New trapdoor-knapsack public-key cryptosystem

The paper presents a new trapdoor-knapsack public-key cryptosystem. The encryption equation is based on the general modular knapsack equation, but, unlike the Merkle-Hellman scheme, the knapsack components do not have to have a superincreasing structure. The trapdoor is based on transformations between the modular and radix form of the knapsack components, via the Chinese remainder theorem. The security is based on factoring a number composed of 256 bit prime factors. The resulting cryptosystem has high density, approximately 30% message expansion and a public key of 14 Kbits. This compares very favourably with the Merkle-Hellman scheme which has over 100% expansion and a public key of 80 Kbits. The major advantage of the scheme when compared with the RSA scheme is one of speed. Typically, knapsack schemes such as the one proposed here are capable of throughput speeds which are orders of magnitude faster than the RSA scheme

New trapdoor-knapsack public-key cryptosystem

The paper presents a new trapdoor-knapsack public-key cryptosystem. The encryption equation is based on the general modular knapsack equation, but, unlike the Merkle-Hellman scheme, the knapsack components do not have to have a superincreasing structure. The trapdoor is based on transformations between the modular and radix form of the knapsack components, via the Chinese remainder theorem. The security is based on factoring a number composed of 256 bit prime factors. The resulting cryptosystem has high density, approximately 30% message expansion and a public key of 14 Kbits. This compares very favourably with the Merkle-Hellman scheme which has over 100% expansion and a public key of 80 Kbits. The major advantage of the scheme when compared with the RSA scheme is one of speed. Typically, knapsack schemes such as the one proposed here are capable of throughput speeds which are orders of magnitude faster than the RSA scheme

An Implementation of the Chor-Rivest Knapsack Type Public Key Cryptosystem

The Chor-Rivest cryptosystem is a public key cryptosystem first proposed by MIT cryptographers Ben Zion Chor and Ronald Rivest [Chor84]. More recently Chor has imple mented the cryptosystem as part of his doctoral thesis [Chor85]. Derived from the knapsack problem, this cryptosystem differs from earlier knapsack public key systems in that computa tions to create the knapsack are done over finite algebraic fields. An interesting result of Bose and Chowla supplies a method of constructing higher densities than previously attain able [Bose62]. Not only does an increased information rate arise, but the new system so far is immune to the low density attacks levied against its predecessors, notably those of Lagarias- Odlyzko and Radziszowski-Kreher [Laga85, Radz86]. An implementation of this cryptosystem is really an instance of the general scheme, dis tinguished by fixing a pair of parameters, p and h , at the outset. These parameters then remain constant throughout the life of the implementation (which supports a community of users). Chor has implemented one such instance of his cryptosystem, where p =197 and h =24. This thesis aspires to extend Chor\u27s work by admitting p and h as variable inputs at run time. In so doing, a cryptanalyst is afforded the means to mimic the action of arbitrary implementations. A high degree of success has been achieved with respect to this goal. There are only a few restrictions on the choice of parameters that may be selected. Unfortunately this general ity incurs a high cost in efficiency; up to thirty hours of (VAX1 1-780) processor time are needed to generate a single key pair in the desired range (p = 243 and h =18)

A New Lattice-Based Cryptosystem Mixed with a Knapsack

In this paper, we present a new lattice-based public-key cryptosystem mixed with a knapsack, which has reasonable key size and quick encryption and decryption. The module strategy in our cryptosystem can also be used to construct a framework for some GGH-type cryptosystems to improve their security