RM- RSA algorithm

Abstract

The RSA public key cryptographic strength (either security of encryption and decryption schemes or efficiency of algorithms) depends upon the complexity in factorizing the largest integer into odd primes. For every chosen integer, the RSA’s strength varies. RSA key generation space is the group of non-negative integers relatively prime to φ(n) and encryption, decryption spaces are both equal to the group of integers relatively prime to n. Operational time and data storage are two of its efficiency aspects. To reduce the operational time along with reduction data storage is a difficult task in RSA public key cryptography. In addition that the Security of RSA public key cryptography for an adversary with polynomial bounds computations is another biggest task. In this paper, we are going to propose a new kind of public key cryptographic system, nearly four times more efficient in data storage and operational time to that of RSA and probably one fourth of security complexity of RSA. This new crypto system is possible only based on one of the strong pseudo prime test :Rabin-Miller test. So, name it as RM-RSA. In this way,we are going to compare the efficiency of that RM-RSA and previously our proposed S-RSA in “Solovay-Strassen test in a RSA Pubic key Cryptosystem”.

Subject Classification:

• 94A60

Keywords:

• Relatively prime
• Euler test
• Fermat test
• Solovay Strassen test
• Rabin-Miller test