Paillier's cryptosystem modulo p2q and its applications to trapdoor commitment schemes

Katja Schmidt-Samoa, Tsuyoshi Takagi

研究成果: Chapter in Book/Report/Conference proceedingConference contribution

15 被引用数 (Scopus)

抄録

In 1998/99, T. Okamoto and S. Uchiyama on the one hand and P. Paillier on the other hand introduced homomorphic encryption schemes semantically secure against passive adversaries (IND-CPA). Both schemes follow in the footsteps of Goldwasser-Micali, Benaloh-Fischer and Naccache-Stern cryptosystems, and yield their improvements above the latter by changing the group structure. Paillier's scheme works in the group ℤn2x where n is an RSA modulus, whilst Okamoto-Uchiyama is located in the group Zn x for n of p2q type. The new schemes attracted much attention because of their rich mathematical structure. It is notable that Okamoto-Uchiyama is one-way under the p2q factoring assumption, whilst there is no reduction known from the one-wayness of Paillier's scheme to a standard computational assumption. In this paper we point out that the combination of both techniques yields a new scheme that inherits all the nice properties of Paillier's scheme and that is one-way under the p2q factoring assumption. The one-wayness is based on a new trapdoor one-way function which might be of independent interest. In addition, we show how to construct trapdoor commitment schemes with practical applications based on our new scheme and on the trapdoor function. Among other things, we propose a trapdoor commitment scheme that perfectly meets the requirements to construct Shamir-Tauman on-line/off-line signatures.

本文言語英語
ホスト出版物のタイトルLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
ページ296-313
ページ数18
DOI
出版ステータス出版済み - 12 1 2005
イベント1st International Conference on Cryptology in Malaysia on Progress in Cryptology - Mycrypt 2005 - Kuala Lumpur, マレーシア
継続期間: 9 28 20059 30 2005

出版物シリーズ

名前Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
3715 LNCS
ISSN(印刷版)0302-9743
ISSN(電子版)1611-3349

その他

その他1st International Conference on Cryptology in Malaysia on Progress in Cryptology - Mycrypt 2005
国/地域マレーシア
CityKuala Lumpur
Period9/28/059/30/05

All Science Journal Classification (ASJC) codes

  • 理論的コンピュータサイエンス
  • コンピュータ サイエンス(全般)

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