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RSA (cryptosystem)

| nosplit | ↑ parent "Public-key cryptography" | words: 213 | descendant words: 376 | descendants: 2
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Based on the fact that we don't have a P algorithm for integer factorization as of 2020. But nor proof that one does not exist!
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The private key is made of two randomly generated prime numbers: and . How such large primes are found: how large primes are found for RSA.
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The public key is made of:
• n = p*q
• a randomly chosen integer exponent between 1 and e_max = lcm(p -1, q -1), where lcm is the Least common multiple
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Given a plaintext message m, the encrypted cyphertext version is:
c = m^e mod n
This operation is called modular exponentiation can be calculated efficiently with the Extended Euclidean algorithm.
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The inverse operation of finding the private m from the public c, e and is however believed to be a hard problem without knowing the factors of n.
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However, if we know the private p and q, we can solve the problem. As follows.
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First we calculate the modular multiplicative inverse. TODO continue.
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