Cryptographic Attack Possibilities over RSA Algorithm through Classical and Quantum Computation

Cryptographic attack possibilities have several parameters and one of the possibilities is to attack over the cryptographic algorithm. Large integer factorization is still a challenging problem since the emergence of mathematics and computer science. Benchmark cryptographic protocol, the RSA Algorithm requires factorization of large integers. Classical computation does not have any polynomial time algorithm that can factor any arbitrary large integer. The remarkable but not efficient, classical algorithms for integer factorization are Trial Division, General Number Field Sieve and Quadratic Sieve. The influence of Shor's algorithm assures to get the efficient solution of such factorization problem in polynomial time and challenges the security parameters of the existing cryptosystem, but algorithm implementation limits to be executed on a quantum computer. The article illustrates the algorithms along with flowcharts and implements, Trial Division, Quadratic Sieve Algorithm and Shor's Algorithm for factoring integers and lastly concludes with the observed facts and analyzed results.