are respectively quantum versions of HGJ and BCJ. They both rely on the framework of quantum walks, use exponential quantum memory with quantum random-access and require an unproven conjecture on quantum walk updates. We devise a new algorithm, using quantum search only, that achieves the first quantum speedup in the model of \emph{classical} memory with quantum random access. Next, we study improvements for the quantum walks. We show how to avoid the quantum walk conjecture and give a better quantum walk time complexity for subset-sum.<br/> lien: http://desktop.visio.renater.fr/scopia?ID=725403***3883&autojoin
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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