Adjusting Three Schemes of Anonymous User Identification and Key Distribution

User identification, user anonymity, mutual authentication and key distribution are desirable features for securing communication in a distributed network. Yang et al, Mangipudi-Katti and Hsu-Chuang in a new efficient user identification and key distribution scheme providing enhanced security, a secure identification and key agreement protocol with user anonymity (SIKA) and a novel user identification scheme with key distribution preserving user anonymity respectively were schemes proposed for these security features. They all have a problem related with not existence of inverses of identifiers used in them. Identifiers and signatures were selected and not all the identifiers have inverse identifiers modulus N. The inverse of identifiers selected for use will not exist in all cases as the probability of selecting of non-invertible identifiers modulus N goes to one leading to the failure of the schemes that is demonstrated in this present research. In this thesis, we propose a way to improve the problem by coming up with a two theorems. The first theorem is a procedure which will ensure selection of identifiers that will always have inverse identifiers under condition of usage of RSA – likekey settings which are kept secret (prime factorization of N =p*q). This procedure has one input N=p*q which is the public parameter received from a Smart Card producing Center, a trusted third party, where p, q>2 are unknown primes, and one output identifier which is any integer number between 2 and N-1, invertible modulo N. We also show that the output identifier will always have invertible mod N and invertible signatures mod N. The second theorem guarantees that the output identifier selected in the first theorem will also have invertible identifier modulo N and it’s encrypted value will also invertible modulo N. The proposed improvement ensures the schemes preserve their features and will be efficient with no computational complexities and increased communication cost. Keywords: Identifier, inverse, authentication, prime number, factorization