Transcription of Lattice-based Cryptography
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Lattice-based CryptographyDaniele Micciancio Oded Regev July 22, 20081 IntroductionIn this chapter we describe some of the recent progress inlattice- based Cryptography . Lattice-based cryp-tographic constructions hold a great promise for post- quantum Cryptography , as they enjoy very strongsecurity proofs based on worst-case hardness, relatively efficient implementations, as well as great addition, Lattice-based Cryptography is believed to be secure against quantum computers. Our focus herewill be mainly on the practical aspects of Lattice-based Cryptography and less on the methods used to es-tablish their security.
of the period finding problem to non-Abelian groups can be used to give quantum algorithms for lattice problems. This approach, unfortunately, has so far not led to any interesting quantum algorithms for lattice problems. A possibly more interesting connection is the use of a quantum hardness assumption in the lattice-based cryptosystem of [71].
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