Card-Based Arithmetic Operations Using Integer Commitments and Their Application to Statistical Data Aggregation

Card-based cryptography enables players to compute logical and arithmetic operations securely, such as bitwise AND and addition of integers. Several multiparty computation protocols and zero-knowledge proof protocols utilizing these secure computations have been developed as its applications. However, the realization of an efficient protocol for an arithmetic operation other than addition and subtraction remains an open problem. This paper proposes card-based protocols, based on integer commitment, for multiplication, division, and square root. Compared to general constructions for protocols for these operations based on binary integer commitment, the proposed protocols exhibit superior simplicity and efficiency. Furthermore, these protocols introduce novel applications for card-based cryptography to secure statistical data aggregation.