Şifreleme ve Matematiksel İşlemler

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Python programlama dilinde yazılmış bazı şifreleme algoritmaları ve matematiksel işlemleri içeren örnek kodları sizlerle paylaşmak istiyorum.

Aşağıda her bir konu için kısa bir açıklama ve ilgili Python dosyalarını bulabilirsiniz.


Don't reinvent the wheel; use libraries and frameworks wisely.​

Advanced Encryption Standard (AES) Implementation + ElGamal

ElGamal şifreleme algoritması ile yapılan bir şifreleme ve ardından elde edilen şifreli veriyi AES kullanarak şifrelemektedir

from Crypto.Util import number
from Crypto.Random import get_random_bytes
from Crypto.Cipher import AES

def eg_encrypt(m, pub_key):
    p, g, h = pub_key
    k = number.getRandomRange(1, p-1)
    c1 = pow(g, k, p)
    s = pow(h, k, p)
    c2 = [(ord(m[i]) * s) % p for i in range(len(m))]
    return c1, c2

def eg_decrypt(c, priv_key):
    c1, c2 = c
    x, p = priv_key
    s = pow(c1, x, p)
    m = ''.join([chr((c2[i] * pow(s, p-2, p)) % p) for i in range(len(c2))])
    return m

message = "Mekatronik.org bir forum sitesidir."

key = get_random_bytes(16)
iv = get_random_bytes(AES.block_size)

p = number.getPrime(1024)
g = number.getRandomRange(1, p-1)
x = number.getRandomRange(1, p-2)
h = pow(g, x, p)

pub_key = (p, g, h)
priv_key = (x, p)

eg_ciphertext = eg_encrypt(message, pub_key)


print("ElGamal ile Şifrelenmiş Mesaj:")
for pair in eg_ciphertext:
    print(pair)

decrypted_message = eg_decrypt(eg_ciphertext, priv_key)

print("\nOrijinal Mesaj:", message)
print("Çözülen Mesaj:", decrypted_message)

