Discrete logarithm based cryptosystems in quadratic function fields of characteristic 2
A key exchange scheme in the infrastructure of a quadratic function field of even characteristic is described. It extends earlier work of \textit{R. Scheidler, J. A. Buchmann} and \textit{H. C. Williams} [J. Cryptology 7, 171-199 (1994; Zbl 0816.94018)] in fields of odd characteristic, using the equivalence class in the ideal class group, to function fields of even characteristic. Such key exchanges take place in an algebraic system which is not a group. The infrastructure of quadratic function fields of even characteristic is first examined. Two operations in the infrastructure are defined, the Baby-Step and the Giant-Step. The Baby-Step corresponds to one iteration of the continued fraction algorithm and a Giant-Step corresponds to ideal multiplication and reduction. The concept of distance in the algebraic system is introduced and algorithms are developed for computing ideals `closest to' a given value. These algorithms are used to define the key exchange and digital signature schemes in the structure. Section 3 of the paper gives the algorithms needed to implement the key exchange and digital signature protocols using the quadratic function fields. The following two sections give the protocols and examine their security in a manner similar to the Pohlig-Hellman attack in finite groups. The final section discusses implementations of the protocols.
scientific article; zbMATH DE number 1164303
scientific article