Can we beat three halves lower bound? (Im)possibility of reducing communication cost for garbled circuits

IF 1.4 2区数学 Q3 COMPUTER SCIENCE, THEORY & METHODS Designs, Codes and Cryptography Pub Date : 2025-02-08 DOI:10.1007/s10623-025-01577-0

Chunghun Baek, Taechan Kim

引用次数: 0

Abstract

Recent improvements to garbled circuits are mainly focused on reducing their size. The state-of-the-art construction of Rosulek and Roy (Crypto 2021) requires \(1.5\kappa \) bits for garbling AND gates in the free-XOR setting. This is below the previously proven lower bound \(2\kappa \) in the linear garbling model of Zahur, Rosulek, and Evans (Eurocrypt 2015). Whether their construction is optimal in a more inclusive model than the linear garbling model still remains open. This paper begins by providing a comprehensive model for a large class of practical garbling schemes and proves the lower bound for the size of the garbled AND gates in our model. We show that garbled AND gates require at least \(1.5\kappa \) bits in our new model with the free-XOR setting. It is remarkable to see that the construction by Rosulek and Roy is already optimal despite the fact that our model possibly captures any potential extension of their construction.

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来源期刊

Designs, Codes and Cryptography 工程技术-计算机：理论方法

CiteScore

2.80

自引率

12.50%

发文量

157

审稿时长

16.5 months

期刊介绍： Designs, Codes and Cryptography is an archival peer-reviewed technical journal publishing original research papers in the designated areas. There is a great deal of activity in design theory, coding theory and cryptography, including a substantial amount of research which brings together more than one of the subjects. While many journals exist for each of the individual areas, few encourage the interaction of the disciplines. The journal was founded to meet the needs of mathematicians, engineers and computer scientists working in these areas, whose interests extend beyond the bounds of any one of the individual disciplines. The journal provides a forum for high quality research in its three areas, with papers touching more than one of the areas especially welcome. The journal also considers high quality submissions in the closely related areas of finite fields and finite geometries, which provide important tools for both the construction and the actual application of designs, codes and cryptographic systems. In particular, it includes (mostly theoretical) papers on computational aspects of finite fields. It also considers topics in sequence design, which frequently admit equivalent formulations in the journal’s main areas. Designs, Codes and Cryptography is mathematically oriented, emphasizing the algebraic and geometric aspects of the areas it covers. The journal considers high quality papers of both a theoretical and a practical nature, provided they contain a substantial amount of mathematics.

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