kodun çıktısı şu şekildedir

Orijinal Mesaj: Mekatronik.org bir forum sitesidir.
ElGamal ile Şifrelenmiş Mesaj:
(662757319321818644631891752222606451508131849094599825724688873557197478825328725162722262160706298476500536489808559135640825081585193316712315295843736501948438030114901922965830111673454416438677719630526347243241728829733071044053928501199348700728234634918218503395155465360542678854783818114671678029757406196820405422017983845622558336001961190029879586690554122185902286678932696542983023417926336132953823430502268219960319431902138844601364389065272856525231350750153193972131923489585124647099372466173014038381551034798457745893240996873252333175570511457029951367804135956746778255482762178808319937501961322358704154373493300152489696098496106693073902038167623729442557963832196501968033389290936262033499793087609062729053312226847356916902746434128084531016961666186964206376824487586796183122508372540011890631061460359920898412254631524127120086725656031899862614563417213059665228219682139461115037214656703747309042798477194030216087747752512053077332350465396987292831823660350642591942133842967465336450370665487828694813109256021011193404056184832161228403888723740438823008622313651768258998750048204849129072713692551936251786810959565537268989622441794550331238480683480340430128227651662843388170568155545437534129771853600751022325978874994700346148582854720803035122757698041064853299772091580579095227239998329555454233858734314750004731255776982998682024743662442556090145394669692956796163336708712953308639447943925484768243653556263176416350843455389052971246556259244987016140136443408838668635046012901045257332578861615557652461699741128508853328788329534628784444866282565739687207064741602569462150023649635509334250330694106929495883675541251224823798879585531843610679072579961561506301261740978286380940759674856292223077742370971134472956448787676980018382113149818552618156268235631745432971896870486536692238050946500788689028572218598249674370344667416213224329626839861769953573485049729671420361064870804257661203773158307072010185190868441849207474332870926315336023219516077621234933172802826789162369622606376078936297631727618314050665270595585565722463827225174202630624007997420751735151362496386495246667090019678543723977142735187502104009841973914263204669818827207221861388606946097108297611336189548987773801398272248842198366825035398324322074090537649671661468853469429142303473720038526330073406167176202952779196683320565930070914643729650829568219471386966481154248735393576802550591932527273387621336792265141586168473832742554196031801548080600396653693991940953740699303755181990061215151682472091248811523728017091619935776989094263967148742134177933557738261854511536785754166104961890413843446596225802689961536061529892037186057034241473631558367735369541072844499315930541898954697005210648626146473510452754081028529151488903950324206959598578758862735997259070693080034750412582729625961678354272875256091893740631392816384215748697097370173267267399062443953236310773289192708218642764933405929711723697253380129032697565704822686780924338451123633447171036038115574573572257632876325381694109341092032685569877404578280724515509257217891479539693002790162123786853662661261712557854185070288196111800888769754007585880502377145476048558288796175470176579614543084808733500988199853768861936168151188054848953388911200225203268702080474068295791355804295399004507196384168657028199218202498330273384193025053160991315312318601708228823792798818208052776453810253583347952211466846167290033516991265725071856523429191680725668315938209002238289857041796656303191869306626332661927429016056566722008341717351117229158987985019398586363437767470520079917919383547678417515345184443621551706042295221846050195758216768297424734240762043451053347858925693603086746656890076061472335067172987291108581563496150686251776265436623210054477771044530049633091227890997986427265711318102176112621692330232419689678424107283422313306122722551586580163648471114331803964151862288938131927611358140107161612399314503245430960024819199203582639328221004466136175320245547188078164591635971549698121502013986226783153287069086246396233267848124086512855264242004906398545215404198351495016169217896808139682152849090198021685922546050056777206964235047163332189507244738938201454804692570779996864266070078512513317439465083196432824407341587745457640947363777771004586586042776623169905586290734124787425818341557137998067547896250404221130256165146342564215480938631243243275158574184268402433004163522660467654878275408913902206106101868693942332772719675826195064744581476894340907307738721932466246992158564688114389541375108512850313565161805365450789077263367396695642898362230502525690697358973436426462948218745717866199396792006110504858678276595481102598454603292572931593712473667169088358830343186513297988273267128796250190784747896003862790882100495774594868899322575429142686219966911041583600875460474419024952476576066976926623346518273159251323558775628731508758033330736883947975094624171901793646432161193855450077346635582646556062344540417358556347193114272029465309942585269783564906558496341380481034684828703005095784056131827833854361105703818303721540437042379961849504303581371174050540251353848138456732077680459000312050882569791198256858431124071843932556763261155494109836794746167567372990951471227636641030041605235234674379848042677770855654187301700077311461334110446880132328583682166881861264566150943027184034476163980359675743654905555154265086825548561274555497607334000582721665582765012804751141588906264610021286140267489202173654088029190733859785314692403232836757847441987721002682341079332078051974508143254004423322968273750625837754369922618395537257896508960281541334427767640041258829785190787042790088012606430214546545328410218558963358926812823905689393503365011646260460457939742245204660145582650926675746466724894559487156109930762663987411725676305990292587797857428727711669007744580030983046416858791803539614066019341264130119343365205635529697957051102646907187037020282758925048840221125251769424135334429396413541361515038449632344584738071373986134550313361291802908601246573977707696901550754121213697501013223540651224122447630503562324776305346559513583150588199163178867994481003595038470996907915942716715319956533800952582581972454461514890309388452774876681059340674238431171097070256468092622733699221789164730736376485262541949743453906365675589539678994318764276639169692073509284504788624642407060100855743156161225652425568927667693590788776331556963695489301109126362103808671293195007374900758529421686654562698828743898879116738293839735080395444541845926802236864368290999554575305036082174607237153378490706229049139003602967671731015632692)
Çözülen Mesaj: Mekatronik.org bir forum sitesidir.

