Reference no: EM13346909

构建RSA加密系统参数的一般方法可以描述如下：

• Select two primes p and q
• Let  =  and determine Φ (N) = (p - 1)(q - 1)
• Randomly choose  in the range 1 < e < Φ , such that gcd (e,N) = 1
• 确定为ED◦1modφ（）的解决方案
• Publish (e,N) as the public key

a. Show that a valid public key pair can still be constructed if we use only one prime , such that N =  and Φ (N) = (p - 1).
b. If we use this "one-prime" RSA construction and publish the public key (e, N),why is it easy to recover the secret key ?

C。令RSA（M）表示使用对（M）表示消息的加密₁, M₂). Show that the RSA encryption function has the following property for any two messages M₁and M₂

RSA (M1 x M2) = RSA(M1) x RSA(M2)

That is, the encryption of a product is equal to the product of the encryptions.

Tasks:

a. Show that "one-prime" construction produces a valid public key

b. Show the steps to recover

数学argume c。nt to show the property

Referencing style: APA style