A New Method to Establish Cryptosystems Based on Elliptic Curves

Miller, in 1985 and Koblitz, in 1987 pointed out notable methods to make out cryptosystems based on elliptic curves over finite field F_q. They both used one elliptic curve to set up cryptosystems. However, there exists one obvious fault in their methods such that some plantexts can not be imbedded in elliptic curve. So, some plantexts can not be encrypted.     

关于幂数的几个问题

S.W.Gotemo 在1976年于[1]中给出了幂数的概念。正整数r若满足p|n则pAn,此处p为素数,则n叫做一个幂数。 S.W.Golomb考虑了连续幂数的问题。显然4个连续整数不可能为幂数,因为其中之一必为2(2b-1)形状。对两个连续幂数问题,他证明了,若其中之一为完全平方数,则可通过pell方程的构造出来,并且,S.W.Golomb 在[1]中指出,对连续奇幂数仅能给出的一对为25、27。