 

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Base64 Encoding and Decoding Implementation

Base64 kodlama ve çözme işlemlerinin bir Python kodu.

import base64

original_text = "mekatronik.org"

encoded_text = base64.b64encode(original_text.encode('utf-8')).decode('utf-8')

print("Orjinal:", original_text)
print("Base64:", encoded_text)

decoded_text = base64.b64decode(encoded_text).decode('utf-8')

print("Çözülen:", decoded_text)

Orjinal: mekatronik.org
Base64: bWVrYXRyb25pay5vcmc=
Çözülen: mekatronik.org

 

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RSA Encryption and Decryption Implementation
RSA şifreleme ve çözme algoritmaları

bunu yazmıcam

 

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Diffie-Hellman Key Exchange Implementation
Diffie-Hellman anahtar değişimi algoritmasının basit bir kod ile anlatımını içerir.

from pyDH import DiffieHellman

dh_obj1 = DiffieHellman()
dh_obj2 = DiffieHellman()

public_key1 = dh_obj1.gen_public_key()
public_key2 = dh_obj2.gen_public_key()

shared_key1 = dh_obj1.gen_shared_key(public_key2)
shared_key2 = dh_obj2.gen_shared_key(public_key1)

assert shared_key1 == shared_key2

print("Açık Anahtar 1: ", public_key1)
print("Açık Anahtar 2: ", public_key2)
print("Ortak Anahtar: ", shared_key1)

Açık Anahtar 1:  8808555100307987004470763486609437964827589034261284258692381125075489796030912865484094624503527997652400000244471268377823672388985700742873528603800761593947647161483465789787554651613405139377942873348738383662149806431120156252482146127931971962251987456212660538080288130069743149916323522328780590512483059785094085875248750187838267520925459826155789892349727831784680721656351910126738130661443014415393465329195838231209478781852651443227170134990050204254978604621523629673119941362648656313942014874390502839072392554393185137874146181527198693364515659811093428964546378449119486792010588352142471441945519529536795395953640285430841599079606431020521245530271589296199684568604088783131242343145379243037033281921809168131381962699942148335569379921581447128729441527759743474698391912407383870221128468702183317261493163090243966626958461118483229220523915636071642319053592621662760364013671410544524221519723608433885728585041305857475262248190451948853462151103111127551015528011812205787260993482474780674806257042286828180659876430953081281633003988659408123890094939463542447268160895585787780677100445954676650403624019
Açık Anahtar 2:  363839087246641225914980143442042369604591495001033454815759271595308003132209358106351489297527354693816579469138876660972440121197643245373799331823600959316271204198231265675915501441132991994854300214769289572309546708153456547994558092799359164529001460124389162257865115141938667327122612724037935826219105381354073188254837347727278078774012331284308135813238598800567138960230260165542498572193246809334604973651217268161557283261650112262338963413088769057809499021235423191008351028454964937651622472199413710310951111178424832011380348696070669464261115630000632997290258049837457379623980578310723285938932711438029128510315079524280855838400315165468854274894685942529551544754930670845656379501585837690635236131225127362462686868744192964665922927152373161588264348311185416242781703967849076237454348744091777396394594106879760497970348127856146072765037013939272875717482079854735479777367929810905448372439946411536647606198614974873923507646802051220009185132321636605074367368538514721346661043250546631656221879832537081850581330120442473855079687587780554386024472145958011109415021012448631174464676134620361466765702476924801586765387873071009855669488221306860536882246441050937088937745754970272533535348161133885373866661861852358295567314569095098477054053938227512405515873292292461601692420609448832192282755640606312628178285128736077209353152583013663920777939914165937780637451538694070117792485636630775368370741833010961503905298765994385352120276218775950387983871299981219539088329407651401294553610458439788041508216785111177427227289854327926987017243407145271128003853696829427259452671376048156067195400061433628117288836005860109195065013804868458433033253174030287389019881120474034070897567598301235653943893238150158647386963024250634624271899707923974679196605846961480415150126057630848619605571336752215295021312220740846336610336086336656405651556693391890923822725080790741870
Ortak Anahtar:   25914980143442042369604591495001033454815759271595308003132209358106351489297527354693816579469138876660972440121197643245373799331823600959316271204198231265675915501441132991994854300214769289572309546708153456547994558092799359164529001460124389162257865115141938667327122612724037935826219105381354073188254837347727278078774012331284308135813238598800567138960230260165542498572193246809334604973651217268161557283261650112262338963413088769057809499021235423191008351028454964937651622472199413710310951111178424832011380348696070669464261115630000632997290258049837457379623980578310723285938932711438029128510315079524280855838400315165468854274894685942529551544754930670845656379501585837690635236131225127362462686868744192964665922927152373161588264348311185416242781703967849076237454348744091777396394594106879760497970348127856146072765037013939272875717482079854735479777367929810905448372439946411536647606198614974873923507646802051220009185132321636605074367368538514721346661043250546631656221879832537081850581330120442473855079687587780554386024472145952591498014344204236960459149500103345481575927159530800313220935810635148929752735469381657946913887666097244012119764324537379933182360095931627120419823126567591550144113299199485430021476928957230954670815345654799455809279935916452900146012438916225786511514193866732712261272403793582621910538135407318825483734772727807877401233128430813581323859880056713896023026016554249857219324680933460497365121726816155728326165011226233896341308876905780949902123542319100835102845496493765162247219941371031095111117842483201138034869607066946426111563000063299729025804983745737962398057831072328593893271143802912851031507952428085583840031516546885427489468594252955154475493067084565637950158583769063523613122512736246268686874419296466592292715237316158826434831118541624278170396784907623745434874409177739639459410687976049797034812785614607276503701393927287571748207985473547977736792981090544837243994641153664760619861497487392350764680205122000918513232163660507436736853851472134666104325054663165622187983253708185058133012044247385507968758778055438602447214595

