Security Analysis of Compressed Encryption With Sparse Matrices Against Chosen Plaintext Attacks

Abstract

In this paper, we study the security of a compressed sensing (CS) based cryptosystem that encrypts a plaintext with a sparse measurement matrix. The secret matrix is constructed by a bipolar keystream and a random permutation, and renewed at each encryption. The CS-based cryptosystem performs efficient encryption with a small number of nonzero entries in the matrix, and guarantees reliable decryption for a legitimate recipient. Through a quantitative analysis, we demonstrate that the CS-based cryptosystem achieves the security against a chosen plaintext attack (CPA) with overwhelmingly high probability, by showing that an adversary needs to distinguish a prohibitively large number of candidate keystreams.