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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Polytopes in the Fiat-Shamir with Aborts Paradigm
Speaker : Hugo Beguinet - ENS Paris / Thales
The Fiat-Shamir with Aborts paradigm (FSwA) uses rejection sampling to remove a secret’s dependency on a given source distribution. Recent results revealed that unlike the uniform distribution in the hypercube, both the continuous Gaussian and the uniform distribution within the hypersphere minimise the rejection rate and the size of the proof of knowledge. However, in practice both these[…]-
Cryptography
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Asymmetric primitive
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Mode and protocol
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Post-quantum Group-based Cryptography
Speaker : Delaram Kahrobaei - The City University of New York