The Beta Cryptosystem

The Elliptic Curve Cryptosystem

The Elliptic Curve Cryptosystem (ECC) provides the highest strength-per-bit of any cryptosystem known today. This paper provides an overview of the three hard mathematical problems which provide the basis for the security of publickey cryptosystems used today: the integer factorization problem (IFP), the discrete logarithm problem (DLP), and the elliptic curve discrete logarithm problem (ECDLP)...

The RSA Cryptosystem

This paper explores the history and mathematics be­ hind the RSA cryptosystem, including the idea of public key cryp­ tosystems and number theory. It outlines the applications of RSA including secure information transfers and electronic signatures. It also analyzes why RSA is a secure way of transmitting information and the ways that it has been defeated in the past. In particular, we focus on ...

Cryptanalysis of the Sidelnikov Cryptosystem

We present a structural attack against the Sidelnikov cryptosystem [8]. The attack creates a private key from a given public key. Its running time is subexponential and is effective if the parameters of the Reed-Muller code allow for efficient sampling of minimum weight codewords. For example, the length 2048, 3rd-order Reed-Muller code as proposed in [8] takes roughly an hour to break on a sto...

Implementation of the GBD Cryptosystem

We present our experience from implementing the public-key cryptosystem of González, Boyd and Dawson. We discuss different computational methods and compare their relative efficiency experimentally. We also compare the efficiency of this cryptosystem with that of the ElGamal cipher.

Attacks On the RSA Cryptosystem