scholarly journals Lattice basis reduction, Jacobi sums and hyperelliptic cryptosystems

1998 ◽  
Vol 58 (1) ◽  
pp. 147-154 ◽  
Author(s):  
Joe Buhler ◽  
Neal Koblitz
Keyword(s):  
Lattice Basis Reduction ◽  
Lll Algorithm ◽  
Prime Field ◽  
Jacobi Sums ◽  
Jacobi Sum ◽  
Basis Reduction

Using the LLL-algorithm for finding short vectors in lattices, we show how to compute a Jacobi sum for the prime field Fp in Q(e2πi/n) in time O(log3p), where n is small and fixed, p is large, and p = 1 (mod n). This result is useful in the construction of hyperelliptic cryptosystems.

Solving the FCSR synthesis problem for multi-sequences by lattice basis reduction

2017 ◽  
Vol 86 (5) ◽  
pp. 1023-1038 ◽  
Author(s):  
Weihua Liu ◽  
Andrew Klapper ◽  
Zhixiong Chen
Keyword(s):  
Synthesis Problem ◽  
Lattice Basis Reduction ◽  
Basis Reduction

scholarly journals Perturbation Analysis of the QR factor R in the context of LLL lattice basis reduction

2012 ◽  
Vol 81 (279) ◽  
pp. 1487-1511 ◽  
Author(s):  
Xiao-Wen Chang ◽  
Damien Stehlé ◽  
Gilles Villard
Keyword(s):  
Perturbation Analysis ◽  
Lattice Basis Reduction ◽  
Basis Reduction
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