https://wwb.lanzouh.com/i8uxY05qu1mf
题目2：RSA-OAEP的实现
具体要求
RSA算法是应用最为广泛的公钥加密算法之一，但由于基本算法具有的同态性，在实际使用过程中，通常需要对基本的RSA算法进行改进，而RSA-OAEP算法即为实际使用算法之一。本课题致力于对RSA-OAEP算法的模拟实现，使学生深入了解基本RSA算法如何应用到实际的机密性问题解决中，提升编程能力。
题目的具体要求
1.查阅相关资料，深入了解RSA-OAEP算法的实现思想和原理；
2.选择一种编程语言和开发工具，模拟实现RSA-OAEP算法的加解密，并能够实现对文字信息的加解密；
3.程序具有图形化用户界面，输出美观；
4.可根据自己能力，在完成以上基本要求后，对程序功能进行适当扩充；
5.撰写报告，对所采用的算法、程序结构和主要函数过程以及关键变量进行详细的说明；对程序的调试过程所遇到的问题进行回顾和分析，对测试和运行结果进行分析；总结软件设计和实习的经验和体会，进一步改进的设想；
6.提供关键程序的清单、源程序及可执行文件和相关的软件说明。
附（RSA-OAEP算法）
加密1) Alice 填充信息来制成一个m比特的信息，我们称之为M。
加密2) Alice 选择一个k比特的随机数r（注意r只能使用一次然后就要销毁）。Alice运用MD4函数G，用r生成一个m比特的整数，创建部分明文然后创建部分明文
这里函数H也选用MD4，将m比特的输入生成k比特的输出。
加密3) Alice 创建密文并且把C发送给Bob。
解密1) Bob 创建
解密2) Bob 首先运用重新创建r的值。然后运用
重新创建填充信息的值。
解密3) 从M当中取消填充后，Bob得到了原信息。
# OAEP_easyRealize.py
from Crypto.PublicKey import RSA
from Crypto.Cipher import PKCS1_OAEP
import base64
rsa_key_pair = RSA.generate(1024)
pubkey = rsa_key_pair.publickey().export_key()
privkey = rsa_key_pair.export_key()
print(pubkey.decode())
print(privkey.decode())
# 公钥加密
text = "hello world"
rsa_pubkey = RSA.import_key(pubkey)
cipher_pub = PKCS1_OAEP.new(rsa_pubkey)
ciphervalue_enc = base64.b64encode(cipher_pub.encrypt(text.encode("utf-8")))
print("加密内容:\n{}".format(ciphervalue_enc.decode()))
#私钥解密
rsa_privkey = RSA.import_key(privkey)
cipher_priv = PKCS1_OAEP.new(rsa_privkey)
ciphervalue_dec = cipher_priv.decrypt(base64.b64decode(ciphervalue_enc))
print("解密内容:\n{}".format(ciphervalue_dec.decode()))
-----BEGIN PUBLIC KEY-----
MIGfMA0GCSqGSIb3DQEBAQUAA4GNADCBiQKBgQCwwyKOjYBImX1onWvJNBMNmp+0
f0sp71Fhzj2EPQQv5puPP7dNpSdqQ1GgMIKRgc5tClyaw+gtuY1MGaL++oQg543t
pnPfFVXzmi1j0rRl1KSljfI8eiQ5XLu/t+FCn9kVltZTWaXBxmloWwPbphhkgVur
yxCxhCKAf2n4KSJM/wIDAQAB
-----END PUBLIC KEY-----
-----BEGIN RSA PRIVATE KEY-----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-----END RSA PRIVATE KEY-----
加密内容:
U4hxfy8iHhw/L2ZWF2y1Mq9fO3xuxHHqDe7rt9lG38TeB8pwNgRQcQOBa90aiEQfZTu0JnCHm69riV2yAXk9Q/Khk0jp5Xmb/QcLa+ndTO7ncOsESwDA9BLYgPV0qEF2MCeJx3f2374dq3oSBC8cv+SIUb98WLQ0nPpH+tMW2Ag=
解密内容:
hello world
# MD4_Realize.py
maxInt = 0x100000000
S = [3, 7, 11, 19, 3, 7, 11, 19,
3, 7, 11, 19, 3, 7, 11, 19,
3, 5, 9, 13, 3, 5, 9, 13,
3, 5, 9, 13, 3, 5, 9, 13,
3, 9, 11, 15, 3, 9, 11, 15,
3, 9, 11, 15, 3, 9, 11, 15, ]
K = [0x00000000, 0x00000000, 0x00000000, 0x00000000,
0x00000000, 0x00000000, 0x00000000, 0x00000000,
0x00000000, 0x00000000, 0x00000000, 0x00000000,
0x00000000, 0x00000000, 0x00000000, 0x00000000,
0x5A827999, 0x5A827999, 0x5A827999, 0x5A827999,
0x5A827999, 0x5A827999, 0x5A827999, 0x5A827999,
0x5A827999, 0x5A827999, 0x5A827999, 0x5A827999,
0x5A827999, 0x5A827999, 0x5A827999, 0x5A827999,
0X6ED9EBA1, 0X6ED9EBA1, 0X6ED9EBA1, 0X6ED9EBA1,
0X6ED9EBA1, 0X6ED9EBA1, 0X6ED9EBA1, 0X6ED9EBA1,
0X6ED9EBA1, 0X6ED9EBA1, 0X6ED9EBA1, 0X6ED9EBA1,
0X6ED9EBA1, 0X6ED9EBA1, 0X6ED9EBA1, 0X6ED9EBA1, ]
def fill(sequence):
'将字节序列按小端序填充成512位【16整数*4字节】的倍数'
count = len(sequence)
multi_16s = ((count + 8) // 64 + 1) * 16 # 共需要整数的个数，每个整数存储4个字节的数据
sequence += [0] * (multi_16s * 4 - count) # 用 0 填充
sequence[count] |= 128 # 用一个 1 补在后面
multi_4bytes = []
