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Bit-commitment is a fundamental cryptographic task, in which Alice commits abit to Bob such that she cannot later change the value of the bit, while,simultaneously, the bit is hidden from Bob. It is known that idealbit-commitment is impossible within quantum theory. In this work, we show thatit is also impossible in generalised probabilistic theories (under a small setof assumptions) by presenting a quantitative trade-off between Alice's andBob's cheating probabilities. Our proof relies crucially on a formulation ofcheating strategies as cone programs, a natural generalisation of semidefiniteprograms. In fact, using the generality of this technique, we prove that thisresult holds for the more general task of integer-commitment.

Simple proof of the impossibility of bit-commitment in generalised probabilistic theories using cone programming