Self-Witnessing Polynomial-Time Complexity and Prime Factorization

For a number of computational search problems the existence of a polynomial time algorithm for the problem implies that a polynomial time algorithm for the problem is constructively known Some instances of such self witnessing polynomial time complexity are presented Our main result demonstrates this property for the problem of computing the prime factorization of a positive integer based on a lemma which shows that a certi cate for primality or compositeness can be constructed for a positive integer p in deterministic polynomial time given a complete factorization of p