Improvements on results of representation of elements in cyclotomic subgroup - JIANG Zheng-tao1; LIU Jian-wei2; YUAN Ping-zhi3; WANG Yu-min4 (Tongxin xuebao)
Further investigations on efficient public-key cryptosystems based on discrete logarithm in finite field（exten-sion） were provided,and in case of the degree of field extension being odd,the ordinary results proposed by Wieb Bosma et al were optimized.It was pointed out that even though the degree（k=de） of field extension is odd,the minimal poly nomial overFpd of any element in cyclotomic polynomial subgroup can still be represented with（e?1）/2 elements of Fpd,in the case of e=3,no matter what d is,a cryptosystem with optimization 3 can always be constructed based on the dis-crete logarithm in field extension.Further,it was pointed out that for any e,positive or negative,there exists k=de such that Wieb Bosma’s conjecture is true.