Introduction to the Generalized Principle of Rivest-Shamir-Adleman (RSA)
Public-Key Cryptosystem
Abstract
This result engenders the availability of a larger integer from which the encryption
keys are derivable. The RSA algorithm limits the set of such numbers to that
consisting of products of two primes. Such numbers as 2310, 4199, 2210269 for
example are excluded since each of these is a product of more than two primes.
This generalization makes such numbers as these available for use in encryption
key derivation. The security assurance is not compromised. In the RSA algorithm
all that is needed is to be able to find two factors of number from which the keys
have been derived. In the generalized version, what is involved in obtaining them
is a strong disincentive. That the complexity of the generalized algorithm is of the
same order as that of the original one is clear. What has changed is the cost of
obtaining the number n which is the product of s primes and not the encryption
operation itself.
This presentation will highlight the basic concepts of RSA, and its generalized
algorithm with examples.