Commitments via Physically Related Functions

Commitment schemes are one of the basic building blocks to construct secure protocols for multi party computation. Many recent works are exploring hardware primitives like physically unclonable functions to build keyless cryptographic protocols, with minimal assumptions. The asymmetric nature and non-invertibility property of PUFs are widely exploited to build oblivious transfer protocols that are extended to build bit-commitment schemes. However, these schemes require the physical transfer of the PUF device between the interacting parties. In this work, we introduce a new class of hardware-based primitives called physically related functions that enable hardware circuits to securely communicate with each other over insecure channels. We propose a bit-commitment protocol based on this hardware primitive without needing any physical transfer. Our scheme is statistically hiding and computationally binding, requiring only one round of communication while being practically deployable. We explore the security properties of physically related functions, under which we prove the security of our scheme. We experimentally show that it is impossible to break the security of the scheme with more than negligible probability.