for i in range(len(sequence) // 4):
sequence[i * 4 + 3], sequence[i * 4 + 2], sequence[i * 4 + 1], sequence[i * 4] = tuple(
sequence[i * 4:(i + 1) * 4]) # 大端序存储
multi_4bytes.append(
int("".join(["{:08b}".format(ii) for ii in sequence[i * 4:(i + 1) * 4]]), 2)) # 每四个Ascii合并成一个4字节整数
multi_4bytes[-2], multi_4bytes[-1] = int("{:064b}".format(count * 8)[32:], 2), int("{:064b}".format(count * 8)[:32],
2)
return multi_4bytes
def fill(sequence):
'将字节序列按小端序填充成512位【16整数*4字节】的倍数'
count = len(sequence)
multi_16s = ((count + 8) // 64 + 1) * 16 # 共需要整数的个数，每个整数存储4个字节的数据
sequence += [0] * (multi_16s * 4 - count) # 用 0 填充
sequence[count] |= 128 # 用一个 1 补在后面
multi_4bytes = []
for i in range(len(sequence) // 4):
sequence[i * 4 + 3], sequence[i * 4 + 2], sequence[i * 4 + 1], sequence[i * 4] = tuple(
sequence[i * 4:(i + 1) * 4]) # 大端序存储
multi_4bytes.append(
int("".join(["{:08b}".format(ii) for ii in sequence[i * 4:(i + 1) * 4]]), 2)) # 每四个Ascii合并成一个4字节整数
multi_4bytes[-2], multi_4bytes[-1] = int("{:064b}".format(count * 8)[32:], 2), int("{:064b}".format(count * 8)[:32],
2)
return multi_4bytes
def shift(x, n):
'循环左移'
return ((x << n) | (x >> (32 - n)))
def F(X, Y, Z): return (X & Y) | ((~X) & Z)
def G(X, Y, Z): return (X & Y) | (X & Z) | (Y & Z)
def H(X, Y, Z): return X ^ Y ^ Z
def Go(a, b, c, d, fun, m, s, K):
thesum = (a + fun(b, c, d) + int(m) + K) % maxInt
return shift(thesum, s) % maxInt
def int32ToHex(a):
'32位整型集合转16进制'
md4 = ''
for i in a:
x = "{:08x}".format(i) # 整型【32位2】->8位16
md4 += x[6:] + x[4:6] + x[2:4] + x[:2] # 每两位切割, 切割4刀->逆序【大端变小端】
return md4
def MD4(text):
# 程序中：大端字节序
A = 0X67452301
B = 0XEFCDAB89
C = 0X98BADCFE
D = 0X10325476
sequence = list(bytes(text, 'utf-8')) # 将unicode转换为字节序列
text_int4 = fill(sequence) # 将字节序列按小端序填充成4字节整数
for i in range(len(text_int4) // 16): # 主循环
a, b, c, d = A, B, C, D
M = [text_int4[i * 16 + ii] for ii in range(16)] # 取出16个整数
for ii in range(48):
if ii < 16:
A, B, C, D = D, Go(A, B, C, D, F, M[ii], S[ii], K[ii]), B, C
elif ii == 16:
A = Go(A, B, C, D, G, M[0], S[ii], K[ii])
elif ii == 17:
D = Go(D, A, B, C, G, M[4], S[ii], K[ii])
elif ii == 18:
C = Go(C, D, A, B, G, M[8], S[ii], K[ii])
elif ii == 19:
B = Go(B, C, D, A, G, M[12], S[ii], K[ii])
elif ii == 20:
A = Go(A, B, C, D, G, M[1], S[ii], K[ii])
elif ii == 21:
D = Go(D, A, B, C, G, M[5], S[ii], K[ii])
elif ii == 22:
C = Go(C, D, A, B, G, M[9], S[ii], K[ii])
elif ii == 23:
B = Go(B, C, D, A, G, M[13], S[ii], K[ii])
elif ii == 24:
A = Go(A, B, C, D, G, M[2], S[ii], K[ii])
elif ii == 25:
D = Go(D, A, B, C, G, M[6], S[ii], K[ii])
elif ii == 26:
C = Go(C, D, A, B, G, M[10], S[ii], K[ii])
elif ii == 27:
B = Go(B, C, D, A, G, M[14], S[ii], K[ii])
elif ii == 28:
A = Go(A, B, C, D, G, M[3], S[ii], K[ii])
elif ii == 29:
D = Go(D, A, B, C, G, M[7], S[ii], K[ii])
elif ii == 30:
C = Go(C, D, A, B, G, M[11], S[ii], K[ii])
elif ii == 31:
B = Go(B, C, D, A, G, M[15], S[ii], K[ii])
elif ii == 32:
A = Go(A, B, C, D, H, M[0], S[ii], K[ii])
elif ii == 33:
D = Go(D, A, B, C, H, M[8], S[ii], K[ii])
elif ii == 34:
C = Go(C, D, A, B, H, M[4], S[ii], K[ii])
elif ii == 35:
