标题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，但由于根本算法具有的同态性，在现实利用过程中，通常必要对根本的RSA算法举行改进，而RSA-OAEP算法即为现实利用算法之一。本课题致力于对RSA-OAEP算法的模仿实现，使门生深入相识根本RSA算法怎样应用到现实的秘密性题目办理中，提升编程本事。
标题的具体要求
1.查阅相干资料，深入相识RSA-OAEP算法的实现头脑和原理；
2.选择一种编程语言和开发工具，模仿实现RSA-OAEP算法的加解密，并可以大概实现对笔墨信息的加解密；
3.程序具有图形化用户界面，输出雅观；
4.可根据自己本事，在完成以上根本要求后，对程序功能举行恰当扩充；
5.撰写报告，对所采取的算法、程序布局和重要函数过程以及关键变量举行具体的阐明；对程序的调试过程所碰到的题目举行回首和分析，对测试和运行结果举行分析；总结软件筹划和训练的履历和领会，进一步改进的假想；
6.提供关键程序的清单、源程序及可实行文件和相干的软件阐明。
附（RSA-OAEP算法）
加密1) Alice 添补信息来制成一个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（留意r只能利用一次然后就要烧毁）。Alice运用MD4函数G，用r生成一个m比特的整数，创建部门明文然后创建部门明文这里函数H也选用MD4，将m比特的输入生成k比特的输出。
加密3) Alice 创建密文而且把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。然后运用重新创建添补信息的值。
解密3) 从M当中取消添补后，Bob得到了原信息。
# OAEP_easyRealize.pyfrom Crypto.PublicKey import RSAfrom Crypto.Cipher import PKCS1_OAEPimport base64rsa_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+0f0sp71Fhzj2EPQQv5puPP7dNpSdqQ1GgMIKRgc5tClyaw+gtuY1MGaL++oQg543tpnPfFVXzmi1j0rRl1KSljfI8eiQ5XLu/t+FCn9kVltZTWaXBxmloWwPbphhkgVuryxCxhCKAf2n4KSJM/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.pymaxInt = 0x100000000S = [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添补成512位【16整数*4字节】的倍数' count = len(sequence) multi_16s = ((count + 8) // 64 + 1) * 16 # 共必要整数的个数，每个整数存储4个字节的数据 sequence += [0] * (multi_16s * 4 - count) # 用 0 添补 sequence[count] |= 128 # 用一个 1 补在反面 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 * 4i + 1) * 4]]), 2)) # 每四个Ascii归并成一个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_4bytesdef fill(sequence): '将字节序列按小端序添补成512位【16整数*4字节】的倍数' count = len(sequence) multi_16s = ((count + 8) // 64 + 1) * 16 # 共必要整数的个数，每个整数存储4个字节的数据 sequence += [0] * (multi_16s * 4 - count) # 用 0 添补 sequence[count] |= 128 # 用一个 1 补在反面 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 * 4i + 1) * 4]) # 大端序存储 multi_4bytes.append( int("".join(["{:08b}".format(ii) for ii in sequence[i * 4i + 1) * 4]]), 2)) # 每四个Ascii归并成一个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_4bytesdef 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 ^ Zdef Go(a, b, c, d, fun, m, s, K): thesum = (a + fun(b, c, d) + int(m) + K) % maxInt return shift(thesum, s) % maxIntdef int32ToHex(a): '32位整型聚集转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 md4def 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添补成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.pyimport randomimport binasciiimport easyguiimport MD4_Realizedef gcd(a, b): # 求最大公因数 while a != 0: a, b = b % a, a return bdef 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 % nif __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剩余部门): " + 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: abcdefg1024位随机数r: 0010010100110100100001010111001011101110100010111001000011111011011101110001101010001010111110101010011101110011101000111110011100101001010101001111111010101001011011110101000101101000111110100011000110011010000011111111110001010101010011000101001000100110011111011100101000001001110100100101101110101001111000011011000010000100111000101001000100010100111010001011101110001101111011011001110100100111010110000111010000110001000100101110011000110001111100010101111000100100011100101101001100010110000000001110101100000111101001010111111011110011100101111001011110010101011001111111111101100100101101001100001111000101110001000001001101010011110110011010100110001101100011011011011001000110111010100110001101001101110101000011101101100100111110101101111110000010101110010110011111100011101111100111101111100111010000100111000001101100001000111000111100100001110000100110111100110111111100101011111101010000111010001001011000100011111001110011001101100101000000100110101001011100101110111101000110001001000101010101001001101111输入值M的ascii值: b'61626364656667'r的md4值: ebc978722af2bf6eb9fc505c63e6c46fP1的md4值: a91dc46963752f5cb5f7da5305836c8d明文P=(P1+P2): 0xebc978722af2bf6eb99d323f0783a20825348572ee8b90fb771a8afaa773a3e72954fea96f5168fa319a0ffc554c52267dca09d25ba9e1b084e29114e8bb8ded9d2758743112e631f15e2472d31600eb07a57ef397979567ff64b4c3c5c41353d9a98d8db646ea634dd43b64fadf82b967e3be7be742706c238f21c26f37f2bff9f5524a84464a5edfab61828c963ee2大素数p = 168995677594036943498896698249502579045415356147450286903574977915675215654000852466242837180568368549600306461919095156035850147291191251838345423003548737288250427664794031697769270068290742307294644975782315875706815176748955712747679225674789516554407102487179525812178429394677953163553303283966837950227q = 73250114511939221297189302708624091354575379476811068897570041621344734046574044427415715091676742616301137831925511472461697934230365993146217113253076136386575575868816429181422361239620593954716878229091392314316476106540409390466346705287246245765228049884691190461308813988563356306637349832642629018559n = p * q: 12378952735785967421587876705989141498268850112196988040049473122006332676906044151498263826692270309125082373057093260664066396610236677683178624141001666648197090648303849825916354930186572209641520317512055055334099206541249675660097014166164940637694313192602999978844377200322202173154177984637778469358230375803525955958820029213002877725482468824045354087099096215852070204795481708079214127782986770087379200735916520872486000023245277376434002562642631172704562868269846650086718216208821320277688012375175773547390602961590412662108816162610739104457309428194480238546108099867035541068483564120972301262893φ(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): 56342340711826069541413772838184518837709350913150351018793773491775814688941635351710013086668389205376906521762156595155945044663082632323832546315089294869517263981313583862309801851905854642025977283238207101665880369615651380303339690747636683744518917750681305477070052587129682828817201369349285188210863135129756680686281991497547712446178deP2(deP后1024位): 0x25348572ee8b90fb771a8afaa773a3e72954fea96f5168fa319a0ffc554c52267dca09d25ba9e1b084e29114e8bb8ded9d2758743112e631f15e2472d31600eb07a57ef397979567ff64b4c3c5c41353d9a98d8db646ea634dd43b64fadf82b967e3be7be742706c238f21c26f37f2bff9f5524a84464a5edfab61828c963ee2deP1(deP剩余部门): 0xebc978722af2bf6eb99d323f0783a208deP1的md4值: a91dc46963752f5cb5f7da5305836c8dr的md4值: ebc978722af2bf6eb9fc505c63e6c46f解密结果M: abcdefg
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