RSA—非对称加密算法

RSA:非对称加密算法
加解密原理如下：
已知：p,q,n,e,d,m,c
其中：p与q互为大质数，n=p*q
      公钥Pk（n,e）:加密使用，是公开的
      私钥Sk（n,d）:解密使用，不公开
      c:明文  m:密文
      一般情况下取e=65537
要求： e与(p-1)*(q-1)互质
       (e*d)mod((p-1)*(q-1))=1
那么： m = c**e mod n
       c = m**d mod n

例如: Bob:公钥（50429,65537）
     Alice:私钥（50429,46793）
其中：n=50429,e=65537,d=46793,p=239,q=211，c=37
求：(1)Bob发送给Alice的密文m
    (2)Alice收到m解密后的明文c

解：(1)m = c**e mod 50429 = 37**65537 mod 50429 = 25804
    (2)c = m**d mod 50429 = 25804**46793 mod 50429 = 37
Python实现：

#-*- coding: UTF-8 -*-

__author__ = ''
__date__ = '2016/4/18'

from Tkinter import *

class RSA_hash():
    rsa_hash_en = []
    rsa_hash_de = []
    def __init__(self):
        self.root = Tk()
        self.root.title("RSA加/解密器")
        self.root.geometry()

        Label(self.root, text="RSA加/解密器", font=("Arial",15), width=15).pack()
        self.frm = Frame(self.root)

        self.frm_T = Frame(self.frm)
        self.frm_Tp = Frame(self.frm_T)
        Label(self.frm_Tp, text="素数p：", bg="red", font=("Arial",15), width=6).pack(side=LEFT)
        self.var_p = Variable()
        Entry(self.frm_Tp,textvariable=self.var_p, font=("Arial",12), width=24).pack(side=RIGHT)
        self.frm_Tp.pack()

        self.frm_Tq = Frame(self.frm_T)
        Label(self.frm_Tq, text="素数q：", bg="orange", font=("Arial",15), width=6).pack(side=LEFT)
        self.var_q = Variable()
        Entry(self.frm_Tq,textvariable=self.var_q, font=("Arial",12), width=24).pack(side=RIGHT)
        self.frm_Tq.pack()

        self.frm_Te = Frame(self.frm_T)
        Label(self.frm_Te, text="公钥e：", bg="yellow", font=("Arial",15), width=6).pack(side=LEFT)
        self.var_Pke = Variable()
        Entry(self.frm_Te,textvariable=self.var_Pke, font=("Arial",12), width=24).pack(side=RIGHT)
        self.frm_Te.pack()

        self.frm_Td = Frame(self.frm_T)
        Label(self.frm_Td, text="私钥d：", bg="green", font=("Arial",15), width=6).pack(side=LEFT)
        self.var_Skd = Variable()
        Entry(self.frm_Td,textvariable=self.var_Skd, font=("Arial",12), width=24).pack(side=RIGHT)
        self.frm_Td.pack()
        self.frm_T.pack()

        self.frm_B = Frame(self.frm)
        self.frm_TB = Frame(self.frm_B)
        Label(self.frm_TB, text="请输入：", bg="cyan", font=("Arial",15), width=6).pack(side=LEFT)
        self.var_char = Variable()
        Entry(self.frm_TB,textvariable=self.var_char, font=("Arial",12), width=24).pack(side=RIGHT)
        self.frm_TB.pack()

        self.frm_MB = Frame(self.frm_B)
        self.rsa_show = Text(self.frm_MB, bg="lavender", font=("Arial",12), width=32, height=6)
        self.rsa_show.insert("1.0","")
        self.rsa_show.pack()
        self.frm_MB.pack()

        self.frm_BB = Frame(self.frm_B)
        Button(self.frm_BB, text="清除", command=self.clear, font=("Arial",12), bd=3).pack(side=LEFT)
        Button(self.frm_BB, text="加密", command=self.encrypt, font=("Arial",12), bd=3).pack(side=RIGHT)
        Button(self.frm_BB, text="解密", command=self.decrypt, font=("Arial",12), bd=3).pack(side=RIGHT)
        self.frm_BB.pack()
        self.frm_B.pack()
        self.frm.pack()

    def clear(self):
        self.var_char.set("")
        self.var_p.set("")
        self.var_q.set("")
        self.var_Pke.set("")
        self.var_Skd.set("")
        self.rsa_show.delete("1.0",END)

    def encrypt(self):
        self.rsa_show.delete("1.0",END)
        p = int(self.var_p.get())
        q = int(self.var_q.get())
        if self.isprimer(p,q):
            phi = (p - 1) * (q - 1)
            n = p * q
        else:
            self.rsa_show.insert("1.0","请重新输入p和q（要求p与q互素）")
        e = int(self.var_Pke.get())

        if self.isprimer(e,phi):
            var_c = self.var_char.get()
            if var_c.isdigit():
                c = int(self.var_char.get())
                m = c ** e % n
                self.rsa_show.insert("1.0","密文为：%d" % m)

            else:
                for i in var_c:
                    c = ord(i)
                    if self.isprimer(e,phi):
                        m = c ** e % n
                        self.rsa_show.insert(END,"密文依次为：%d\n" % m)
        else:
            self.rsa_show.insert("1.0","e与phi互相不为素数，请重新输入公钥e")

    def decrypt(self):
        self.rsa_show.delete("1.0",END)
        p = int(self.var_p.get())
        q = int(self.var_q.get())
        if self.isprimer(p,q):
            phi = (p - 1) * (q - 1)
            n = p * q
        else:
            self.rsa_show.insert("1.0","请重新输入p和q（要求p与q互素）")
        d = int(self.var_Skd.get())
        m = int(self.var_char.get())
        e = int(self.var_Pke.get())
        if self.isprimer(e*d,phi):
            c = m ** d % n
            if c in range(0,128):
                self.rsa_show.insert("1.0","明文为： %d 或者 %s" % (c,chr(c)))
            else:
                self.rsa_show.insert("1.0","明文为： %d" % c)
        else:
            self.rsa_show.insert("1.0","您输入的密钥d不满足要求，请重新输入私钥d")

    #判断是否互素
    def isprimer(self,g,f):
        if g > f:
            s = f
        else:
            s = g
        L = []
        for i in range(s,0,-1):
            if g % i==0 and f %i ==0:
                L.append(i)
        if max(L) == 1:
            return True
        else:
            self.var_p.set("")
            self.var_q.set("")
def main():
    rsa = RSA_hash()
    mainloop()

if __name__ == "__main__":
    main()

下载 rsa_hash.exe（提取码：aef1）