Formula omitted] Lanczos revisited

Abstract

We present a new variant of the block Lanczos algorithm for finding vectors in the kernel of a symmetric matrix over F 2 . Our algorithm is at least as efficient as that of Montgomery [Peter L. Montgomery, A block Lanczos algorithm for finding dependencies over GF(2). in: Advances in Cryptology—EUROCRYPT’95 (Saint-Malo, 1995), Lecture Notes in Comput. Sci., vol. 921, Springer, Berlin, 1995, pp. 106–120], while the sequence of matrices W i constructed here have different algebraic properties that may be useful in eventually providing a provable upper bound on the time required to solve this problem. Namely, our W i satisfy W i T W j = 0 for i ≠ j as opposed to W i T AW j = 0 in [6].