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Harunaga HIWATARI Keisuke TANAKA
At Eurocrypt '02, Cramer and Shoup [1] proposed a general paradigm to construct practical public-key encryption schemes secure against the adaptive chosen ciphertext attack as well as several concrete examples. One of these example is the scheme based on the quadratic residuosity (QR) problem. However this scheme is less efficient than the other examples. In this paper, we construct a new variant of the Cramer-Shoup encryption scheme which is related to the QR problem. Our variant is more efficient than the scheme based on the QR problem.
Taiichi SAITO Takeshi KOSHIBA Akihiro YAMAMURA
This paper examines similarities between the Decision Diffie-Hellman (DDH) assumption and the Quadratic Residuosity (QR) assumption. In addition, we show that many cryptographic protocols based on the QR assumption can be reconstructed using the DDH assumption.
We formalize a model of "demonstration of program result-correctness," and investigate how to prove this fact against possible adversaries, which naturally extends Blum's theory of program checking by adding zero-knowledge requirements. The zero-knowledge requirements are universal for yes and no instances alike.
We define the communication complexity of a perfect zero-knowledge interactive proof (ZKIP) as the expected number of bits communicated to achieve the given error probabilities (of both the completeness and the soundness). While the round complexity of ZKIPs has been studied greatly, no progress has been made for the communication complexity of those. This paper shows a perfect ZKIP whose communication complexity is 11/12 of that of the standard perfect ZKIP for a specific class of Quadratic Residuosity.