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Commit 483431b

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[IMPLEMENTATION] RSA algorithm (#727)
* [IMPLEMENTATION] RSA algorithm * [UPDATE] Intended keyGen algorithm with randomness * [FIX] comment fixed * [UPDATE] Implement suggestions * [FIX] Implement suggestions
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‎cipher/rsa/rsa2.go‎

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/*
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rsa2.go
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description: RSA encryption and decryption including key generation
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details: [RSA wiki](https://en.wikipedia.org/wiki/RSA_(cryptosystem))
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author(s): [ddaniel27](https://github.com/ddaniel27)
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*/
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package rsa
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import (
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"encoding/binary"
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"fmt"
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"math/big"
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"math/rand"
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"github.com/TheAlgorithms/Go/math/gcd"
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"github.com/TheAlgorithms/Go/math/lcm"
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"github.com/TheAlgorithms/Go/math/modular"
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"github.com/TheAlgorithms/Go/math/prime"
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)
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// rsa struct contains the public key, private key and modulus
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type rsa struct {
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publicKey uint64
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privateKey uint64
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modulus uint64
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}
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// New initializes the RSA algorithm
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// returns the RSA object
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func New() *rsa {
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// The following code generates keys for RSA encryption/decryption
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// 1. Choose two large prime numbers, p and q and compute n = p * q
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p, q := randomPrime() // p and q stands for prime numbers
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modulus := p * q // n stands for common number
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// 2. Compute the totient of n, lcm(p-1, q-1)
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totient := uint64(lcm.Lcm(int64(p-1), int64(q-1)))
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// 3. Choose an integer e such that 1 < e < totient(n) and gcd(e, totient(n)) = 1
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publicKey := uint64(2) // e stands for encryption key (public key)
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for publicKey < totient {
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if gcd.Recursive(int64(publicKey), int64(totient)) == 1 {
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break
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}
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publicKey++
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}
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// 4. Compute d such that d * e ≡ 1 (mod totient(n))
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inv, _ := modular.Inverse(int64(publicKey), int64(totient))
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privateKey := uint64(inv)
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return &rsa{
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publicKey: publicKey,
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privateKey: privateKey,
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modulus: modulus,
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}
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}
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// EncryptString encrypts the data using RSA algorithm
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// returns the encrypted string
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func (rsa *rsa) EncryptString(data string) string {
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var nums []byte
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for _, char := range data {
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slice := make([]byte, 8)
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binary.BigEndian.PutUint64( // convert uint64 to byte slice
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slice,
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encryptDecryptInt(rsa.publicKey, rsa.modulus, uint64(char)), // encrypt each character
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)
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nums = append(nums, slice...)
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}
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return string(nums)
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}
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// DecryptString decrypts the data using RSA algorithm
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// returns the decrypted string
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func (rsa *rsa) DecryptString(data string) string {
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result := ""
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middle := []byte(data)
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for i := 0; i < len(middle); i += 8 {
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if i+8 > len(middle) {
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break
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}
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slice := middle[i : i+8]
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num := binary.BigEndian.Uint64(slice) // convert byte slice to uint64
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result += fmt.Sprintf("%c", encryptDecryptInt(rsa.privateKey, rsa.modulus, num))
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}
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return result
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}
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// GetPublicKey returns the public key and modulus
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func (rsa *rsa) GetPublicKey() (uint64, uint64) {
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return rsa.publicKey, rsa.modulus
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}
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// GetPrivateKey returns the private key
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func (rsa *rsa) GetPrivateKey() uint64 {
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return rsa.privateKey
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}
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// encryptDecryptInt encrypts or decrypts the data using RSA algorithm
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func encryptDecryptInt(e, n, data uint64) uint64 {
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pow := new(big.Int).Exp(big.NewInt(int64(data)), big.NewInt(int64(e)), big.NewInt(int64(n)))
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return pow.Uint64()
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}
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// randomPrime returns two random prime numbers
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func randomPrime() (uint64, uint64) {
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sieve := prime.SieveEratosthenes(1000)
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sieve = sieve[10:] // remove first 10 prime numbers (small numbers)
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index1 := rand.Intn(len(sieve))
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index2 := rand.Intn(len(sieve))
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for index1 == index2 {
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index2 = rand.Intn(len(sieve))
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}
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return uint64(sieve[index1]), uint64(sieve[index2])
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}

‎cipher/rsa/rsa2_test.go‎

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package rsa_test
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import (
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"testing"
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"github.com/TheAlgorithms/Go/cipher/rsa"
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)
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func TestRSA(t *testing.T) {
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tests := []struct {
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name string
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message string
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}{
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{
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name: "Encrypt letter 'a' and decrypt it back",
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message: "a",
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},
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{
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name: "Encrypt 'Hello, World!' and decrypt it back",
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message: "Hello, World!",
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},
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}
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for _, tt := range tests {
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t.Run(tt.name, func(t *testing.T) {
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rsa := rsa.New()
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encrypted := rsa.EncryptString(tt.message)
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decrypted := rsa.DecryptString(encrypted)
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if decrypted != tt.message {
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t.Errorf("expected %s, got %s", tt.message, decrypted)
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}
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})
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}
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}
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func BenchmarkRSAEncryption(b *testing.B) {
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rsa := rsa.New()
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for i := 0; i < b.N; i++ {
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rsa.EncryptString("Hello, World!")
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}
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}
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func BenchmarkRSADecryption(b *testing.B) {
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rsa := rsa.New()
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encrypted := rsa.EncryptString("Hello, World!")
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for i := 0; i < b.N; i++ {
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rsa.DecryptString(encrypted)
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}
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}

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