RSAPublic-Key Encryption and Signature Lab

1.推导RSA私钥

import gmpy2

p = 0xF7E75FDC469067FFDC4E847C51F452DF
q = 0xE85CED54AF57E53E092113E62F436F4F
e = 0x0D88C3

n = q * p
phi = (p - 1) * (q - 1)
d = gmpy2.invert(e, phi)

print("public key:(" + hex(e) + ',' + hex(n) + ")")
print("private key:" + hex(d))

2.用RSA加密一个消息

import gmpy2

n = 0xDCBFFE3E51F62E09CE7032E2677A78946A849DC4CDDE3A4D0CB81629242FB1A5
e = 0x010001

m = "A top secret!".encode("utf-8").hex()
m = int(m, 16)
c = gmpy2.powmod(m, e, n)
print(hex(c))

3.解密这个消息

 C  =  8C0F971DF2F3672B28811407E2DABBE1DA0FEBBBDFC7DCB67396567EA1E2493F

import gmpy2

n = 0xDCBFFE3E51F62E09CE7032E2677A78946A849DC4CDDE3A4D0CB81629242FB1A5
d = 0x74D806F9F3A62BAE331FFE3F0A68AFE35B3D2E4794148AACBC26AA381CD7D30D
C = 0x8C0F971DF2F3672B28811407E2DABBE1DA0FEBBBDFC7DCB67396567EA1E2493F

M = gmpy2.powmod(C, d, n)
m = str(hex(M))[2:]
print("M:" + bytes.fromhex(m).decode("utf-8"))

4.产生一个消息的数字签名

import gmpy2

n = 0xDCBFFE3E51F62E09CE7032E2677A78946A849DC4CDDE3A4D0CB81629242FB1A5
e = 0x010001
d = 0x74D806F9F3A62BAE331FFE3F0A68AFE35B3D2E4794148AACBC26AA381CD7D30D

msg = ["I owe you $2000", "I owe you $3000"]
for m in msg:
    print(m)
    m = int(m.encode("utf-8").hex(), 16)
    c = gmpy2.powmod(m, d, n)
    print(hex(c))

5.验证这个数字签名是否正确

import gmpy2

M = "Launch a missile."
Sorg = 0x643D6F34902D9C7EC90CB0B2BCA36C47FA37165C0005CAB026C0542CBDB6802F
Serr = 0x643D6F34902D9C7EC90CB0B2BCA36C47FA37165C0005CAB026C0542CBDB6802A
n = 0xAE1CD4DC432798D933779FBD46C6E1247F0CF1233595113AA51B450F18116115
e = 0x010001

sig = [Sorg, Serr]
for S in sig:
    m = gmpy2.powmod(S, e, n)
    m = str(hex(m))[2:]
    try:
        msg = bytes.fromhex(m).decode('utf-8')
        print(msg)
        if m == M:
            print("signature valid!")
        else:
            print("signature invalid!")
    except:
        print(bytes.fromhex(m))
        print("signature invalid!")