On Accuracy of Testing Decryption Failure Rate for Encryption Schemes under the LWE Assumption

Abstract

Lattice-based encryption schemes are significant cryptographic primitives to defend information security against quantum menace, and the decryption failure rate is related to both theoretical and realistic security. We quantitatively analyze how the floating-point arithmetic and neglecting small probabilities impact the precision, and propose a new effective and efficient test of the failure probability. Therein explicit criteria are given to select the floating-point datatype and to decide which small probabilities should be abandoned. Furthermore, the outcome is theoretically ensured to meet a given precision. Moreover, by combining the heuristic estimate and the precise simulation, this test is more efficient than previously neglecting small probabilities in a practical way.