Application of Logistic Equations for Generation of Symmetric Keys in Cryptography

Abstract

Key management deals with the planning, secure generation, distribution, and storage of keys. Once a key is randomly generated, it must remain secret to avoid unfortunate mishaps and is used for encryption and decryption. Modern cryptographic systems include symmetric key algorithms and public key algorithms for the purpose of providing confidentiality. Symmetric system requires prior sharing of key; hence it is impossible to communicate with unknown users. The key generation in the symmetric crypto system has highly complicated internal structure which involves more number of iterations and cannot be supported by embedded systems and other low powered devices. Considering asymmetric systems, even though it avoids pre sharing of keys, the usage of large primes increases the time complexity of encryption and decryption and also the storage space requirement. Our proposed system for random key generation is designed using logistic equations aiming at independent generation of keys at sender and receiver with minimal parameter exchange offering the same level of security. Key generation involves the exchange of seed value, start value, skip value and precision supported by the calculating machines. The keys generated can be used as session keys which are used for very short duration of time. This enables the encryption algorithm to be as simple as possible like use of Exclusive-OR operations between keys and the plain text. Experimental results proves the efficiency of key generation exhibiting high randomness as specified by National Institute of Standards and Technology (NIST) involving less computational power in terms of time and space and with no compromise in security.