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DTEND:20221214T120000Z
UID:00b9a6273bef7d0b38b6636e8ab28bd4-369
DTSTAMP:19700101T120015Z
DESCRIPTION:Applications of Dedekinds Index Theorem to Lattice-based Cryptography
URL;VALUE=URI:https://www.csa.iisc.ac.in/newweb/event/369/applications-of-dedekinds-index-theorem-to-lattice-based-cryptography/
SUMMARY:Computationally hard problems on integer lattices, such as shortest vector problem (SVP), have become an important tool in designing modern cryptographic schemes, especially since these problems are considered post-quantum secure. For example, Shors quantum polynomial-time algorithm for integer factorization has rendered the famous RSA cryptosystem insecure, assuming existence of quantum computers.

Instead of basing hardness on worst-case integer lattices, to make the lattice-based encryption schemes more efficient, there has been a significant push to use ideal lattices in ring of integers of number fields, and such a scheme has even been standardized by NIST recently. However, it is not clear if the additional algebraic structure of such ideal lattices, which lie in well known Dedekind-domains, can withstand quantum attacks. In this work we show that we can base similar and natural cryptosystems on hardness of ideal lattices in non Dedekind-domains which have less algebraic structure.  This allows the security of the efficient cryptosystems to be based on problems closer to the worst-case integer lattices. The main technical contribution of the work is a novel and generalized way to prove the “ideal-clearing lemma” of Lyubashevsky et al (Eurocrypt 2010). This is joint work with Chengyu Lin.
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