Abstract
The compression feature of compressed sensing (CS) enables that the ciphertext lengths of multimedia encryption schemes have reduced dramatically, and the simple linear measurements make the encryption process extremely efficient. Therefore, CS based image encryption schemes have attached wide attentions in recent years. However, almost all CS based image encryption schemes follow the framework of symmetric encryption. In this paper, we propose the first CS based public key image encryption scheme PKIE-CS with accurate decryption. As is known to all, two important conditions for successful signal reconstruction in CS are signal sparsity and measurement matrix satisfying some properties (e.g., restricted isometry property). In our scheme, the relationship between the public key and the secret key can be expressed by B P [T; I] = A T P, where BP and A are public parameters, T is the secret key, and BP can not be used as the measurement matrix in CS. Thus, anyone can not extract the secret key T from public key. We first give the specific descriptions of PKIE-CS and then give some theoretical analysis for providing strong security evidence. Last, the experimental results and the comparison with similar works demonstrate the feasibility and the superiority of the proposed scheme.
Highlights
Based on sparse representations of signals, a famous signal sampling theory, called compressed sensing (CS), has been presented approximately fifteen years ago [1]–[3]
The results show that if the number of source messages goes to infinity and the number of measurements is more than two times of the sparsity level, the Shannon-sense perfect secrecy is achievable when the measurement matrix satisfies the restricted isometery property
We present a method for constructing public key image encryption (PKIE) scheme based on CS
Summary
Based on sparse representations of signals, a famous signal sampling theory, called compressed sensing (CS), has been presented approximately fifteen years ago [1]–[3]. What’s more, CS-based encryption schemes can directly act on the plaintext, and some traditional cryptographic encryption schemes (e.g., DES and AES) are bit-level data processing approaches. It is very time-consuming for multimedia plaintexts (e.g., image and video). Almost all proposed CS-based encryption schemes follow the framework described, where the measurement matrix plays the role of the private key in this cryptosystem. This encryption model is very simple, and the efficiency of encryption process is very high because it just requires one matrix multiplication.
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