Hash-enhanced elliptic curve bit-string generator for medical image encryption

Abstract

Bit-string generator (BSG) is based on the hardness of known number theoretical problems, such as the discrete logarithm problem with the elliptic curve (ECDLP). Such type of generators will have good randomness and unpredictability properties as it is challenged to find a solution regarding this mathematical dilemma. Hash functions in turn play a remarkable role in many cryptographic tasks to accomplish different security levels. Hash-enhanced elliptic curve bit-string generator (HEECBSG) mechanism is proposed in this study based on the ECDLP and secure hash function. The cryptographic hash function is used to achieve integrity and security of the obtained bit-strings for highly sensitive plain data. The main contribution of the proposed HEECBSG is transforming the x-coordinate of the elliptic curve points using a hash function H to generate bit-strings of any desirable length. The obtained pseudo-random bits are tested by the NIST test suite to analyze and verify its statistical and randomness properties. The resulted bit-string is utilized here for encrypting various medical images of the vital organs, i.e. the brain, bone, fetuses, and lungs. Then, extensive evaluation metrics have been applied to analyze the successful performance of the cipherimage, including key-space analysis, histogram analysis, correlation analysis, entropy analysis and sensitivity analysis. The results demonstrated that our proposed HEECBSG mechanism is feasible for achieving security and privacy purposes of the medical image transmission over unsecure communication networks.