Secret sharing schemes protect secrecy and integrity of information by dividing it into shares and distributing these shares among different locations. In k + 1 out of n threshold schemes, security is assured if throughout the entire life-time of the secret the adversary compromises no more than k of the n locations. For long-lived and sensitive secrets this protection may be insufficient. We p...

We introduce new eecient techniques for sharing cryptographic functions in a distributed dynamic fashion. These techniques dynamically and securely transform a distributed function (or secret sharing) representation between tout of -l (polynomial sharing) and tout of -t (additive sharing). We call the techniques poly-to-sum and sum-to-poly, respectively. Employing these techniques, we solve a n...

At CT-RSA 2006, Wang et al. [WYHL06] introduced the MFE cryptosystem, which was subsequently broken by Ding et al. [DHNW07]. Inspired by their work, we present a more general framework for multivariate public key cryptosystems, which combines ideas from both triangular and oil-vinegar schemes. We also propose a new public key cryptosystem, based on Diophantine equations, which implements the fr...

In this paper we propose a new MPKC, called PPS, based on (i) the 2-layer nonlinear piece in hand method, (ii) PMI, and (iii) STS. The PPS is a specific MPKC obtained by applying the 2-layer nonlinear piece in hand method to STS, in the manner that the rank and randomness of the lower rank steps in the original secret polynomial vector of STS are enhanced by adding a perturbation polynomial vec...

We present a new proposal for a trapdoor one-way function, from which we derive public-key encryption and digital signatures. The security of the new construction is based on the conjectured computational difficulty of lattice-reduction problems, providing a possible alternative to existing public-key encryption algorithms and digital signatures such as RSA and DSS. Keywards; Public-Key Cryptos...

Cryptography is the study of techniques which is used to communicate, store in forma tion or data securely, without being intercepted by third parties. In the real world, there are so many organizations working on large databases over a public network. The security of data is the primary concern in the public network. Encryption is the mos t commonly used technique where transactions continuous...

Passwords bootstrap symmetric and asymmetric cryptography, tying keys to an individual user. Biometrics are intended to strengthen this tie. Unfortunately, biometrics exhibit noise between repeated readings. Fuzzy extractors (Dodis et al., Eurocrypt 2004) derive stable symmetric keys from noisy sources. We ask if it is also possible for noisy sources to directly replace private keys in asymmetr...

We present attacks against the McEliece Public-Key Cryptosystem, the Atjai-Dwork Public-Key Cryptosystem, and variants of those systems. Most of these systems base their security on the apparent intractibility of one or more problems. The attacks we present do not violate the intractibility of the underlying problems, but instead obtain information about the private key or plaintext by watching...

Based on the ideas: “invertible cycle”, “tame transformation” and “special oil and vinegar”, three different nonlinear invertible transformations were constructed separately. Then making use of the idea of the extended multivariate public key cryptosystem, and combining the nonlinear invertible transformations above with Matsumoto-Imai (MI) scheme, three methods of designing extended multivaria...

Asymmetric cryptographic systems using multivariate polynomials over finite fields have been proposed several times since the 1980s. Although some of them have been successfully broken, the area is still vital and promises interesting algorithms with low computational costs, short message, and signature sizes. In this paper, we present two novel strategies “base transformation” and “adapted eva...