Study on Quantum Bit Commitment

2012 ◽  
Vol 263-266 ◽  
pp. 3076-3078
Author(s):  
Xiao Qiang Guo ◽  
Li Hong Li ◽  
Cui Ling Luo ◽  
Yi Shuo Shi
Keyword(s):  
Information Security ◽  
Secret Sharing ◽  
Oblivious Transfer ◽  
Zero Knowledge ◽  
Quantum Bit ◽  
Bit Commitment ◽  
Commitment Scheme ◽  
Zero Knowledge Proof ◽  
Turing Award

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.

scholarly journals Practical Quantum Bit Commitment Protocol Based on Quantum Oblivious Transfer

2018 ◽  
Vol 8 (10) ◽  
pp. 1990 ◽  
Author(s):  
Yaqi Song ◽  
Li Yang
Keyword(s):  
Real World ◽  
Unitary Transformation ◽  
Fault Tolerant ◽  
Cryptographic Protocols ◽  
Oblivious Transfer ◽  
Physical Security ◽  
Quantum Bit ◽  
Bit Commitment ◽  
Quantum Oblivious Transfer ◽  
Definition Of

Oblivious transfer (OT) and bit commitment (BC) are two-party cryptographic protocols which play crucial roles in the construction of various cryptographic protocols. We propose three practical quantum cryptographic protocols in this paper. We first construct a practical quantum random oblivious transfer (R-OT) protocol based on the fact that non-orthogonal states cannot be reliably distinguished. Then, we construct a fault-tolerant one-out-of-two oblivious transfer ( O T 1 2 ) protocol based on the quantum R-OT protocol. Afterwards, we propose a quantum bit commitment (QBC) protocol which executes the fault-tolerant O T 1 2 several times. Mayers, Lo and Chau (MLC) no-go theorem proves that QBC protocol cannot be unconditionally secure. However, we find that computing the unitary transformation of no-go theorem attack needs so many resources that it is not realistically implementable. We give a definition of physical security for QBC protocols and prove that the practical QBC we proposed is physically secure and can be implemented in the real world.

scholarly journals Lower bounds for quantum oblivious transfer

2013 ◽  
Vol 13 (1&2) ◽  
pp. 158-177
Author(s):  
Andre Chailloux ◽  
Iordanis Kerenidis ◽  
Jamie Sikora
Keyword(s):  
Lower Bounds ◽  
Oblivious Transfer ◽  
Information Theoretic ◽  
Quantum Bit ◽  
Bit Commitment ◽  
Information Theoretic Security ◽  
Quantum Oblivious Transfer ◽  
Open Question ◽  
Bounded Below ◽  
Transfer Protocol

Oblivious transfer is a fundamental primitive in cryptography. While perfect information theoretic security is impossible, quantum oblivious transfer protocols can limit the dishonest player's cheating. Finding the optimal security parameters in such protocols is an important open question. In this paper we show that every 1-out-of-2 oblivious transfer protocol allows a dishonest party to cheat with probability bounded below by a constant strictly larger than $1/2$. Alice's cheating is defined as her probability of guessing Bob's index, and Bob's cheating is defined as his probability of guessing both input bits of Alice. In our proof, we relate these cheating probabilities to the cheating probabilities of a bit commitment protocol and conclude by using lower bounds on quantum bit commitment. Then, we present an oblivious transfer protocol with two messages and cheating probabilities at most $3/4$. Last, we extend Kitaev's semidefinite programming formulation to more general primitives, where the security is against a dishonest player trying to force the outcome of the other player, and prove optimal lower and upper bounds for them.

scholarly journals Linear Zero-Knowledgde. A Note on Efficient Zero-Knowledge Proofs and Arguments

1996 ◽  
Vol 3 (7) ◽  
Author(s):  
Ivan B. Damgård ◽  
Ronald Cramer
Keyword(s):  
Error Probability ◽  
Communication Complexity ◽  
Boolean Formula ◽  
Interactive Proof ◽  
Zero Knowledge ◽  
Bit Commitment ◽  
Commitment Scheme ◽  
Commitment Schemes ◽  
Realistic Situation ◽  
Language L

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.

scholarly journals A discrete logarithm blob for noninteractive XOR gates

1990 ◽  
Vol 19 (327) ◽  
Author(s):  
Joan Boyar ◽  
Ivan Bjerre Damgård
Keyword(s):  
Building Block ◽  
Discrete Logarithm ◽  
Zero Knowledge ◽  
Discrete Logarithms ◽  
Bit Commitment ◽  
Commitment Scheme

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.

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