Claus-Peter Schnorr

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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 reduc tion We propose a practical oating point version of the L algorithm of Lenstra Lenstra Lov asz We present a variant of the L algorithm with deep insertions and a practical algorithm for block Korkin Zolotarev reduction a concept introduced by Schnorr Empirical tests show that the strongest(More)
(1) We propose an efficient algorithm to preprocess the exponentiation of random numbers. This preprocessing makes signature generation very fast. It also improves the efficiency of the other discrete log-cryptosystems. The preprocessing algorithm is based on two fundamental principles local randomization and internal randomization. (2) We use a prime(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)
In this paper we prove a 3n upper and lower bound on the complexity of sorting on a n × n mesh connected parallel computer , and describe an exceptionally simple algori thm which sorts the array by al ternately sorting its rows and columns log log n times. 1. I n t r o d u c t i o n Sorting is a fundamental problem with a rich theory and important practical(More)
Let Ai(L), Ai(L*) denote the successive minima of a lattice L and its reciprocal lattice L*, and let [b l , . . . , 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)