2022-01-31 19:15:01 +00:00
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= RSA =
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2022-01-31 19:30:01 +00:00
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RSA is an asymetric encryption algorithm based on the difficulty of factoring
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large prime numbers.
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== algoirthm ==
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2022-01-31 19:45:01 +00:00
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1) choose some `p` and `q`
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* where `p` and `q` are very large primes
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* `n = p * q`
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2022-01-31 19:30:01 +00:00
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2) T = (p-1)(q-1)
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* known as eulers totient
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3) choose 2 values e and d
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* where (e * d) mod T = 1
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* where e < T
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* [[../math/relative_prime]] with T and N
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4) we now have our keys
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* n and e are public keys
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* n and d are private keys
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2022-01-31 19:38:26 +00:00
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=== encryption ===
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`(plaintext value)^e mod N = ciphertext value`
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=== decryption ===
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`(ciphertext value)^d mod N = plaintext vlaue`
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2022-01-31 19:30:01 +00:00
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=== example ===
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2022-01-31 19:38:26 +00:00
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`p = 2; q = 7`
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2022-01-31 19:30:01 +00:00
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therefore,
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2022-01-31 19:38:26 +00:00
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`n = 14; T = 6`
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2022-01-31 19:30:01 +00:00
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Due to restrictions, choose e = 5
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2022-01-31 19:38:26 +00:00
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Then choose d from pool of canidiates satisfying `(e * d) mod T = 1`
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For example then, choose 14 as d
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Private key `(11,14)` and public key `(5,14)`
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For example Encrypt B
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`2^5 mod 14 = 4` or `D`
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Decrypt value
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`4^11 mod 14 = 2` or our original `B`
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2022-01-31 20:00:01 +00:00
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== Also see ==
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* [[Eliptic_Curve]]
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