  The principle of compressed sensing (CS) can be applied in a cryptosystem by
providing the notion of security. In information-theoretic sense, it is known
that a CS-based cryptosystem can be perfectly secure if it employs a random
Gaussian sensing matrix updated at each encryption and its plaintext has
constant energy. In this paper, we propose a new CS-based cryptosystem that
employs a secret bipolar keystream and a public unitary matrix, which can be
suitable for practical implementation by generating and renewing the keystream
in a fast and efficient manner. We demonstrate that the sensing matrix is
asymptotically Gaussian for a sufficiently large plaintext length, which
guarantees a reliable CS decryption for a legitimate recipient. By means of
probability metrics, we also show that the new CS-based cryptosystem can have
the indistinguishability against an adversary, as long as the keystream is
updated at each encryption and each plaintext has constant energy. Finally, we
investigate how much the security of the new CS-based cryptosystem is sensitive
to energy variation of plaintexts.
