Primality Testing and Integer Factorization in Public-Key Cryptography

The book delves into the significant advancement in computational number theory, highlighting the AKS algorithm's ability to solve the Primality Testing Problem in deterministic polynomial time. In contrast, it emphasizes the ongoing challenge of the Integer Factorization Problem, which lacks a polynomial-time solution and underpins the security of widely used public-key cryptosystems like RSA. The discussion underscores the implications of these findings for cryptography and computational complexity.