Abstract
This paper will propose an efficient algorithm that utilizes the signed-digit representation to compute the kth term of a characteristic sequence generated by a linear feedback shift register of order 3 over GF(q). We will also propose an efficient algorithm to compute the (h-dk)th term of the characteristic sequence based on the knowledge of the kth term where k is unknown. Incorporating these results, we construct the ElGamal-like digital signature algorithm for the public-key cryptography based on the 3rd-order characteristic sequences which was proposed by Gong and Harn in 1999.
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Gong, G., Harn, L., Wu, H. (2001). The GH Public-Key Cryptosystem. In: Vaudenay, S., Youssef, A.M. (eds) Selected Areas in Cryptography. SAC 2001. Lecture Notes in Computer Science, vol 2259. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45537-X_22
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DOI: https://doi.org/10.1007/3-540-45537-X_22
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