{'fraction_non_alphanumeric': 0.029259896729776247, 'fraction_numerical': 0.0, 'mean_word_length': 4.82, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, '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}}
Some Properties of Algebraic Structures of RSA-like Systems

The algebraic structure Z_n^* , with n being a product of safe primes, is widely used in RSA-like cryptosystems. We have investigated some properties of this kind of structure. Isomorphic structures are presented to represent elements of Z_n^* in a unique way. They also help to determine the form and the number of possible subgroups, to find, in a deterministic rather than probabilistic manner, the elements of any possible orders. The properties of quadratic and high degree residues are analyzed in detail, as well.