{'fraction_non_alphanumeric': 0.031724137931034485, 'fraction_numerical': 0.002758620689655172, 'mean_word_length': 5.205128205128205, '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}}
Cryptosystems with a multi prime composite modulus

Multi-Prime (MP)RSA is an RSA construction in which the public modulus is a product of more than two primes, and its private key operations can be accelerated by using the Chinese Reminder Theorem (CRT). While MPRSA has been studied extensively, only limited information is found for other MP constructions, such as Paillier cryptosystem. This paper shows how to extend the security proofs for Quadratic Residue Problem (QRP), Higher Residuosity Problem (HRP) and Decisional Composite Residuosity Problem (DCRP), formulated for a two-primes modulus, to a MP setting. For the Paillier cryptosystem, we demonstrate how this technique can speed up decryption by more than 17x.