In this paper we propose a new class of cryptosystems that utilizes metric continuity. The geometric cryptosystem considered in this paper as the main example of metric cryptosystems has a number of interesting properties such as resistance to several basic cryptographic attacks, efficiency and detection of transmission errors.
Geometric Key Establishment
We propose a new class of key establishment schemes which are based on geometric generalizations of the classical Diffie-Hellman. The simplest of our schemes ? based on the geometry of the unit circle ? uses only multiplication of rational numbers by integers and addition of rational numbers in its key creation. Its first computer implementation works significantly faster than all known implementations of Diffie-Hellman. Preliminary estimations show that our schemes are resistant to attacks. This resistance follows the pattern of the discrete logarithm problem and hardness of multidimensional lattice problems
- Leon Chernyak (2)