B = Go(B, C, D, A, H, M[12], S[ii], K[ii])
elif ii == 36:
A = Go(A, B, C, D, H, M[2], S[ii], K[ii])
elif ii == 37:
D = Go(D, A, B, C, H, M[10], S[ii], K[ii])
elif ii == 38:
C = Go(C, D, A, B, H, M[6], S[ii], K[ii])
elif ii == 39:
B = Go(B, C, D, A, H, M[14], S[ii], K[ii])
elif ii == 40:
A = Go(A, B, C, D, H, M[1], S[ii], K[ii])
elif ii == 41:
D = Go(D, A, B, C, H, M[9], S[ii], K[ii])
elif ii == 42:
C = Go(C, D, A, B, H, M[5], S[ii], K[ii])
elif ii == 43:
B = Go(B, C, D, A, H, M[13], S[ii], K[ii])
elif ii == 44:
A = Go(A, B, C, D, H, M[3], S[ii], K[ii])
elif ii == 45:
D = Go(D, A, B, C, H, M[11], S[ii], K[ii])
elif ii == 46:
C = Go(C, D, A, B, H, M[7], S[ii], K[ii])
else:
B = Go(B, C, D, A, H, M[15], S[ii], K[ii])
A, B, C, D = (A + a) % maxInt, (B + b) % maxInt, (C + c) % maxInt, (D + d) % maxInt # 此处还是大端字节
md4 = int32ToHex([A, B, C, D])
return md4
# OAEP_Realize.py
import random
import binascii
import easygui
import MD4_Realize
def gcd(a, b): # 求最大公因数
while a != 0:
a, b = b % a, a
return b
def findModReverse(e, n): # 已知e和n，求d，满足关系式：ed = 1 mod φ(n)
if gcd(e, n) != 1:
return None
u1, u2, u3 = 1, 0, e
v1, v2, v3 = 0, 1, n
while v3 != 0:
q = u3 // v3 # 整除
u1, u2, u3, v1, v2, v3 = v1, v2, v3, (u1 - q * v1), (u2 - q * v2), (u3 - q * v3)
return u1 % n
if __name__ == "__main__":
p = 168995677594036943498896698249502579045415356147450286903574977915675215654000852466242837180568368549600306461919095156035850147291191251838345423003548737288250427664794031697769270068290742307294644975782315875706815176748955712747679225674789516554407102487179525812178429394677953163553303283966837950227
q = 73250114511939221297189302708624091354575379476811068897570041621344734046574044427415715091676742616301137831925511472461697934230365993146217113253076136386575575868816429181422361239620593954716878229091392314316476106540409390466346705287246245765228049884691190461308813988563356306637349832642629018559
plaintext = easygui.enterbox("请输入加密字符串:")
Pri_Key = 17340019
print("\n输入值M: " + plaintext)
r = ""
for i in range(1024):
r += str(random.randint(0, 1))
print("\n1024位随机数r: " + r)
pad_paintext = binascii.hexlify(plaintext.encode('utf8'))
print("\n输入值M的ascii值: " + str(pad_paintext))
# RSA-OAEP
mark_r = str(hex(int(r, 2)))
P1 = MD4_Realize.MD4(mark_r)
print("\nr的md4值: " + P1)
P1 = str(hex(int(P1, 16) ^ int(pad_paintext, 16)))
mark_r = P1
P2 = MD4_Realize.MD4(mark_r)
print("\nP1的md4值: " + P2)
P2 = str(hex(int(P2, 16) ^ int(r, 2)))
P1 = P1 + P2[2:]
print("\n明文P=(P1+P2): " + P1)
xx = int(P1, 16)
mul_pq = p * q
print("\n大素数p = " + str(p) + "\nq = " + str(q))
print("\nn = p * q: " + str(mul_pq))
fn = (p - 1) * (q - 1)
print("\nφ(n) = (p - 1) * (q - 1): " + str(fn))
Pub_Key = findModReverse(Pri_Key, fn)
print("\n私钥e: " + str(Pri_Key) + "\n公钥d = reverseMod(e, φ(n)): " + str(Pub_Key))
Ey = int(pow(xx, Pub_Key, mul_pq))
print("\n密文C = p^e (mod n): " + str(Ey))
easygui.msgbox("1024位随机数r:\n" + r)
easygui.msgbox("\n\nOAEP加密结果:\n" + str(P1[2:])
+ "\n\nOAEP十进制结果:\n" + str(xx)
+ "\n\nRSA加密后密文:\n" + str(hex(Ey)))
# decode
Ex = int(pow(Ey, Pri_Key, mul_pq))
