Short vector problems and simultaneous approximation

Abstract: In 1982, Lagarias showed that solving the approximate Shortest Vector Problem also solves the problem of finding simultaneous Diophantine approximations. Here we provide the reverse reduction with polynomial complexity. It is gap-preserving provided a consistent norm is used to measure approximation quality in both problems. We also give an alternative to the Lagarias algorithm by first reducing his version of simultaneous approximation to one with no explicit range in which a solution is sought.

cryptography and securityalgebraic geometrynumber theory

Audience: researchers in the topic

( chat | paper | slides | video )

Comments: The slides used in the pre-recorded video can be found here.

Chair: Divesh Aggarwal and Emmanuel Thomé

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Algorithmic Number Theory Symposium (ANTS XIV)

Series comments: Registration is now open. Registration is free but required to access the chat and livestream.

This is a hybrid synchronous/asynchronous conference with several ways to participate.

• Click the "paper" link to view contributed papers and posters (open to all).
• Click the "video" link to view pre-recorded talks of accepted papers (open to all).
  These are 15-20 minutes aimed at a general algorithmic number theory audience.
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The invited talks will be recorded and made available via the "video" link after the talk is over. None of the other sessions will be recorded.

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