On the Powerline System

Abstract.

The powerline system introduced by H.W. Lenstra in 1991 is a modification of the Chor-Rivest system, which was based upon a theorem by Bose and Chowla. The powerline system was proved by his author to be at least as secure as the Chor-Rivest system and has the main advantage of a greater freedom in choosing the system parameters. It does not rely on a hard problem from number theory. However its information rate is low. An improved powerline system called fractional powerline is introduced here. It has a better information rate and as a consequence, the brute-force attack already considered by Chor and Rivest which is adapted to this new system, is much more laborious. The system is still improved by introducing other irreducible polynomials. Improving the powerline system leads to results in arithmetic which are an extention and a variant to the theorem of Bose and Chowla. The main practical implication is to be able to transmit a 135 bit key over an channel together with an interactive signature by conveying only 208 × 2 binary digits.