print("\n解密后明文deP = C^d (mod n): " + str(Ex))
deS = bin(Ex)
deP2 = hex(int(deS[len(deS) - 1024:], 2))
deP1 = hex(int(deS[:len(deS) - 1024], 2))
print("\ndeP2(deP后1024位): " + deP2)
print("\ndeP1(deP剩余部分): " + deP1)
demark_r = deP1
demark_P1 = MD4_Realize.MD4(demark_r)
print("\ndeP1的md4值: " + demark_P1)
demark_r = str(hex(int(demark_P1, 16) ^ int(deP2, 16)))
demark_P1 = MD4_Realize.MD4(demark_r)
print("\nr的md4值: " + demark_P1)
Last_M = str(hex(int(deP1, 16) ^ int(demark_P1, 16)))
print("\n解密结果M: " + binascii.a2b_hex(Last_M[2:]).decode("utf8"))
easygui.msgbox("\n\n复原的1024位值r:\n" + bin(int(demark_r, 16))
+ "\n\n解密结果:" + binascii.a2b_hex(Last_M[2:]).decode("utf8"))
输入值M: abcdefg
1024位随机数r: 0010010100110100100001010111001011101110100010111001000011111011011101110001101010001010111110101010011101110011101000111110011100101001010101001111111010101001011011110101000101101000111110100011000110011010000011111111110001010101010011000101001000100110011111011100101000001001110100100101101110101001111000011011000010000100111000101001000100010100111010001011101110001101111011011001110100100111010110000111010000110001000100101110011000110001111100010101111000100100011100101101001100010110000000001110101100000111101001010111111011110011100101111001011110010101011001111111111101100100101101001100001111000101110001000001001101010011110110011010100110001101100011011011011001000110111010100110001101001101110101000011101101100100111110101101111110000010101110010110011111100011101111100111101111100111010000100111000001101100001000111000111100100001110000100110111100110111111100101011111101010000111010001001011000100011111001110011001101100101000000100110101001011100101110111101000110001001000101010101001001101111
输入值M的ascii值: b'61626364656667'
r的md4值: ebc978722af2bf6eb9fc505c63e6c46f
P1的md4值: a91dc46963752f5cb5f7da5305836c8d
明文P=(P1+P2): 0xebc978722af2bf6eb99d323f0783a20825348572ee8b90fb771a8afaa773a3e72954fea96f5168fa319a0ffc554c52267dca09d25ba9e1b084e29114e8bb8ded9d2758743112e631f15e2472d31600eb07a57ef397979567ff64b4c3c5c41353d9a98d8db646ea634dd43b64fadf82b967e3be7be742706c238f21c26f37f2bff9f5524a84464a5edfab61828c963ee2
大素数p = 168995677594036943498896698249502579045415356147450286903574977915675215654000852466242837180568368549600306461919095156035850147291191251838345423003548737288250427664794031697769270068290742307294644975782315875706815176748955712747679225674789516554407102487179525812178429394677953163553303283966837950227
q = 73250114511939221297189302708624091354575379476811068897570041621344734046574044427415715091676742616301137831925511472461697934230365993146217113253076136386575575868816429181422361239620593954716878229091392314316476106540409390466346705287246245765228049884691190461308813988563356306637349832642629018559
n = p * q: 12378952735785967421587876705989141498268850112196988040049473122006332676906044151498263826692270309125082373057093260664066396610236677683178624141001666648197090648303849825916354930186572209641520317512055055334099206541249675660097014166164940637694313192602999978844377200322202173154177984637778469358230375803525955958820029213002877725482468824045354087099096215852070204795481708079214127782986770087379200735916520872486000023245277376434002562642631172704562868269846650086718216208821320277688012375175773547390602961590412662108816162610739104457309428194480238546108099867035541068483564120972301262893