 

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Elliptic Curve Cryptography (ECC) Implementation

Elliptic Curve Cryptography (ECC) algoritmasının P-256 eğrisini kullanır basit bir kod

from Crypto.PublicKey import ECC

key = ECC.generate(curve='P-256')

private_key = key.export_key(format='PEM')
public_key = key.public_key().export_key(format='PEM')

message = b"Mekatronik.org/forum çakır öldümü?"

encrypted_message = key.public_key().encrypt(message, None)

decrypted_message = key.decrypt(encrypted_message)

print("Özel Anahtar: ", private_key.decode('utf-8'))
print("Açık Anahtar: ", public_key.decode('utf-8'))
print("Orijinal Mesaj: ", message)
print("Şifreli Mesaj: ", encrypted_message)
print("Çözümlenmiş Mesaj: ", decrypted_message)

Özel Anahtar:  -----BEGIN PRIVATE KEY-----
MHcCAQEEIE6WBtcdLO2R1RFIgs13wtylXhBwx2MHw21b2qC5NJ1woAoGCCqGSM49
AwEHoUQDQgAE7Tl5aRmVlQtvtdtjJhDFaaH8ZXtRJQGbGcPnKPVgY9W5Fibjqd7h
Uy3uE7zw5HWws+tTe/xs+aOYS1yyqIrW8g==
-----END PRIVATE KEY-----
Açık Anahtar:  -----BEGIN PUBLIC KEY-----
MFkwEwYHKoZIzj0CAQYIKoZIzj0DAQcDQgAE7Tl5aRmVlQtvtdtjJhDFaaH8ZXtR
JQGbGcPnKPVgY9W5Fibjqd7hUy3uE7zw5HWws+tTe/xs+aOYS1yyqIrW8g==
-----END PUBLIC KEY-----
Orijinal Mesaj:  b'Mekatronik.org/forum \xc3\xa7ak\xc4\xb1r \xc3\xb6ld\xc3\xbcm\xc3\xbc?'
Şifreli Mesaj:  b'0\xd7\xcd@\x96\xcf)\xfc\xb8\x19t(\xe2\x15x\t\xd5+\x9d*\xe9\xa4o\xf3\xd9\xe4y\xe3\xcf9\x95\x84\x0e\xbd\xf0'
Çözümlenmiş Mesaj:  b'Mekatronik.org/forum \xc3\xa7ak\xc4\xb1r \xc3\xb6ld\xc3\xbcm\xc3\xbc?'

