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Table 2 Symmetric-key CS-based cryptosystem

From: On the security of compressed encryption with partial unitary sensing matrices embedding a secret keystream

Public

Subsampling operator R Ω

 

Unitary matrices U 1 and U 2

 

Structure of a keystream generator

Secret

Initial seed (or state) k∈{0,1}L of a keystream generator

Keystream generation

With the initial seed k, a keystream s∈{−1,+1}N is generated. The keystream s is renewed at each encryption.

CS encryption

With the keystream s and a plaintext \(\mathbf {x} \in {\mathbb {R}}^{N}\), a ciphertext is generated by \(\mathbf {r} = \boldsymbol {\Phi } \mathbf {x} + \mathbf {n} \in {\mathbb {R}}^{M} \), where \(\boldsymbol {\Phi } = \frac {1}{\sqrt {MN}} \mathbf {R}_{\Omega } \mathbf {U}_{1} \text {diag} (\mathbf {s}) \mathbf {U}_{2}\) and n is a measurement noise.

CS decryption

The plaintext x is reconstructed by a CS recovery algorithm with the knowledge of s.