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Journal Articles Chicago Journal of Theoretical Computer Science Year : 2016

Optimal bounds for quantum weak oblivious transfer

Abstract

Oblivious transfer is a fundamental cryptographic primitive in which Bob transfers one of two bits to Alice in such a way that Bob cannot know which of the two bits Alice has learned. We present an optimal security bound for quantum oblivious transfer protocols under a natural and demanding definition of what it means for Alice to cheat. Our lower bound is a smooth tradeoff between the probability B with which Bob can guess Alice's bit choice and the probability A with which Alice can guess both of Bob's bits given that she learns one of the bits with certainty. We prove that 2B + A is greater than or equal to 2 in any quantum protocol for oblivious transfer, from which it follows that one of the two parties must be able to cheat with probability at least 2/3. We prove that this bound is optimal by exhibiting a family of protocols whose cheating probabilities can be made arbitrarily close to any point on the tradeoff curve.

Dates and versions

hal-00927537 , version 1 (13-01-2014)

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André Chailloux, Gus Gutoski, Jamie Sikora. Optimal bounds for quantum weak oblivious transfer. Chicago Journal of Theoretical Computer Science, 2016, ⟨10.4086/cjtcs.2016.013⟩. ⟨hal-00927537⟩

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