54 lines
1.2 KiB
Markdown
54 lines
1.2 KiB
Markdown
# Procedure
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We have 4 primary values that we deal with:
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* p
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* q
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* e
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* m
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There are a few components which must be calculated before we can safely determine a cipher text:
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`n = p * q` : note that `p` and `q` values should be primes in this case.
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`Φ(n) = (p - 1) * (q - 1)` is used later to verify that we have a value `d` which is the inverse of `e`. _We call this the quotient function_.
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## Encryption
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To produce a cipher text `C` we take `m` and raise it to the power of `e`(from earlier) then take the modulo of it by `n`:
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```
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C = (m^e) % n
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```
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`m` is the desired message to encrypt.
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The public and private keys are using the above cipher text functions whose unknown parameters are passed as follows
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`PublicKey(e, n)`
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`PrivateKey(d, n)`
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## Decryption
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The reverse of this is the following:
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```
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M = (c^d) % n
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```
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## E inverse e^1
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To find `d` the following _must_ be true: `GCD(e, Φ(n)) == 1`.
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If this is not the case then there is no `d` or `e^-1`.
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> how do i actually this trash tho???
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Let's say we have `e=17` and `Φ(n)=60`:
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We know the GCD(17,60) == 1 [17 is prime] so we can find an `e` inverse.
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_Check the notes at the bottom for an easy to rationalize method of verifying this_.
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