In 1995, Shamir proposed a variant of the RSA cryptosystem in which one the two secret primes is much larger than the other one. Some \at-tacks" were subsequently reported by Gilbert, Gupta, Odlyzko and Quisquater. In this report, we show that the cryptosystem recently proposed by Okamoto and Uchiyama (1998) is subject to similar attacks.

A secret sharing scheme allows to share a secret among several participants such that only certain groups of them can recover it. Veri able secret sharing has been proposed to achieve security against cheating participants. Its rst realization had the special property that everybody, not only the participants, can verify that the shares are correctly distributed. We will call such schemes publi...

This report introduces the basics of two-party secret sharing protocols based on additive secret sharing implemented in Sharemind. The main contribution is the multiplication protocol which uses Paillier’s additively homomorphic cryptosystem. One approach is to directly use this protocol for multiplication and the other is to generate Beaver’s triples and use them for the multiplication. The be...

Traditional definitions of encryption guarantee security for plaintexts which can be derived by the adversary. In some settings, such as anonymous credential or disk encryption systems, one may need to reason about the security of messages potentially unknown to the adversary, such as secret keys encrypted in a self-loop or a cycle. A public-key cryptosystem is n-circular secure if it remains s...

Image encryption based on elliptic curve cryptosystem and reducing its complexity is still being actively researched. Generating matrix for algorithm secret key together with Hilbert will be involved in this study. For a first case we need not to compute the inverse decryption processing cause that generated step was self invertible matrix. While second case, computing required. Peak signal noi...

Function sharing deals with the problem of distribution of the computation of a function (such as decryption or signature) among several parties. The necessary values for the computation are distributed to the participating parties using a secret sharing scheme (SSS). Several function sharing schemes have been proposed in the literature, with most of them using Shamir secret sharing as the unde...

Cryptographic computations (decryption, signature generation, etc.) are often performed on a relatively insecure device (e.g., a mobile device or an Internet-connected host) which cannot be trusted to maintain secrecy of the private key. We propose and investigate the notion of key-insulated security whose goal is to minimize the damage caused by secret-key exposures. In our model, the secret k...

The rapid evolution of imaging and communication technologies has transformed images into a widespread data type. Different types of data, such as personal medical information, official correspondence, or governmental and military documents, are saved and transmitted in the form of images over public networks. Hence, a fast and secure cryptosystem is needed for high-resolution images. In this p...