scholarly journals A discrete logarithm blob for noninteractive XOR gates

1990 ◽  
Vol 19 (327) ◽  
Author(s):  
Joan Boyar ◽  
Ivan Bjerre Damgård

We present a bit commitment scheme based on discrete logarithms. Unlike earlier discrete log based schemes, our system allows non-interactive XORing and negation of bits contained in commitments. When used as a building block in zero-knowledge protocols, our scheme leads to protocols that are statistical (almost perfect) zero-knowledge, and where the prover is unable to break the system, unless he can find a secret discrete logarithm.

1996 ◽  
Vol 3 (7) ◽  
Author(s):  
Ivan B. Damgård ◽  
Ronald Cramer

We present a zero-knowledge proof system [19] for any NP language L, which<br />allows showing that x in L with error probability less than 2^−k using communication<br />corresponding to O(|x|^c) + k bit commitments, where c is a constant depending only<br />on L. The proof can be based on any bit commitment scheme with a particular set<br />of properties. We suggest an efficient implementation based on factoring.<br />We also present a 4-move perfect zero-knowledge interactive argument for any NP-language<br />L. On input x in L, the communication complexity is O(|x|^c) max(k; l)<br />bits, where l is the security parameter for the prover. Again, the protocol can be<br />based on any bit commitment scheme with a particular set of properties. We suggest<br />efficient implementations based on discrete logarithms or factoring.<br />We present an application of our techniques to multiparty computations, allowing<br />for example t committed oblivious transfers with error probability 2^−k to be done<br />simultaneously using O(t+k) commitments. Results for general computations follow<br />from this.<br />As a function of the security parameters, our protocols have the smallest known<br />asymptotic communication complexity among general proofs or arguments for NP.<br />Moreover, the constants involved are small enough for the protocols to be practical in<br />a realistic situation: both protocols are based on a Boolean formula Phi containing and-<br />, or- and not-operators which verifies an NP-witness of membership in L. Let n be<br />the number of times this formula reads an input variable. Then the communication<br />complexity of the protocols when using our concrete commitment schemes can be<br />more precisely stated as at most 4n + k + 1 commitments for the interactive proof<br />and at most 5nl +5l bits for the argument (assuming k <= l). Thus, if we use k = n,<br />the number of commitments required for the proof is linear in n.<br />Both protocols are also proofs of knowledge of an NP-witness of membership in<br />the language involved.


2012 ◽  
Vol 263-266 ◽  
pp. 3076-3078
Author(s):  
Xiao Qiang Guo ◽  
Li Hong Li ◽  
Cui Ling Luo ◽  
Yi Shuo Shi

The Bit Commitment (BC) is an important basic agreement in cryptography . The concept was first proposed by the winner of the Turing Award in 1995 ManuelBlum. Bit commitment scheme can be used to build up zero knowledge proof, verified secret sharing, throwing coins etc agreement.Simultaneously and Oblivious Transfer together constitute the basis of secure multi-party computations. Both of them are hotspots in the field of information security. We investigated unconditional secure Quantum Bit Commitment (QBC) existence. And we constructed a new bit commitment model – double prover bit commitment. The Quantum Bit Commitment Protocol can be resistant to errors caused by noise.


2001 ◽  
Vol 18 (2) ◽  
pp. 155-159
Author(s):  
Ming Zhong ◽  
Yixian Yang

2002 ◽  
Vol 38 (2) ◽  
pp. 247-255 ◽  
Author(s):  
Jue-Sam Chou ◽  
Yi-Shiung Yeh

2014 ◽  
Vol 14 (9&10) ◽  
pp. 888-900
Author(s):  
Martin Rotteler ◽  
Rainer Steinwandt

Improving over an earlier construction by Kaye and Zalka \cite{KaZa04}, in \cite{MMCP09b} Maslov et al. describe an implementation of Shor's algorithm, which can solve the discrete logarithm problem on ordinary binary elliptic curves in quadratic depth $\bigO(n^2)$. In this paper we show that discrete logarithms on such curves can be found with a quantum circuit of depth $\bigO(\log^2n)$. As technical tools we introduce quantum circuits for ${\mathbb F}_{2^n}$-multiplication in depth $\bigO(\log n)$ and for ${\mathbb F}_{2^n}$-inversion in depth $\bigO(\log^2 n)$.


1990 ◽  
Vol 2 (2) ◽  
pp. 63-76 ◽  
Author(s):  
Joan F. Boyar ◽  
Stuart A. Kurtz ◽  
Mark W. Krentel

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