  Bit-commitment is a fundamental cryptographic task, in which Alice commits a
bit 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 ideal
bit-commitment is impossible within quantum theory. In this work, we show that
it is also impossible in generalised probabilistic theories (under a small set
of assumptions) by presenting a quantitative trade-off between Alice's and
Bob's cheating probabilities. Our proof relies crucially on a formulation of
cheating strategies as cone programs, a natural generalisation of semidefinite
programs. In fact, using the generality of this technique, we prove that this
result holds for the more general task of integer-commitment.
