Secure and Efficient Compressed Sensing-Based Encryption With Sparse Matrices

Abstract

In this paper, we study the security of a compressed sensing (CS) based cryptosystem called a sparse one-time sensing (S-OTS) cryptosystem, which encrypts a plaintext with a sparse measurement matrix. To construct the secret matrix and renew it at each encryption, a bipolar keystream and a random permutation pattern are employed as cryptographic primitives, which can be obtained by a keystream generator of stream ciphers. With a small number of nonzero elements in the measurement matrix, the S-OTS cryptosystem achieves efficient CS encryption in terms of memory and computational cost. In security analysis, we show that the S-OTS cryptosystem can be indistinguishable as long as each plaintext has constant energy, which formalizes computational security against ciphertext only attacks (COA). In addition, we consider a chosen plaintext attack (CPA) against the S-OTS cryptosystem, which consists of two sequential stages, keystream and key recovery attacks. Against keystream recovery under CPA, we demonstrate that the S-OTS cryptosystem can be secure with overwhelmingly high probability, as an adversary needs to distinguish a prohibitively large number of candidate keystreams. Finally, we conduct an information-theoretic analysis to show that the S-OTS cryptosystem can be resistant against key recovery under CPA by guaranteeing that the probability of success is extremely low. In conclusion, the S-OTS cryptosystem can be computationally secure against COA and the two-stage CPA, while providing efficiency in CS encryption.

Computationally Efficient and Secure Kronecker-based Compressive Sensing

“…In [65], the security of a CS-based cryptosystem called Sparse One-Time Sensing (S-OTS) cryptosystem is studied. S-OTS encrypts plaintext with a sparse measurement matrix.…”

“…In the security analysis, the authors of [65] show that S-OTS cryptosystem can be indistinguishable as long as each plaintext has constant energy, which formalizes computational security against COA. In addition, a chosen PA [49] is considered against the proposed method, which consists of two sequential stages: keystream and key recovery attacks.…”

“…We choose two most relevant methods proposed in the literature in order to compare with our method described in Chapter 3: SBCM [59] and S-OTS [65]. The main reason behind this choice is that we have control on the sparsity of the measurement matrix.…”

“…A literature review on the security aspects of CS has been provided in Section 2.2. We propose a structure for CSC and compare it with a recent most relevant method in the literature called S-OTS [65].…”

“…The matrix P is created by rearranging columns of the identity matrix. We sequentially select columns of identity matrix according to the generated array of N distinct random numbers and place them in P. The number of SSG bits needed to shuffle the identity matrix to generate P is in the order of N log 2 (N ) [65].…”