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We report on improved practical algorithms for lattice basis reduction. We propose a practical floating point version of the L 3 -algorithm of Lenstra, Lenstra, Lovász (1982). We present a variant of the L 3 -algorithm with "deep insertions" and a practical algorithm for block Korkin-Zolotarev reduction, a concept introduced by Schnorr (1987). Empirical tests show that the strongest of these algorithms solves almost all subset sum problems with up to 66 random weights of arbitrary bit length within at most a few hours on a UNISYS 6000/70 or within a couple of minutes on a SPARC 1+ computer.

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We present an efficient interactive identification scheme and a related signature scheme that are based on discrete logarithms and which are particularly suited for smart cards. Previous cryptosystems, based on the discrete logarithm, have been proposed by El Gamal (1985),