Secure multi-party equality testing

One or more computer-readable storage media storing one or more instructions that, when executable by one or more computers, cause the one or more computers to perform operations comprising:

• generating, by a first party of a secure multi-party computation (MPC), a first difference between a first secret share of a first value and a first secret share of a second value;
• during a first iteration of the secure MPC:
• partitioning the first difference into N sections each comprising M bits, where N and M are positive integers;
• for each section of the N sections:
• generating a first random bit;
• generating, based on the first random bit, a first group of 2M bits;
• and
• sending, to a second party of the secure MPC based on oblivious transfer (OT) protocol, a first selected bit from the first group of 2M bits;
• and
• concatenating first random bits of the N sections as a first input of a second iteration of the secure MPC;
• and
• determining whether the first value equals the second value based on performing a plurality of iterations of the secure MPC comprising at least the first iteration and the second iteration.

A computer-implemented system comprising:

• one or more computers;
• and
• one or more computer memory devices interoperably coupled with the one or more computers and having computer-readable storage media storing one or more instructions that, when executed by the one or more computers, perform one or more operations comprising:
• generating, by a first party of a secure multi-party computation (MPC), a first difference between a first secret share of a first value and a first secret share of a second value;
• during a first iteration of the secure MPC:
• partitioning the first difference into N sections each comprising M bits, where N and M are positive integers;
• for each section of the N sections:
• generating a first random bit;
• generating, based on the first random bit, a first group of 2M bits;
• and
• sending, to a second party of the secure MPC based on oblivious transfer (OT) protocol, a first selected bit from the first group of 2M bits;
• and
• concatenating first random bits of the N sections as a first input of a second iteration of the secure MPC;
• and
• determining whether the first value equals the second value based on performing a plurality of iterations of the secure MPC comprising at least the first iteration and the second iteration.