A study of prime numbers distribution based on support vector domain description

Abstract

Prime numbers are fundamental to the most common type of asymmetric encryption used today, namely Diffie-Hellman key exchange, Rivest-Shamir-Adleman cryptosystems, ElGamal Cryptosystem, Elliptic curve cryptosystems, etc. The strength of primes lies in the fact that they are the ‘building blocks’ of mathematics and in addition there is infinity of them with no apparent regularity in their distribution. Given these characteristics, they were used to build efficient one way functions used in public key cryptography. This work aims at exploring sets of prime numbers with the objective of finding patterns in their structure. For this purpose an efficient supervised learning model called Support Vector Domain Description was used as an explorer. The experimental results have shown a good generalization capability of this model to describe new prime numbers.

Subject Classification:

• 68T05
• 68Q32
• 68T10
• 11A41
• 11A51

Keywords:

• Prime numbers
• Cryptology
• Patterns
• Support vector domain description
• Generalization capacity