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Title:
Zero knowledge proofs from ring-LWE
Author: Xie, Xiang (1) ; Xue, Rui (2) ; Wang, Minqian (1)
Conference Name: 12th International Conference on Cryptology and Network Security, CANS 2013
Conference Date: November 20, 2013 - November 22, 2013
Issued Date: 2013
Conference Place: Paraty, Brazil
Publish Place: Springer Verlag, Tiergartenstrasse 17, Heidelberg, D-69121, Germany
Indexed Type: EI
ISSN: 3029743
ISBN: 9783319029368
Department: (1) Trusted Computing and Information Assurance Laboratory, Institute of Software, Chinese Academy of Sciences, China; (2) State Key Laboratory of Information Security, Institute of Information Engineering, Chinese Academy of Sciences, China
Abstract: Zero-Knowledge proof is a very basic and important primitive, which allows a prover to prove some statement without revealing anything else. Very recently, Jain et al. proposed very efficient zero-knowledge proofs to prove any polynomial relations on bits, based on the Learning Parity with Noise (LPN) problem (Asiacrypt'12). In this work, we extend analogous constructions whose security is based on the Ring Learning with Errors (RLWE) problem by adapting the techniques presented by Ling et al. (PKC'13). Specifically, we show a simple zero-knowledge proof of knowledge (Σ-protocol) for committed values, and prove any polynomial relations in the underlying ring. I.e. proving committed ring elements m, m1 , ..., mt satisfying m = f (m 1 , ..., mt) for any polynomial f. Comparing to other existing Σ-protocols, the extracted witness (error vector) has length only small constant times than the one possessed by the prover. When representing ring element as elements in &Zdbl;q, our protocol has amortized communication complexity O˜(λ·|f|) with exponentially small soundness in security parameter λ, where |f| is the size of the circuit in &Zdbl;q computing f. © Springer International Publishing 2013.
English Abstract: Zero-Knowledge proof is a very basic and important primitive, which allows a prover to prove some statement without revealing anything else. Very recently, Jain et al. proposed very efficient zero-knowledge proofs to prove any polynomial relations on bits, based on the Learning Parity with Noise (LPN) problem (Asiacrypt'12). In this work, we extend analogous constructions whose security is based on the Ring Learning with Errors (RLWE) problem by adapting the techniques presented by Ling et al. (PKC'13). Specifically, we show a simple zero-knowledge proof of knowledge (Σ-protocol) for committed values, and prove any polynomial relations in the underlying ring. I.e. proving committed ring elements m, m1 , ..., mt satisfying m = f (m 1 , ..., mt) for any polynomial f. Comparing to other existing Σ-protocols, the extracted witness (error vector) has length only small constant times than the one possessed by the prover. When representing ring element as elements in &Zdbl;q, our protocol has amortized communication complexity O˜(λ·|f|) with exponentially small soundness in security parameter λ, where |f| is the size of the circuit in &Zdbl;q computing f. © Springer International Publishing 2013.
Language: 英语
Content Type: 会议论文
URI: http://ir.iscas.ac.cn/handle/311060/16690
Appears in Collections:软件所图书馆_会议论文

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Recommended Citation:
Xie, Xiang ,Xue, Rui ,Wang, Minqian . Zero knowledge proofs from ring-LWE[C]. 见:12th International Conference on Cryptology and Network Security, CANS 2013. Paraty, Brazil. November 20, 2013 - November 22, 2013.
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