Six-Card Finite-Runtime XOR Protocol with Only Random Cut

Abstract

Executing a card-based cryptographic protocol is an attractive way to perform secure multiparty computation (MPC) with a deck of physical cards. Crèpeau and Kilian at CRYPTO 1993 proposed cardbased AND and XOR protocols that can deal with a logical conjunction and exclusive-or of variables. Their protocols use a familiar shuffling action called a random cut that can be easily implemented by humans, while the numbers of required cards and shuffles are not small enough to be efficient and the protocols are Las Vegas algorithms, i.e., they are not finite-runtime. Several researchers have improved upon the protocols for a quarter of a century. Eventually, there are many AND protocols in the literature, some of which are quite efficient and practical to execute. By contrast, there are only three XOR protocols including the Crèpeau-Kilian protocol mentioned above. In this paper, we design an efficient XOR protocol using only random cuts; the numbers of required cards and shuffles are six and two (which is fixed), respectively. Our proposed XOR protocol is the first construction of a finite-runtime XOR protocol if we restrict ourselves to use only random cuts. CCS CONCEPTS • Security and privacy → Cryptography.

Card-Based Cryptographic Protocols with Malicious Players Using Private Operations

“…den Boer [2] first showed a five-card protocol to securely calculate logical AND of two inputs. Since then, many protocols have been proposed to realize primitives to calculate any logical functions [14,18,24,37,42,48,49,62,63] and specific computations such as a specific class of logical functions [1,7,13,19,23,25,31,33,43,46,54,58,61,68], universal computation such as Turing machines [6,16], millionaires' problem [27,40,47], voting [32,41,44,69,70], random permutation [8,10,11,39], grouping [9], ranking [66], lottery [64], proof of knowledge of a puzzle solution [3, 5, 12, 21, 26, 28, 29, 50-53, 55-57, 59], and so on. This paper considers calculations of logical functions and a copy operation under the malicious model since any logical function can be realized with a combination of these calculations.…”

Graph Automorphism Shuffles from Pile-Scramble Shuffles

“…Indeed, most card-based protocols are constructed with these shuffles only 1 (cf. protocols with RCs only [2,6,7,12,15,17,22,23,32,34,35,40,41,44,48,52], protocols with RBCs only [27-29, 31, 36-38, 45], protocols with PSSs only [3,10,14,33,39,42,43,46], protocols with RCs and RBCs only [1,16,24,51], protocols with RCs and PSSs only [4,8,18,49,50], and protocols with RBCs and PSSs only [11,13,26,47]). With this background, it is essential to study further what can be done by these shuffles.…”