In this paper, based on the implementation of semiclassical quantum Fourier transform, we first propose the concept of generation vector of ternary binary representation, construct the generation function's truth table, prove that the generation vector of ternary binary representation is one kind of k 's NAF representation and further find that its number of nonzero is not more than [(「logk」+1) /2]. Then we redesign a quantum circuit for Shor's algorithm, whose computation resource is approximately equal to that of Parker (Their requirements of elementary quantum gate are both O (「logN」3), and our circuit requires 2 qubits more than Parker's). However, our circuit is twice as fast as Parker's.
Quantum algorithms bring great challenges to classical public key cryptosystems, which makes cryptosystems based on non-commutative algebraic systems hop topic. The braid groups, which are non-commutative, have attracted much attention as a new platform for constructing quantum attack-resistant cryptosystems. A ring signature scheme is proposed based on the difficulty of the root extraction problem over braid groups, which can resist existential forgery against the adaptively cho-sen-message attack under the random oracle model.
