37 lines
1.1 KiB
Markdown
37 lines
1.1 KiB
Markdown
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# RSA
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* `p * q = n`
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* Coprime Phi is calculated either by [Euler Totient](https://en.wikipedia.org/wiki/Euler's_totient_function) or [greatest common divisor](https://en.wikipedia.org/wiki/Greatest_common_divisor) via [euclidean algorithm](https://crypto.stanford.edu/pbc/notes/numbertheory/euclid.html)
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* \\(1 < $\phi$ < n \\)
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* There is also $\phi$ = (p-1) * (q-1)
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* Encryption, public key `e` is a prime between 2 and phi --> \\( 2 < e < $\phi$ \\)
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```python
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possible_e = []
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for i in range (2, phi):
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if gcd(n, i) == 1 and gcd(phi, i) == 1:
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possible_e.append()
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```
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* Decryption, private key `d` --> \\( d * e mod $\phi$ = 1 \\)
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```python
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possible_d = []
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for i in range (phi + 1, phi + foo):
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if i * e mod phi == 1 :
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possible_d.append()
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```
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* \\( Cipher = msg ** d mod $\phi$ \\)
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* \\( Cleartext = cipher ** e mod $\phi$ )
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## Euklid
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```python
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def gcd(a, b):
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if b == 0:
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return a
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return gcd(b, a % b)
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```
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## Links
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* [Encryption+Decryption](https://www.cs.drexel.edu/~jpopyack/Courses/CSP/Fa17/notes/10.1_Cryptography/RSA_Express_EncryptDecrypt_v2.html)
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