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 On the (Im)possibility of Basing Oblivious Transfer and Bit Commitment on Weakened Security Assumptions

1998 ◽  
Vol 5 (37) ◽  
Author(s):  
Ivan B. Damgård ◽  
Joe Kilian ◽  
Louis Salvail
Keyword(s):  
Realistic Model ◽  
Oblivious Transfer ◽  
Partial Result ◽  
Noisy Channels ◽  
Information Theoretic ◽  
Bit Commitment ◽  
Information Theoretic Security ◽  
Threshold Phenomenon ◽  
Special Cases ◽  
Similar Threshold

We consider the problem of basing Oblivious Transfer (OT)<br />and Bit Commitment (BC), with information theoretic security, on seemingly weaker primitives.We introduce a general model for describing such primitives, called Weak Generic Transfer (WGT). This model includes as important special cases Weak Oblivious Transfer (WOT), where both<br />the sender and receiver may learn too much about the other party's input, and a new, more realistic model of noisy channels, called unfair noisy channels. An unfair noisy channel has a known range of possible noise levels; protocols must work for any level within this range against adversaries who know the actual noise level. We give a precise characterization for when one can base OT on WOT. When the deviation of the WOT from the ideal is above a certain threshold, we show that no information-theoretic reductions from OT (even against passive adversaries) and BC exist; when the deviation is below this threshold, we give a reduction from OT (and hence BC) that is information-theoretically secure against active adversaries.<br />For unfair noisy channels we show a similar threshold phenomenon for bit commitment. If the upper bound on the noise is above a threshold (given as function of the lower bound) then no information-theoretic reduction from OT (even against passive adversaries) or BC exist; when it is below this threshold we give a reduction from BC. As a partial result, we give<br />a reduction from OT to UNC for smaller noise intervals.

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 On the existence of loss-tolerant quantum oblivious transfer protocols

2012 ◽  
Vol 12 (7&8) ◽  
pp. 609-619
Author(s):  
Jamie Sikora
Keyword(s):  
Quantum Communication ◽  
Oblivious Transfer ◽  
Classical Communication ◽  
Cryptographic Primitive ◽  
Quantum Oblivious Transfer ◽  
Better Than ◽  
Transfer Protocol

Oblivious transfer is the cryptographic primitive where Alice sends one of two bits to Bob but is oblivious to the bit received. Using quantum communication, we can build oblivious transfer protocols with security provably better than any protocol built using classical communication. However, with imperfect apparatus, one needs to consider other attacks. In this paper, we present an oblivious transfer protocol which is impervious to lost messages.

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 Impossibility of Quantum Bit Commitment, a Categorical Perspective

Axioms ◽  
2020 ◽  
Vol 9 (1) ◽  
pp. 28 ◽  
Author(s):  
Xin Sun ◽  
Feifei He ◽  
Quanlong Wang
Keyword(s):  
Quantum Theory ◽  
Simple Proof ◽  
Monoidal Categories ◽  
Unitary Equivalence ◽  
Information Theoretic ◽  
Quantum Bit ◽  
Bit Commitment

Bit commitment is a cryptographic task in which Alice commits a bit to Bob such that she cannot change the value of the bit after her commitment and Bob cannot learn the value of the bit before Alice opens her commitment. According to the Mayers–Lo–Chau (MLC) no-go theorem, ideal bit commitment is impossible within quantum theory. In the information theoretic-reconstruction of quantum theory, the impossibility of quantum bit commitment is one of the three information-theoretic constraints that characterize quantum theory. In this paper, we first provide a very simple proof of the MLC no-go theorem and its quantitative generalization. Then, we formalize bit commitment in the theory of dagger monoidal categories. We show that in the setting of dagger monoidal categories, the impossibility of bit commitment is equivalent to the unitary equivalence of purification.

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