Reducibility Among Protocols

Mark M. Wilde

Yevgeniy Dodis, Silvio M. Micali

Abstract. Secure Function Evaluation (SFE) protocols are very hard to design, and reducibility has been recognized as a highly desirable property of SFE protocols. Informally speaking, reducibility (sometimes called modular composition) is the automatic ability to break up the design of complex SFE protocols into several simpler, individually secure components. Despite much effort, only the most basic type of reducibility, sequential reducibility (where only a single sub-protocol can be run at a time), has been considered and proven to hold for a specific class of SFE protocols. Unfortunately, sequential reducibility does not allow one to save on the number of rounds (often the most expensive resource in a distributed setting), and achieving more general notions is not easy (indeed, certain SFE notions provably enjoy sequential reducibility, but fail to enjoy more general ones). In this paper, for information-theoretic SFE protocols, we • Formalize the notion of parallel reducibility, where sub-protocols can be run at the same time; • Clarify that there are two distinct forms of parallel reducibility: ⋆ Concurrent reducibility, which applies when the order of the subprotocol calls is not important (and which reduces the round complexity dramatically as compared to sequential reducibility); and ⋆ Synchronous reducibility, which applies when the sub-protocols must be executed simultaneously (and which allows modular design in settings where sequential reducibility does not even apply). • Show that a large class of SFE protocols (i.e., those satisfying a slight modification of the original definition of Micali and Rogaway [15]) provably enjoy (both forms of) parallel reducibility. 1

Mark M. Wilde

Eun‐Jun Yoon, Kyeoung-Ju Ha, Kee-Young Yoo

In 2006, Lee and Ahn proposed a matrix-based RFID authentication protocol which eliminates the security problems in HB and RFID authentication protocols. Their proposed protocol provides the following three merits: (1) it reduces the computational costs of the RFID tag. (2) it reduces the communication overhead between the reader and the tag. (3) it protects the user privacy. However, this paper points out that Lee and Ahn's proposed protocol is insecure to various attacks because it does not provide mutual authentication which the RFID tag does not authenticate the legality of the RFID reader unlike their claims. In addition, this paper proposes an improved matrix-based RFID mutual authentication protocol that can provide the mutual authentication. As a result, the proposed protocol not only can provide strong security and but also guarantee high efficiency because it reduces the communication rounds compare with Lee-Ahn's protocol.

Naoto Kiribuchi, Ryo Kato, Takashi Nishide +2 more

It is becoming more and more important to make use of personal or classified information while keeping it confidential. A promising tool for meeting this challenge is secure multi-party computation (MPC). However, one of the biggest problems with MPC is that it requires a vast amount of communication. We analyzed existing MPC protocols and found that the random number bitwise-sharing protocol used by many of them is notably inefficient. By devising a representation of the truth values and using special form prime numbers, we propose efficient random number bitwise-sharing protocols, dubbed “Extended-Range I and II,” which reduce the communication complexity to approximately 1/6th that of the best of the existing such protocol. We reduced the communication complexity to approximately 1/26th by reducing the abort probability, thereby making previously necessary backup computation unnecessary. Using our improved protocol, “Lightweight Extended-Range II,” we reduced the communication complexities of equality testing, comparison, interval testing, and bit-decomposition, all of which use the random number bitwise-sharing protocol, by approximately 91, 79, 67, and 23% (for 32-bit data), respectively. We also reduce the communication complexity of private exponentiation by about 70% (for 32-bit data and five parties).

Hans Delfs, Helmut Knebl