Asynchronous Proactive RSA

Nowadays, to model practical systems better, such as the Internet network and ad hoc networks, researchers usually regard these systems as asynchronous networks. Meanwhile, proactive secret sharing schemes are often employed to tolerate a mobile adversary. Considering both aspects, an asynchronous proactive threshold signature scheme is needed to keep computer systems secure. So far, two asynchronous proactive secret sharing schemes have been proposed. One is proposed by Zhou in 2001, which is for RSA schemes. The other scheme is proposed by Cachin in 2002, which is a proactive secret sharing scheme for discrete-log schemes. There exist several drawbacks in both schemes. In Zhou¡¯s scheme, the formal security proof of this scheme is missing. Furthermore, Zhou¡¯s scheme needs to resort to the system administrator as the trusted third party for further run when some Byzantine errors occur. In Cachin¡¯s scheme, the building block is based on the threshold RSA scheme proposed by Shoup. However, how to proactivize Shoup¡¯s scheme is omitted in Cachin¡¯s scheme, so this scheme is incomplete. In this paper, we present a complete provably secure asynchronous proactive RSA scheme (APRS). Our paper has four contributions. Firstly, we present a provably secure asynchronous verifiable secret sharing for RSA schemes (asynchronous verifiable additive secret sharing, AVASS), which is based on a verifiable additive secret sharing over integers. Secondly, we propose an asynchronous threshold RSA signature scheme that is based on the AVASS scheme and the random oracle model, and is capable of being proactivized. Thirdly, we present a provably secure threshold coin-tossing scheme on the basis of the above threshold RSA scheme. Fourthly, we propose an asynchronous proactive secret sharing based on the threshold RSA scheme and the coin-tossing scheme. Finally, combining the proactive secret sharing scheme and the threshold RSA scheme, we achieve a complete provably secure asynchronous proactive RSA scheme

An asynchronous protocol for distributed computation of RSA inverses and its applications

This paper presents an efficient asynchronous protocol to compute RSA inverses with respect to a public RSA modulus N whose factorization is secret and shared among a group of parties. Given two numbers x and e, the protocol computes y such that y e ≡ x (mod N). A synchronous protocol for this task has been presented by Catalano, Gennaro, and Halevi (Eurocrypt 2000), but the standard approach for turning this into an asynchronous protocol would require a Byzantine-agreement subprotocol. Our protocol adopts their approach, but exploits a feature of the problem in order to avoid the use of a Byzantine agreement primitive. Hence, it leads to efficient asynchronous protocols for threshold signatures and for Byzantine agreement based on the strong RSA assumption, without the use of random oracles.

Software-implemented attack tolerance for critical information retrieval

The fast-growing reliance of our daily life upon online information services often demands an appropriate level of privacy protection as well as highly available service provision. However, most existing solutions have attempted to address these problems separately. This thesis investigates and presents a solution that provides both privacy protection and fault tolerance for online information retrieval. A new approach to Attack-Tolerant Information Retrieval (ATIR) is developed based on an extension of existing theoretical results for Private Information Retrieval (PIR). ATIR uses replicated services to protect a user's privacy and to ensure service availability. In particular, ATIR can tolerate any collusion of up to t servers for privacy violation and up to ƒ faulty (either crashed or malicious) servers in a system with k replicated servers, provided that k ≥ t + ƒ + 1 where t ≥ 1 and ƒ ≤ t. In contrast to other related approaches, ATIR relies on neither enforced trust assumptions, such as the use of tanker-resistant hardware and trusted third parties, nor an increased number of replicated servers. While the best solution known so far requires k (≥ 3t + 1) replicated servers to cope with t malicious servers and any collusion of up to t servers with an O(n^*^) communication complexity, ATIR uses fewer servers with a much improved communication cost, O(n1/2)(where n is the size of a database managed by a server).The majority of current PIR research resides on a theoretical level. This thesis provides both theoretical schemes and their practical implementations with good performance results. In a LAN environment, it takes well under half a second to use an ATIR service for calculations over data sets with a size of up to 1MB. The performance of the ATIR systems remains at the same level even in the presence of server crashes and malicious attacks. Both analytical results and experimental evaluation show that ATIR offers an attractive and practical solution for ever-increasing online information applications