{'fraction_non_alphanumeric': 0.026260504201680673, 'fraction_numerical': 0.005252100840336135, 'mean_word_length': 5.482993197278912, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 1, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Integer Factorization: Solution via Algorithm for Constrained Discrete Logarithm Problem

Problem statement: During the last thirty years many public-key cryptographic protocols based on either the complexity of integer factorization of large semiprimes or the Discrete Logarithm Problem (DLP) have been developed. Approach: Although several factorization algorithms with sub-exponential complexity have been discovered, the recent RSA Factoring Challenge demonstrated that it was still necessary to use several thousand computers working in a coordinated effort for several months to factor an integer n that was a product of two primes. Results: In this research it was demonstrated how to find integer factors of n using an algorithm for a constrained DLP. Several numerical examples illustrate details of the algorithms. One of these algorithms has O(3√n) complexity and, if the search is balanced, it has complexity O(n1/3log1/α n), where alpha>1.