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- Claus-Peter Schnorr
- J. Cryptology
- 1991

- Claus-Peter Schnorr, M. Euchner
- Math. Program.
- 1991

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)

- Claus-Peter Schnorr
- CRYPTO
- 1989

- Matthijs J. Coster, Antoine Joux, Brian A. LaMacchia, Andrew M. Odlyzko, Claus-Peter Schnorr, Jacques Stern
- Computational Complexity
- 1992

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 suuciently low density. Both methods rely on basis reduction algorithms to nd short non-zero vectors in special lattices. The Lagarias-Odlyzko algorithm… (More)

- Claus-Peter Schnorr
- Theor. Comput. Sci.
- 1987

- Jeffrey C. Lagarias, Hendrik W. Lenstra, Claus-Peter Schnorr
- Combinatorica
- 1990

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)

- Werner Alexi, Benny Chor, Oded Goldreich, Claus-Peter Schnorr
- SIAM J. Comput.
- 1988

- Claus-Peter Schnorr, Horst Helmut Hörner
- Electronic Colloquium on Computational Complexity
- 1995

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)

- Joos Heintz, Claus-Peter Schnorr
- STOC
- 1980

We exploit the fact that the set of all polynomials Pε@@@@[x<subscrpt>1</subscrpt>,..,x<subscrpt>n</subscrpt>] of degree ≤d which can be evaluated with ≤v nonscalar steps can be embedded into a Zariski-closed affine set W(d,n,v),dim W(d,n,v)≤(v+1 +n)<supscrpt>2</supscrpt> and deg… (More)

- Claus-Peter Schnorr, Adi Shamir
- STOC
- 1986

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 algorithm which sorts the array by alternately sorting its rows and columns log log n times.