文件列表:

LICENSE (11347, 2020-05-08)
src (0, 2020-05-08)
src\rsa (0, 2020-05-08)
src\rsa\CreateRandom.java (2169, 2020-05-08)
src\rsa\FME.java (1389, 2020-05-08)
src\rsa\GenerateKeys.java (3077, 2020-05-08)
src\rsa\RSA.java (9287, 2020-05-08)
src\rsa\package-info.java (171, 2020-05-08)

# RSA Algorithm - [x] Generating Key value pair with a multiple options for number of bits to choose from. - [x] Option to store Public and Private Key in .txt file. - [x] Encrypts a message (also gives option to import key stored by the same program) - [x] Option to store Encrypted Message in .txt file. - [X] Decrypts a message (also gives option to import key stored by the same program) ## Implementation #### I. Key Generation > Using [CreateRandom Class](https://github.com/abhi-agrawl/rsa-algorithm/blob/master/src/rsa/CreateRandom.java) - Get two different large prime numbers ***p*** and ***q*** - Using *Miller-Rabin Test* > Using [GenerateKeys Class](https://github.com/abhi-agrawl/rsa-algorithm/blob/master/src/rsa/GenerateKeys.java) - Let ***n*** = *p* * *q* - Let ***φ(n)*** = *(p-1)* * *(q-1)* - Choose a small, odd integer number ***e***, where 1 < e < φ(n) and *e* is a co-prime to ***φ(n)***. - Using *Euclidean Algorithm* - Check *calculateEncryptionExponent()* method - Calculate the integer number ***d***, where *e*d ≡ 1 mod φ(n) and 1 < d < φ(n). - Using *Extended Euclidean Algorithm* - Check *calculateDecryptionExponent()* method - [x] The public key of the RSA is the pair PK = (n, e) - [x] The secret key of the RSA is the pair SK = (n, e) #### II. Encryption > Using [FME Class](https://github.com/abhi-agrawl/rsa-algorithm/blob/master/src/rsa/FME.java) - To encrypt the message **m** (where m < n) using the public key ***PK = (n, e)*** following formula is used: **(Fast Modular Exponent)** ``` c := EncPK(m) = m^e (mod n). ``` #### III. Decryption > Using [FME Class](https://github.com/abhi-agrawl/rsa-algorithm/blob/master/src/rsa/FME.java) - To decrypt the secret message ***c*** using the secret key ***d*** following formula is used: **(Fast Modular Exponent)** ``` m := DecSK(c) = c^d (mod n). ```

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