Secure matrix generation for Compressive Sensing embedded cryptography

Confidentiality, entity authentication and nonrepudiation are security mechanisms, used to protect data against unauthorized access or manipulation. Hereby, the security and the reliability directly depend on the key. To secure a communication using Compressive Sensing (CS), the measurement matrix can be used as a key if it fulfill some requirements. However, the negotiation and the exchange of this matrix as required in standard cryptography, will leads to a massive overhead. Instead, both sides of the communication should share a secret key and additional parameters, which are used to generate the secret measurement matrix. Prior work on the measurement matrix generation mainly focus on sensing requirements and provides neither the requirements for the secret key nor the requirements for the key generation or derivation mechanisms. In this paper we first define the secret matrix requirements as well as the requirements for secret matrix generation or derivation mechanisms, in accordance with the NIST SP 800-90A standard. Then we propose a solution for the generation of secret matrices for CS embedded cryptography. The designed Secure CS Matrix Generator (SCS-MG) uses existing deterministic matrix constructions, which are appropriate for particular applications, as input. The generated secret matrices fulfill the requirements of the corresponding CS based applications and the requirements of a cryptographic key. The SCS-MG, considers the invariance of the Spark, the NSP order and the RIP order of CS measurement matrices, under elementary column and row transformation of this matrices.