Multilevel Threshold Secret and Function Sharing based on the Chinese Remainder Theorem

A recent work of Harn and Fuyou presents the first multilevel (disjunctive) threshold secret sharing scheme based on the Chinese Remainder Theorem. In this work, we first show that the proposed method is not secure and also fails to work with a certain natural setting of the threshold values on compartments. We then propose a secure scheme that works for all threshold settings. In this scheme, we employ a refined version of Asmuth-Bloom secret sharing with a special and generic Asmuth-Bloom sequence called the {\it anchor sequence}. Based on this idea, we also propose the first multilevel conjunctive threshold secret sharing scheme based on the Chinese Remainder Theorem. Lastly, we discuss how the proposed schemes can be used for multilevel threshold function sharing by employing it in a threshold RSA cryptosystem as an example

Identity-based threshold group signature scheme based on multiple hard number theoretic problems

We introduce in this paper a new identity-based threshold signature (IBTHS) technique, which is based on a pair of intractable problems, residuosity and discrete logarithm. This technique relies on two difficult problems and offers an improved level of security relative to an individual hard problem. The majority of the denoted IBTHS techniques are established on an individual difficult problem. Despite the fact that these methods are secure, however, a prospective solution of this sole problem by an adversary will enable him/her to recover the entire private data together with secret keys and configuration values of the associated scheme. Our technique is immune to the four most familiar attack types in relation to the signature schemes. Enhanced performance of our proposed technique is verified in terms of minimum cost of computations required by both of the signing algorithm and the verifying algorithm in addition to immunity to attacks

Threshold cryptography based on Asmuth–Bloom secret sharing

Cataloged from PDF version of article.In this paper, we investigate how threshold cryptography can be conducted with the Asmuth-Bloom secret sharing scheme and present three novel function sharing schemes for RSA, ElGamal and Paillier cryptosysterns. To the best of our knowledge, these are the first provably secure threshold cryptosystems realized using the Asmuth-Bloom secret sharing. Proposed schemes are comparable in performance to earlier proposals in threshold cryptography. (c) 2007 Elsevier Inc. All rights reserved

The Elgamal Cryptosystem is better than Th RSA Cryptosystem for Mental Poker

Cryptosystems are one of the most important parts of secure online poker card games. However, there is no research comparing the RSA Cryptosystem (RC) and Elgamal Cryptosystem (EC) for mental poker card games. This paper compares the RSA Cryptosystem and Elgamal Cryptosystem implementations of mental poker card games using distributed key generation schemes. Each implementation is based on a joint encryption/decryption of individual cards. Both implementations use shared private key encryption/decryption schemes and neither uses a trusted third party (TTP). The comparison criteria will be concentrated on the security and computational complexity of the game, collusions among the players and the debate between the discrete logarithm problem (DLP) and the factoring problem (FP) for the encryption/decryption schemes. Under these criteria, the comparison results demonstrate that the Elgamal Cryptosystem has better efficiency and effectiveness than RSA for mental poker card games