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We say that an encryption scheme or a signature scheme provides anonymity when it is infeasible to determine which user generated a ciphertext or a signature. To construct the schemes with anonymity, it is necessary that the space of ciphertexts or signatures is common to each user. In this paper, we focus on the techniques which can be used to obtain this anonymity property, and propose a new technique for obtaining the anonymity property on RSA-based cryptosystem, which we call “sampling twice.” It generates the uniform distribution over 2k by sampling the two elements from ${\mathbb Z}_N$ where |N| = k. Then, by applying the sampling twice technique, we construct the schemes for encryption, undeniable and confirmer signature, and ring signature, which have some advantage to the previous schemes.

The Sampling Twice Technique for the RSA-Based Cryptosystems with Anonymity