Cryptographically Secure Diffusion Sequences—An Attempt to Prove Sequences Are Random

The use of random numbers in day-to-day digital life is increasing drastically to make the digital data more secure in various disciplines, particularly in cryptography, cloud data storage, and big data applications. Generally, all the random numbers or sequences are not truly random enough to be used in various applications of randomness, predominantly in cryptographic applications. Therefore, the sequences generated by pseudorandom number generator (PRNGs) are not cryptographically secure. Hence, this study proposes a concept that the diffusion sequences which are used during cryptographic operations need to be validated for randomness, though the random number generator produces the random sequences. This study discusses the NIST, Diehard and ENT test suite results of random diffusion sequences generated by two improved random number generators namely, Enhanced Chaotic Economic Map (ECEM), and Improved Linear Congruential Generator (ILCG).