# This file was *autogenerated* from the file my_rsa_pet.sage
from sage.all_cmdline import *   # import sage library

_sage_const_2 = Integer(2); _sage_const_1 = Integer(1); _sage_const_0 = Integer(0); _sage_const_5 = Integer(5); _sage_const_100 = Integer(100); _sage_const_512 = Integer(512); _sage_const_16 = Integer(16)
import hashlib
from time import time
def gen_prime(BITS):
    lb=_sage_const_2 **(BITS-_sage_const_1 )
    ub=_sage_const_2 *lb
    return random_prime(ub,False,lb)

def gen_safe_prime(BITS):
    qq=_sage_const_1 
    while not qq.is_prime():
        pp=gen_prime(BITS-_sage_const_1 )
        qq=_sage_const_2 *pp+_sage_const_1 
    return qq

def RSA_KEY_GEN(BITS):
    p=gen_safe_prime(BITS)
    q=gen_safe_prime(BITS)
    N=p*q
    fi=(p-_sage_const_1 )*(q-_sage_const_1 )
    e=_sage_const_2 **_sage_const_16 +_sage_const_1 
    d=inverse_mod(e,fi)
    dp=inverse_mod(e,p-_sage_const_1 )
    dq=inverse_mod(e,q-_sage_const_1 )
    qInv = inverse_mod(q,p)

    return p,q,e,d,dp,dq,qInv,N,fi

def RSA_Encrypt(m,e,n):
    return pow(m,e,N)
def RSA_Decrypt(c,p,q,d,dp,dq,qInv,N):
    m1=int(pow(c, dp,p))
    m2=int(pow(c, dq,q))
    h = (qInv * (m1 - m2)) % p
    return (m2 + h * q)%N

BITS=_sage_const_512 
print "Please wait, generating parameters..."
p,q,e,d,dp,dq,qInv,N,fi=RSA_KEY_GEN(BITS)
print "Done! Running tests now..."
tA=_sage_const_0 
tB=_sage_const_0 
TESTS=_sage_const_100 
for i in range(TESTS):
    ###Alice
    ts=time()
    lA=_sage_const_5  #2*ZZ.random_element(2**31)+1
    print "lA:", int(lA)
    rA=ZZ.random_element(N)
    print "rA:", int(rA)
    #select a random location
    cA=pow(rA,lA,N)
    print "cA:", int(cA)
    tA+=time()-ts
    ###Bob
    ts=time()
    lB= _sage_const_5  #2*ZZ.random_element(2**31)+1
    print "lB:", int(lB)
    e_B=inverse_mod(lB,fi)
    print "e_B:", int(e_B)
    tmp=pow(cA,e_B,N)
    print "tmp:", tmp
    res=hashlib.sha224(str(tmp)).hexdigest()
    tB+=time()-ts
    ###Alice
    ts=time()
    comp= (res==hashlib.sha224(str(rA)).hexdigest())
    print "Comparison", comp
    tA+=time()-ts

print "Average times:\nAlice:%0.5f\nBob:%0.5f"%(tA/TESTS,tB/TESTS)