Lattice basis reduction, Jacobi sums and hyperelliptic cryptosystems
نویسندگان
چکیده
منابع مشابه
A Polynomial time Jacobi Method for Lattice Basis Reduction
Among all lattice reduction algorithms, the LLL algorithm is the first and perhaps the most famous polynomial time algorithm, and it is widely used in many applications. In 2012, S. Qiao [24] introduced another algorithm, the Jacobi method, for lattice basis reduction. S. Qiao and Z. Tian [25] improved the Jacobi method further to be polynomial time but only produces a Quasi-Reduced basis. In t...
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This paper describes a parallel Jacobi method for lattice basis reduction and a GPU implementation using CUDA. Our experiments have shown that the parallel implementation is more than fifty times as fast as the serial counterpart, which is twice as fast as the well-known LLL lattice reduction algorithm.
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We present a new proposal for a trapdoor one-way function, from which we derive public-key encryption and digital signatures. The security of the new construction is based on the conjectured computational difficulty of lattice-reduction problems, providing a possible alternative to existing public-key encryption algorithms and digital signatures such as RSA and DSS. Keywards; Public-Key Cryptos...
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We propose a practical sampling reduction algorithm for lattice bases based on work by Schnorr [1] as well as two even more effective generalizations. We report the empirical behaviour of these algorithms. We describe how Sampling Reduction allows to stage lattice attacks against the NTRU cryptosystem with smaller BKZ parameters than before and conclude that therefore the recommeded NTRU securi...
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ژورنال
عنوان ژورنال: Bulletin of the Australian Mathematical Society
سال: 1998
ISSN: 0004-9727,1755-1633
DOI: 10.1017/s000497270003207x