RSAは公開鍵暗号の一つ
暗号文 = 平文^E mod N {E, N}が公開鍵
平文 = 暗号文^D mod N {D, N}が秘密鍵
E, D, Nを求めるには素数を使う
N = p * q
L = lmc(p – 1, q – 1) # lmcとは最小公倍数(Least Common Multiple)
1 < E < L
gcd(E,L) = 1 # gcdとは最大公約数、 E, Lは互いに素な整数
1 < D < L
(E・D) mod L = 1 # DはEとの積の余剰が1となる任意の整数
from math import gcd
def lcm(p, q):
return (p * q) // gcd(p, q)
def generate_keys(p, q):
N = p * q
L = lcm(p – 1, q – 1)
for i in range(2, L):
if gcd(i, L) == 1:
E = i
break
for i in range(2, L):
if(E * i) % L == 1:
D = i
break
return (E, N), (D, N)
def encrypt(plain_text, public_key):
E, N = public_key
plain_integers = [ord(char) for char in plain_text]
encrypted_integers = [pow(i, E, N) for i in plain_integers]
encrypted_text = ”.join(chr(i) for i in encrypted_integers)
return encrypted_text
def decrypt(encrypted_text, private_key):
D, N = private_key
encrypted_integers = [ord(char) for char in encrypted_text]
decrypted_integers = [pow(i, D, N) for i in encrypted_integers]
decrypted_text = ”.join(chr(i) for i in decrypted_integers)
return decrypted_text
def sanitize(encrypted_text):
return encrypted_text.encode(‘utf-8’, ‘replace’).decode(‘utf-8’)
if __name__ == ‘__main__’:
public_key, private_key = generate_keys(101, 3259)
plain_text = ‘おはようございます’
encrypted_text = encrypt(plain_text, public_key)
decrypted_text = decrypt(encrypted_text, private_key)
print(f”’
秘密鍵: {public_key}
公開鍵: {private_key}
平文: 「{plain_text}」
暗号文:
「{sanitize(encrypted_text)}」
平文(複合後):
「{decrypted_text}」
”'[1:-1])
なるほど、crypto currencyは暗号通貨ってことね
