By Miklós Ajtai, Ravi Kumar, Dandapani Sivakumar (auth.), Joseph H. Silverman (eds.)

ISBN-10: 3540424881

ISBN-13: 9783540424888

ISBN-10: 3540446702

ISBN-13: 9783540446705

This ebook constitutes the completely refereed post-proceedings of the foreign convention on Cryptography and Lattices, CaLC 2001, held in windfall, RI, united states in March 2001. The 14 revised complete papers offered including an summary paper have been rigorously reviewed and chosen for inclusion within the booklet. All present features of lattices and lattice aid in cryptography, either for cryptographic building and cryptographic research, are addressed.

**Read or Download Cryptography and Lattices: International Conference, CaLC 2001 Providence, RI, USA, March 29–30, 2001 Revised Papers PDF**

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**Extra info for Cryptography and Lattices: International Conference, CaLC 2001 Providence, RI, USA, March 29–30, 2001 Revised Papers**

**Sample text**

Such polynomials have a very special Galois group; order(σ) N for every σ in the Galois group. Extreme examples are the Swinnerton-Dyer polynomials, where order(σ) ≤ 2 for all σ. Other examples are resolvent polynomials, which tend to be polynomials of high degree with small Galois groups. For these polynomials, the computation time is dominated by cEZ , and the algorithm of Zassenhaus will be exponentially slow. The ﬁrst polynomial time algorithm was given by Lenstra, Lenstra and Lov´ asz. In their paper [2] they give a lattice reduction algorithm (the LLL algorithm).

Edu Abstract. A summary is given of an algorithm, published in [4], that uses lattice reduction to handle the combinatorial problem in the factoring algorithm of Zassenhaus. Contrary to Lenstra, Lenstra and Lov´ asz, the lattice reduction is not used to calculate coeﬃcients of a factor but is only used to solve the combinatorial problem, which is a problem with much smaller coeﬃcients and dimension. The factors are then constructed eﬃciently in the same way as in Zassenhaus’ algorithm. 1 Comparison of Three Factoring Algorithms Let f ∈ Q[x] be a polynomial of degree N .

Other examples are resolvent polynomials, which tend to be polynomials of high degree with small Galois groups. For these polynomials, the computation time is dominated by cEZ , and the algorithm of Zassenhaus will be exponentially slow. The ﬁrst polynomial time algorithm was given by Lenstra, Lenstra and Lov´ asz. In their paper [2] they give a lattice reduction algorithm (the LLL algorithm). Many combinatorial problems can be solved in polynomial time with LLL by encoding the solutions of the problem as short vectors in a lattice.

### Cryptography and Lattices: International Conference, CaLC 2001 Providence, RI, USA, March 29–30, 2001 Revised Papers by Miklós Ajtai, Ravi Kumar, Dandapani Sivakumar (auth.), Joseph H. Silverman (eds.)

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