1970-01-01

(2026-08) Upper bounds for failure probabilities of reductions from low density subset sum problems to lattice problems on linearly independent vectors

• Shoichi Kamada

2026-08-11

• #cryptography
• #paper

Abstract

As a new lattice problem, we introduce $l$-Shortest Independent Vectors Problem ($l$-SIVP for short), where $l$ is a positive integer no greater than the rank of a lattice. In the case where $l=1$, $l$-SIVP means SVP, and in the case where $l$ is the rank of a lattice, $l$-SIVP means SIVP. We estimate upper bounds on the failure probabilities of the reductions from the subset sum problems to the $l$-SIVPs in terms of Ehrhart theory. Especially, in the case of $l=1$, our upper bound is tighter than the previous result given by Coster et al. We give some considerations for dominating terms of our upper bounds of failure probabilities when $l$ is general.