New PDF release: A Radical Approach to Algebra (Addison-Wesley Series in

By Mary Gray

ISBN-10: 020102568X

ISBN-13: 9780201025682

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Springer, Heidelberg (2001) 10. : Segment LLL-Reduction with Floating Point Orthogonalization. H. ) CaLC 2001. LNCS, vol. 2146, pp. 81–96. Springer, Heidelberg (2001) 11. : Factoring Polynomials with Rational Coefficients. Math. Ann. 261, 515–534 (1982) 12. : Cryptanalysis of NTRU (preprint) (1999) 13. : Low-Dimensional Lattice Basis Reduction Revisited. A. ) Algorithmic Number Theory. LNCS, vol. 3076, pp. 338–357. Springer, Heidelberg (2004) 14. : Floating-Point LLL Revisited. F. ) EUROCRYPT 2005.

B2i,t(q2i ) xe2i,t(q2i ) , where e2i−1,1 = d(q2i−1 ) and e2i,1 = d(q2i ) and the exponent of each term in q2i−1 (x) is greater than the exponent of each term in q2i (x). If for all indices i = 1, 2, . . G. W. S. Vigklas for any permutation of the positive coefficients c2i−1,j , j = 1, 2, . . , t(q2i−1 ). Otherwise, for each of the indices i for which we have t(q2i−1 ) < t(q2i ), we break up one of the coefficients of q2i−1 (x) into t(q2i ) − t(q2i−1 ) + 1 parts, so that now t(q2i ) = t(q2i−1 ) and apply the same formula (3) given above.

4. Reduction times for fpLLL and xLiDIA using different η at dimension 85 for M1 , dimension 95 for M2 , and dimension 85 for M3 , the reduction time of fpLLL even exceeds that of NTL. This behavior of fpLLL is due to the overhead caused by updating two matrices (Gram matrix and lattice basis) for each transformation in the reduction process. The newly-introduced concept of buffered transformations as part of xLiDIA prevents this kind of behavior. 5 as in the original LLL algorithm and the xLiDIA implementation used for Figures 1 – 3.

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A Radical Approach to Algebra (Addison-Wesley Series in Mathematics) by Mary Gray


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