Given a real vector =(1; : : : ; d) and a real number " > 0 a good Diophantine approximation to is a number Q such that kQQ mod Zk1 ", where k k1 denotes thè1-norm kxk1 := max 1id jxij for x = (x1; :… (More)

We address to the problem to factor a large composite number by lattice reduction algorithms Schnorr Sc has shown that under a reasonable number theoretic assumptions this problem can be reduced to a… (More)

We analyse a continued fraction algorithm (abbreviated CFA) for arbitrary dimension n showing that it produces simultaneous diophantine approximations which are up to the factor 2 (n+2)=4 best… (More)

We call a vector x 2 IR n highly regular if it satisses < x ; m > = 0 for some short, non{zero integer vector m where < : ; : > is the inner product. We present an algorithm which given x 2 IR n and… (More)

We analyse a continued fraction algorithm (abbreviated CFA) for arbitrary dimension n showing that it produces simultaneous diophantine approximations which are up to the factor 2 (n+~)/4 best… (More)

Given x 2 R n an integer relation for x is a non-trivial vector m 2 Z n with inner product hm; xi = 0. In this paper we prove the following: Unless every NP language is recognizable in deterministic… (More)