Parallel DNA Computing Model of Point-Doubling in Conic Curves Cryptosystem over Finite Field GF(2^n)

Abstract

DNA cryptography becomes a burgeoning new area of study along with the fast-developing of DNA computing and modern cryptography. Point-doubling, point-addition and point-multiplication are three fundamental point-operations to construct encryption protocols in some cryptosystem over mathematical curves such as elliptic curves and conic curves. This paper proposes a DNA computing model to calculate point-doubling in conic curves cryptosystem over finite field GF(2^n). By decomposing and rearranging the computing steps of point-doubling, the assembly process could be fulfilled by using 8 different types of computation tiles performing different functions with 1097 encoding ways. This model could also figure out point-multiplication if its coefficient is 2^k. The assembly time complexity is (2k+1)n-k-1, and the space complexity is (kn)^2+k(n^2)-(k^2)n.