φ(n) = (p - 1) * (q - 1): 12378952735785967421587876705989141498268850112196988040049473122006332676906044151498263826692270309125082373057093260664066396610236677683178624141001666648197090648303849825916354930186572209641520317512055055334099206541249675660097014166164940637694313192602999978844377200322202173154177984637778469357988130011419979794023943212044751055082478088421092731297951196315050255094906811185555575510741658921477756442071914243988451941723720131449440026386006299029736864736236189207526584900909984015676489170302065357367311678301047558894790231648703342137674275822609522272620856483794231598292911004362834294108
私钥e: 17340019
公钥d = reverseMod(e, φ(n)): 3072319204072453737306343653935533481312293926073614447951005853992407696592808146082889511413838773453536217334645343450150591445038853551083491317503107325825170520927981475375745031992517559985687240594442119595767725477701532242869466882505815287360520420998354345053176733179117600424111042142752442111367183294624823448090872105232353129797839770752679284809699116616460835070405404257340673059447242478576903179970975361234779832989464641383953590073623511860666046606738481665429583341641154379349258756279398469749734409521008401173446126887957351830297138146414843182234886281526758355953645154096249723311
密文C = p^e (mod n): 8690266636448400378269418726205003112900277567495386429375850444458447796572158361293810625657601251810086273271224889184684916388080176766082690914051978067113164448575992370627181527559726902006574181613169007119234241584141129232711724255030558269342107190042881333739463284002233531205884969841267759982973947856931594586837269247202551775754985743907003991510094180725864546441495718014205230230577847231955254544873833080804873567927270581462454129765764632587975848718924619129646770469418420759534049239294802332121683853607786861658169111933815543554011449161898568916832755658480102315358426226624792795099
解密后明文deP = C^d (mod n): 56342340711826069541413772838184518837709350913150351018793773491775814688941635351710013086668389205376906521762156595155945044663082632323832546315089294869517263981313583862309801851905854642025977283238207101665880369615651380303339690747636683744518917750681305477070052587129682828817201369349285188210863135129756680686281991497547712446178
deP2(deP后1024位): 0x25348572ee8b90fb771a8afaa773a3e72954fea96f5168fa319a0ffc554c52267dca09d25ba9e1b084e29114e8bb8ded9d2758743112e631f15e2472d31600eb07a57ef397979567ff64b4c3c5c41353d9a98d8db646ea634dd43b64fadf82b967e3be7be742706c238f21c26f37f2bff9f5524a84464a5edfab61828c963ee2
deP1(deP剩余部分): 0xebc978722af2bf6eb99d323f0783a208
deP1的md4值: a91dc46963752f5cb5f7da5305836c8d
r的md4值: ebc978722af2bf6eb9fc505c63e6c46f
解密结果M: abcdefg
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