Card-Based Cryptographic Logical Computations Using Private Operations
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Card‑Based Cryptographic Logical Computations Using Private Operations Hibiki Ono1 · Yoshifumi Manabe1 Received: 15 April 2020 / Accepted: 3 October 2020 © The Author(s) 2020
Abstract This paper proposes new card-based cryptographic protocols to calculate logic functions with the minimum number of cards using private operations under the semihonest model. Though various card-based cryptographic protocols were shown, the minimum number of cards used in the protocol has not been achieved yet for many problems. Operations executed by a player where the other players cannot see are called private operations. Private operations have been introduced in some protocols to solve a particular problem or to input private values. However, the effectiveness of introducing private operations to the calculation of general logic functions has not been considered. This paper introduces three new private operations: private random bisection cuts, private reverse cuts, and private reveals. With these three new operations, we show that all of AND, XOR, and copy protocols are achieved with the minimum number of cards by simple three-round protocols. This paper then shows a protocol to calculate any logical functions using these private operations. Next, we consider protocols with malicious players. Keywords Multi-party secure computation · Card-based cryptographic protocols · Private operations · Logical computations · Copy
Preliminary version of the paper was presented as Hibiki Ono and Yoshifumi Manabe: “ Card-based Cryptographic Protocols with the Minimum Number of Cards Using Private Operations,” Proc. of 11th International Symposium on Foundations & Practice of Security (FPS 2018) LNCS Vol. 11358, pp.193–207 (Apr. 2019). * Yoshifumi Manabe [email protected] 1
Faculty of Informatics, Kogakuin University, 1‑24‑2, Nishisinjuku, Shinjuku, Tokyo 163–8677, Japan
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New Generation Computing
Introduction Card-based cryptographic protocols [11, 26] have been proposed in which physical cards are used instead of computers to securely calculate values. den Boer [2] first showed a five-card protocol to securely calculate AND of two inputs. Since then, many protocols have been proposed to calculate logical functions [4, 5, 21, 24, 27, 30, 40, 44, 47] and specific computations such as computations on three inputs [32, 33, 43], calculation of symmetric functions [41], millionaires’ problem [18, 29, 37], voting [22, 28, 51], random permutation [6, 8, 9], grouping [7], matching [17], ranking [48], zero-knowledge proof of puzzle solutions [3, 16, 19, 42] and so on. Most of the protocols assume a semi-honest model, that is, players obey the rule of the protocol but try to obtain secret values. This paper also assumes the semi-honest model in most sections. We discuss malicious players in Sect. 5. Randomization or a private operation is the most important primitive in these card-based protocols. If every primitive executed in a card-based protocol is deterministic and public, the relationship between the privat
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