引言由安全质数p、q的乘积M作模的RSA体制是指采用如下加密和脱密方法的一种公开密钥密码体制。设有一个给定的数组(M,c,d,n),其中M是两个很大的安全质数p、q的乘积,并且M的这种p、q分解是被保密的;c是与φ(M)互质的公开加密指数[其中φ(M)=LCM(p—1,q—l)];d是对应的非公开脱密指数;n是用户号。发方对一个明文信息x(x是明文经数字化后的一个小段),作变换y=X~c mod M即得到密文信息y,并将它通过公开信道传送。当收方获得一个密文信息y后,便可利用仅由收方所掌握的非公开脱密指数d,作相应的变换 Introduction The RSA scheme modeled by the product M of prime numbers p, q is a public-key cryptosystem that employs the following encryption and decryption methods. There is a given array (M, c, d, n), where M is the product of two very large primes p, q, and this p, q decomposition of M is kept secret; c is the sum of (M) = LCM (p-1, q-1)]; d is the corresponding non-public decryption index; and n is the user number. The sender decrypts a plaintext message x (x is a digitized plaintext), transforms y = X ~ c mod M to obtain ciphertext y, and sends it over the open channel. When the receiver gets a ciphertext y, it can make use of the non-public decryption index d