The nearest-colattice algorithm: time-approximation tradeoff for approx-CVP

Abstract: In this paper we exhibit a hierarchy of polynomial time algorithms solving approximate variants of the Closest Vector Problem (\CVP). Our first contribution is a heuristic algorithm achieving the same distance as HSVP algorithms, namely $\approx \beta^{\frac{n}{2\beta}}\mathrm{covol}(\Lambda)^{\frac{1}{n}}$ for a random lattice $\Lambda$ of dimension $n$. Compared to Kannan embedding, our technique allows using precomputations. This implies that some attacks on some lattice-based signatures lead to very cheap forgeries, after a precomputation. Our second contribution is a \emph{proven} reduction from approximating the closest vector with a factor $\approx n^{\frac32}\beta^{\frac{3n}{2\beta}}$ to the Shortest Vector Problem (SVP) in dimension $\beta$.

cryptography and securitynumber theory

Audience: researchers in the topic

( chat | paper | slides | video )

Comments: Chairs: Claus Fieker and Elena Kirshanova

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Algorithmic Number Theory Symposium (ANTS XIV)

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