 

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Linear Formula Implementation

basit bir şifreleme algoritması olan "Cezar Şifreleme" veya "Shift Cipher" uygular. Bu şifreleme türünde her harfi belirli bir sayıda kaydırarak şifreleme yapılır. Bu örnekte key değeri 3 olarak belirlenmiştir, yani her harf 3 pozisyon kaydırılmıştır.

alphabet = 'abcdefghijklmnopqrstuvwxyz'
key = 3
new_message = ''

message = 'mekatronik.org/forum'

for character in message:
    if character in alphabet:
        position = alphabet.find(character)
        new_position = (position + key) % 26
        new_character = alphabet[new_position]
        new_message += new_character
    else:
        new_message += character

print(new_message)

phlwdwqlvnl.rv/huyhb

 

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Digital Signature Algorithm (DSA) Implementation
DSA (Digital Signature Algorithm) algoritması ile dijital imza oluşturma ve doğrulama işlemlerini göstermektedir.

from Crypto.PublicKey import DSA
from Crypto.Signature import DSS
from Crypto.Hash import SHA256

key_pair = DSA.generate(2048)

def sign(key_pair, message):
    hash_obj = SHA256.new(message)
    signer = DSS.new(key_pair, 'fips-186-3')
    signature = signer.sign(hash_obj)
    return signature

def verify(key_pair, message, signature):
    hash_obj = SHA256.new(message)
    verifier = DSS.new(key_pair, 'fips-186-3')
    try:
        verifier.verify(hash_obj, signature)
        print("İmza doğru.")
    except ValueError:
        print("İmza yanlış.")

message = b"1234"

signature = sign(key_pair, message)

verify(key_pair.publickey(), message, signature)

İmza doğru.

 

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Hash Function (Usage of SHA-256)​

SHA-256 hash fonksiyonunu kullanır. Bu tür bir hash fonksiyonu,
veride küçük bir değişiklik olsa bile üretilen hash değerinde büyük farklılıklar sağlar.

import hashlib

def hash_function(data):
    hashed_data = hashlib.sha256(data.encode()).hexdigest()
    return hashed_data


input_data = "mekatronik.org/forum"
hashed_result = hash_function(input_data)
print(f"Orjinal Veri: {input_data}")
print(f"Hash Değeri: {hashed_result}")

Orjinal Veri: mekatronik.org/forum
Hash Değeri: 65dd7f0c7f2362b7e28e09db7d81210da28294f3a05ef2223548a0842e9c81b2

 

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3DES (Triple Data Encryption Standard), DES (Data Encryption Standard)

3DES, temelde aynı DES algoritmasının üç kez kullanılması ilkesine dayanır.
Anahtarlar genellikle ABA şeması veya CBC (Cipher Block Chaining) modu ile birleştirilir

from cryptography.hazmat.primitives.ciphers import Cipher, algorithms, modes
from cryptography.hazmat.backends import default_backend
from cryptography.hazmat.primitives import padding

def encrypt_3des(message, key):
    cipher = Cipher(algorithms.TripleDES(key), modes.ECB(), backend=default_backend())
    encryptor = cipher.encryptor()
    padder = padding.PKCS7(algorithms.TripleDES.block_size).padder()
    padded_data = padder.update(message) + padder.finalize()
    encrypted_message = encryptor.update(padded_data) + encryptor.finalize()
    return encrypted_message

def decrypt_3des(encrypted_message, key):
    cipher = Cipher(algorithms.TripleDES(key), modes.ECB(), backend=default_backend())
    decryptor = cipher.decryptor()
    decrypted_data = decryptor.update(encrypted_message) + decryptor.finalize()
    unpadder = padding.PKCS7(algorithms.TripleDES.block_size).unpadder()
    decrypted_message = unpadder.update(decrypted_data) + unpadder.finalize()
    return decrypted_message

key = b'd3d3l3rAnl4tiy0r'

original_message = b"mekatronik.org/forum"

print("Original :", original_message)

encrypted_message = encrypt_3des(original_message, key)
print("Encrypted:", encrypted_message)
decrypted_message = decrypt_3des(encrypted_message, key)
print("Decrypted Message:", decrypted_message)

