Abstract
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.
Highlights
Bit commitment, used in a wide range of cryptographic protocols, consists of two phases, namely: commit and opening
A bit commitment protocol is concealing if Bob cannot know the bit Alice committed before the opening phase and it is binding if Alice cannot change the bit she committed after the commit phase
We show that the impossibility of bit commitment is equivalent to the unitary equivalence of purification in the setting of dagger monoidal categories
Summary
Bit commitment, used in a wide range of cryptographic protocols (e.g., zero-knowledge proof, multiparty secure computation, and oblivious transfer), consists of two phases, namely: commit and opening. In 1996, Mayers [19] and Lo and Chau [20,21] showed that all previously proposed QBC protocols were vulnerable to an entanglement attack which can be launched by Alice This result was later referred to as the Mayers–Lo–Chau (MLC) no-go theorem. We show that the impossibility of bit commitment is equivalent to the unitary equivalence of purification in the setting of dagger monoidal categories This provides an answer to the problem left by Heunen and Kissinger [30].
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