Investigation on secure random numbers for key generation in cryptographic algorithms

Abstract

Communication is the exchange of information in any form. Cryptography is a diverse field that plays a critical role in modern day communications. Information is shared in every corner of the world in numerous forms. Users have a great concern for privacy and confidentiality of the data they share. Cryptographic algorithms lend them a hand by providing the required security. Encryption is used to provide confidentiality, digital signatures provide authentication, hashing algorithms provide integrity and so on. Cryptographic algorithms encrypt the data using either a shared secret key or a public-private key pair. The secret key cryptography, also known as Symmetric cryptography, is faster in encrypting the data compared to the public key cryptography. The modern day security algorithms greatly depend on secret key encryption. Key generation algorithms have been researched for a long time to produce cryptographically secure random numbers. Key generation enforces some requirements like longer periodicity, uniformity, independence for robustness; the keys must be secure and random enough to be unpredictable by attackers and the keys of enough length must be generated at a low computation cost. Public key cryptography requires a mathematical relation between the public key and its private key. Generating random keys is helpful only for secret key encryption where no relation among the keys is required. Random number generators are widely used in generating secret keys. When a user provides the generator with an initial secret key, the generator starts generating a sequence of secret key bits of required lengths. The cryptographic techniques were used only for securing textual data in olden days. With advancements in communication, users are in need of securing multimedia data. Encryption of multimedia data requires longer secret key sequence and this poses a thrust to generators to produce longer key sequence without repetition of random numbers. Chaotic systems are good key generators and are controlled by their sy