Elliptic Curve Unpredictable Random Number Generator for Cryptographic Applications

Abstract

Random number generators are widely used for cryptographic applications such as interleaver, random key generation, stream cipher and others. Researchers have attempted to generate random numbers using elliptic curve arithmetic. However, one of the limitations of the existing schemes is large computational complexity. This paper presents an Elliptic Curve Unpredictable Random Number Generator (EC-URNG) based on the arithmetic of the elliptic curve and a secret look up table.  The look up table is generated using a secret mask key and a secret generator point. Elliptic Curve Discrete Logarithm Problem (ECDLP) provides strong cryptographic strength to the proposed generator and makes it computationally infeasible to predict the secret look up table. Computational complexity, periodicity and security analysis of the proposed generator show better performance as compared to the existing schemes. In addition, the sequence generated by EC-URNG successfully qualifies the FIPS 140-2 statistical test for the cryptographic standard. Application of the proposed EC-URNG to encrypt images shows an entropy of almost 7.9 and a correlation coefficient of almost 0. On the other hand, the decrypted images show a successful recovery of a secret image with a PSNR greater than 50 dB for an authorized user and a PSNR less than 8 dB for an unauthorized user.