Direct range proofs for Paillier cryptosystem and their applications
The Paillier cryptosystem is renowned for its applications in electronic voting, threshold ECDSA, multi-party computation, and more, largely due to its additive homomorphism. In these applications, range proofs for the Paillier cryptosystem are crucial for maintaining security, because of the mismat...
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sg-smu-ink.sis_research-107492024-12-16T03:25:02Z Direct range proofs for Paillier cryptosystem and their applications XIE, Zhikang LIU, Mengling XUE, Haiyang AU, Man Ho DENG, Robert H. YIU, Siu-Ming The Paillier cryptosystem is renowned for its applications in electronic voting, threshold ECDSA, multi-party computation, and more, largely due to its additive homomorphism. In these applications, range proofs for the Paillier cryptosystem are crucial for maintaining security, because of the mismatch between the message space in the Paillier system and the operation space in application scenarios. In this paper, we present novel range proofs for the Paillier cryptosystem, specifically aimed at optimizing those for both Paillier plaintext and affine operation. We interpret encryptions and affine operations as commitments over integers, as opposed to solely over ZN. Consequently, we propose direct range proof for the updated cryptosystem, thereby eliminating the need for auxiliary integer commitments as required by the current state-of-the-art. Our work yields significant improvements: In the range proof for Paillier plaintext, our approach reduces communication overheads by approximately 60%, and computational overheads by 30% and 10% for the prover and verifier, respectively. In the range proof for Paillier affine operation, our method reduces the bandwidth by 70%, and computational overheads by 50% and 30% for the prover and verifier, respectively. Furthermore, we demonstrate that our techniques can be utilized to improve the performance of threshold ECDSA and the DCR-based instantiation of the Naor-Yung CCA2 paradigm. 2024-10-01T07:00:00Z text application/pdf https://ink.library.smu.edu.sg/sis_research/9749 https://ink.library.smu.edu.sg/context/sis_research/article/10749/viewcontent/2024_1355.pdf http://creativecommons.org/licenses/by-nc-nd/4.0/ Research Collection School Of Computing and Information Systems eng Institutional Knowledge at Singapore Management University Public-key cryptography Paillier cryptosystem. Range proof Multiplicative-to-additive function Threshold ECDSA Naor-Tung CCA2. Sigma protocol Information Security |
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Public-key cryptography Paillier cryptosystem. Range proof Multiplicative-to-additive function Threshold ECDSA Naor-Tung CCA2. Sigma protocol Information Security |
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Public-key cryptography Paillier cryptosystem. Range proof Multiplicative-to-additive function Threshold ECDSA Naor-Tung CCA2. Sigma protocol Information Security XIE, Zhikang LIU, Mengling XUE, Haiyang AU, Man Ho DENG, Robert H. YIU, Siu-Ming Direct range proofs for Paillier cryptosystem and their applications |
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The Paillier cryptosystem is renowned for its applications in electronic voting, threshold ECDSA, multi-party computation, and more, largely due to its additive homomorphism. In these applications, range proofs for the Paillier cryptosystem are crucial for maintaining security, because of the mismatch between the message space in the Paillier system and the operation space in application scenarios. In this paper, we present novel range proofs for the Paillier cryptosystem, specifically aimed at optimizing those for both Paillier plaintext and affine operation. We interpret encryptions and affine operations as commitments over integers, as opposed to solely over ZN. Consequently, we propose direct range proof for the updated cryptosystem, thereby eliminating the need for auxiliary integer commitments as required by the current state-of-the-art. Our work yields significant improvements: In the range proof for Paillier plaintext, our approach reduces communication overheads by approximately 60%, and computational overheads by 30% and 10% for the prover and verifier, respectively. In the range proof for Paillier affine operation, our method reduces the bandwidth by 70%, and computational overheads by 50% and 30% for the prover and verifier, respectively. Furthermore, we demonstrate that our techniques can be utilized to improve the performance of threshold ECDSA and the DCR-based instantiation of the Naor-Yung CCA2 paradigm. |
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XIE, Zhikang LIU, Mengling XUE, Haiyang AU, Man Ho DENG, Robert H. YIU, Siu-Ming |
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XIE, Zhikang LIU, Mengling XUE, Haiyang AU, Man Ho DENG, Robert H. YIU, Siu-Ming |
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XIE, Zhikang |
title |
Direct range proofs for Paillier cryptosystem and their applications |
title_short |
Direct range proofs for Paillier cryptosystem and their applications |
title_full |
Direct range proofs for Paillier cryptosystem and their applications |
title_fullStr |
Direct range proofs for Paillier cryptosystem and their applications |
title_full_unstemmed |
Direct range proofs for Paillier cryptosystem and their applications |
title_sort |
direct range proofs for paillier cryptosystem and their applications |
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Institutional Knowledge at Singapore Management University |
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2024 |
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https://ink.library.smu.edu.sg/sis_research/9749 https://ink.library.smu.edu.sg/context/sis_research/article/10749/viewcontent/2024_1355.pdf |
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