  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.