Original : b'mekatronik.org/forum'
Encrypted: b'8V\x1a\x01\xcd\xaf\x1a\x95\x80%\xd1rB?\xa6\x8c0\xd8O\x98\x82\xa5\xab\xd1'
Decrypted Message: b'mekatronik.org/forum'

 

[nt]

XOR (exclusive or)

def xor(text, key):
    text = ''.join(chr(ord(char) ^ key) for char in text)
    return text

def xor_decrypt(text, key):
    return xor(text, key)

original_text = "mekatronik.org/forum"

encryption_key = 99
print(f"Şifreleme Anahtarı: {encryption_key}")
text = xor(original_text, encryption_key)
print(f"Şifrelenmiş Metin: {text}")
print(f"Şifrelenmiş Metinin Uzunluğu: {len(text)}")
decrypted = xor_decrypt(text, encryption_key)
print(f"Çözülmüş Metin: {decrypted}")

Şifreleme Anahtarı: 99
Şifrelenmiş Metin:

M
 L

Şifrelenmiş Metinin Uzunluğu: 20
Çözülmüş Metin: mekatronik.org/forum

 

[nt]

ÖMER HAYYAM ÜÇGENİ ALGORİTMASI (hayyam üçgeni algoritması "custom")
hayyamın ve ibni Arabinin methotlarını düşünürken aklıma geldi tamamen özel kullanmak isterseniz kullanın metni binom katsayılarını kullanıp adımlara göre şifreler ve o adımlara göre şifreyi çözer

def hayyam_katsayisi(n, k):
    if k == 0 or k == n:
        return 1
    return hayyam_katsayisi(n-1, k-1) + hayyam_katsayisi(n-1, k)

def metni_hayyam_ile_sifrele(metin, hayyam_katsayilari):
    sifreli_metin = ''
    for i, karakter in enumerate(metin):
        katsayi = hayyam_katsayilari[i % len(hayyam_katsayilari)]
        sifreli_karakter = chr(ord(karakter) + katsayi)
        sifreli_metin += sifreli_karakter
    return sifreli_metin

def sifreli_metni_hayyam_ile_coz(sifreli_metin, hayyam_katsayilari):
    cozulmus_metin = ''
    for i, karakter in enumerate(sifreli_metin):
        katsayi = hayyam_katsayilari[i % len(hayyam_katsayilari)]
        cozulmus_karakter = chr(ord(karakter) - katsayi)
        cozulmus_metin += cozulmus_karakter
    return cozulmus_metin

orijinal_metin = "mekatronik.org/forum"
print(f"Orijinal Metin: {orijinal_metin}")

hayyam_katsayilari = [hayyam_katsayisi(10, i) for i in range(10)]
print(hayyam_katsayilari)

sifreli_metin = metni_hayyam_ile_sifrele(orijinal_metin, hayyam_katsayilari)
print(f"Şifrelenmiş Metin: {sifreli_metin}")

cozulmus_metin = sifreli_metni_hayyam_ile_coz(sifreli_metin, hayyam_katsayilari)
print(f"Çözülmüş Metin: {cozulmus_metin}")

Orijinal Metin: mekatronik.org/forum
[1, 10, 45, 120, 210, 252, 210, 120, 45, 10]
Şifrelenmiş Metin: noņŮŁæu/yāŢŁê¢w
Çözülmüş Metin: mekatronik.org/forum