{'fraction_non_alphanumeric': 0.03303055326176713, 'fraction_numerical': 0.00990916597853014, 'mean_word_length': 4.7440758293838865, '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}}
Efficient On-line/Off-line Signature Schemes Based on Multiple-Collision Trapdoor Hash Families

The first on-line/off-line signature scheme introduced by Even et al. in 1990 has two problems: (a) impractical signature length and (b) a one-time use of signature generated during the off-line phase. In 2001, Shamir and Tauman significantly shortened the length of the signature by using trapdoor hash families introduced by Krawczyk and Rabin in 2000. However, each trapdoor hash value and its signature in the off-line phase of Shamir and Tauman's signature scheme can be used for signing only one message in the on-line phase. In this paper, we propose multiple-collision trapdoor hash families based on discrete logarithm and factoring assumptions, and provide formal proofs of their security. We also introduce an efficient on-line/off-line signature scheme based on our proposed trapdoor hash families. Our on-line/off-line signature scheme can re-use a trapdoor hash value for signing multiple messages. If a signer includes this trapdoor hash value in the public-key digital certificate, there is no need to have any regular digital signature scheme to sign the trapdoor hash value in the off-line phase.