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We present a new public-key signature scheme and a corresponding authentication scheme that are based on discrete logarithms in a subgroup of units in ℤ p where p is a sufficiently large prime, e.g., p ≥ 2512. A key idea is to use for the base of the discrete logarithm an integer α in ℤ p such that the order of α is a sufficiently large prime q, e.g., q ≥(More)
We report on improved practical algorithms for lattice basis reduction. We propose a practical oating point v e r s i o n o f t h e L 3 {algorithm of Lenstra, Lenstra, Lovv asz (1982). We present a v ariant o f t h e L 3 { algorithm with \deep insertions" and a practical algorithm for block Korkin{Zolotarev reduction, a concept introduced by S c hnorr(More)
The general subset sum problem is NP-complete. However, there are two algorithms, one due to Brickell and the other to Lagarias and Odlyzko, which in polynomial time solve almost all subset sum problems of sufficiently low density. Both methods rely on basis reduction algorithms to find short non-zero vectors in special lattices. The Lagarias-Odlyzko(More)
Using the concept of test functions, we develop a general framework within which many recent approaches to the definition of random sequences can be described. Using this concept we give some definitions of random sequences that are narrower than those proposed in the literature. We formulate an objection to some of these concepts of randomness. Using the(More)
Let Ai(L), Ai(L*) denote the successive minima of a lattice L and its reciprocal lattice L*, and let [bl,..., bn] be a basis of L that is reduced in the sense of Korkin and Zolotarev. We prove that [4/(/+ 3)]),i(L) 2 _< [bi[ 2 < [(i + 3)/4])~i(L) 2 and Ibil2An_i+l(L*) 2 <_ [(i + 3)/4][(n-i + 4)/417~ 2, where "y~ =-min(Tj : 1 < j _< n} and 7j denotes(More)
We introduce algorithms for lattice basis reduction that are improvements of the famous L 3-algorithm. If a random L 3 {reduced lattice basis b1; : : : ; bn is given such that the vector of reduced Gram{ Schmidt coeecients (fi;jg 1 j < i n) is uniformly distributed in 0; 1) (n 2) , then the pruned enumeration nds with positive probability a shortest lattice(More)