Double Blind Comparisons using Groups with Infeasible Inversion

TL;DR

This paper introduces a cryptographic primitive called Double Blind Comparison, enabling privacy-preserving plaintext equality checks between users with co-operation, based on strong assumptions about group properties.

Contribution

It demonstrates how to implement Double Blind Comparisons using a Strong Associative One-Way Function on a Group with Infeasible Inversion, with security proof.

Findings

Secure implementation of Double Blind Comparison shown

Based on assumptions about Groups with Infeasible Inversion

Potential applications in Anonymous Credentials and Database Aggregation

Abstract

Double Blind Comparison is a new cryptographic primitive that allows a user who is in possession of a ciphertext to determine if the corresponding plaintext is identical to the plaintext for a different ciphertext held by a different user, but only if both users co-operate. Neither user knows anything about the plaintexts corresponding to either ciphertext, and neither user learns anything about the plaintexts as a result of the comparison, other than whether the two plaintexts are identical. Neither user can determine whether the plaintexts are equal without the other user's co-operation. Double Blind Comparisons have potential application in Anonymous Credentials and the Database Aggregation Problem. This paper shows how Double Blind Comparisons can be implemented using a Strong Associative One-Way Function (SAOWF). Proof of security is given, making an additional assumption that the SAOWF is implemented on a Group with Infeasible Inversion (GII), whose existence was postulated by Hohenberger and Molnar.