Signature schemes based on 3rd order shift registers

Abstract

In this paper, we propose two digital signature schemes based on a third order linear feedback shift register. One of them is a normal signature scheme for signing document and the other is with encryption for intended reciever. These two signature schemes are different from most of the signature schemes which are based on discrete logarithm problem, elliptic curves discrete logarithm problem, RSA or quadratic residues. The efficient computational algorithm for computing kth term of a sequence is also presented. The advantage of these two schemes is that the computation is carried out in the ground field and not in an extension field. We also show that the security of these two signature schemes is equivalent to that of Schnorr signature scheme and Signed-ElGamal encryption scheme respectively.