AlgorithmAndLeetCode · pull · Jan 23, 2023 · Jan 23, 2023
diff --git a/Cargo.toml b/Cargo.toml
@@ -5,6 +5,7 @@ version = "0.1.0"
 authors = ["Anshul Malik <malikanshul29@gmail.com>"]
 
 [dependencies]
+lazy_static = "1.4.0"
 num-bigint = { version = "0.4", optional = true }
 num-traits = { version = "0.2", optional = true }
 

diff --git a/src/ciphers/diffie_hellman.rs b/src/ciphers/diffie_hellman.rs
@@ -0,0 +1,350 @@
+// Based on the TheAlgorithms/Python
+// RFC 3526 - More Modular Exponential (MODP) Diffie-Hellman groups for
+// Internet Key Exchange (IKE) https://tools.ietf.org/html/rfc3526
+
+use lazy_static;
+use num_bigint::BigUint;
+use num_traits::{Num, Zero};
+use std::{
+    collections::HashMap,
+    time::{SystemTime, UNIX_EPOCH},
+};
+
+// Using lazy static to initialize statics that require code to be executed at runtime.
+lazy_static! {
+    // A map of predefined prime numbers for different bit lengths, as specified in RFC 3526
+    static ref PRIMES: HashMap<u8, BigUint> = {
+        let mut m:HashMap<u8, BigUint> = HashMap::new();
+        m.insert(
+            // 1536-bit
+            5,
+            BigUint::parse_bytes(
+                b"FFFFFFFFFFFFFFFFC90FDAA22168C234C4C6628B80DC1CD1\
+                    29024E088A67CC74020BBEA63B139B22514A08798E3404DD\
+                    EF9519B3CD3A431B302B0A6DF25F14374FE1356D6D51C245\
+                    E485B576625E7EC6F44C42E9A637ED6B0BFF5CB6F406B7ED\
+                    EE386BFB5A899FA5AE9F24117C4B1FE649286651ECE45B3D\
+                    C2007CB8A163BF0598DA48361C55D39A69163FA8FD24CF5F\
+                    83655D23DCA3AD961C62F356208552BB9ED529077096966D\
+                    670C354E4ABC9804F1746C08CA237327FFFFFFFFFFFFFFFF",
+                16
+            ).unwrap()
+        );
+        m.insert(
+            // 2048-bit
+            14,
+            BigUint::parse_bytes(
+                b"FFFFFFFFFFFFFFFFC90FDAA22168C234C4C6628B80DC1CD1\
+                29024E088A67CC74020BBEA63B139B22514A08798E3404DD\
+                EF9519B3CD3A431B302B0A6DF25F14374FE1356D6D51C245\
+                E485B576625E7EC6F44C42E9A637ED6B0BFF5CB6F406B7ED\
+                EE386BFB5A899FA5AE9F24117C4B1FE649286651ECE45B3D\
+                C2007CB8A163BF0598DA48361C55D39A69163FA8FD24CF5F\
+                83655D23DCA3AD961C62F356208552BB9ED529077096966D\
+                670C354E4ABC9804F1746C08CA18217C32905E462E36CE3B\
+                E39E772C180E86039B2783A2EC07A28FB5C55DF06F4C52C9\
+                DE2BCBF6955817183995497CEA956AE515D2261898FA0510\
+                15728E5A8AACAA68FFFFFFFFFFFFFFFF",
+                16
+            ).unwrap()
+        );
+
+    m.insert(
+    // 3072-bit
+    15,
+    BigUint::parse_bytes(
+            b"FFFFFFFFFFFFFFFFC90FDAA22168C234C4C6628B80DC1CD1\
+            29024E088A67CC74020BBEA63B139B22514A08798E3404DD\
+            EF9519B3CD3A431B302B0A6DF25F14374FE1356D6D51C245\
+            E485B576625E7EC6F44C42E9A637ED6B0BFF5CB6F406B7ED\
+            EE386BFB5A899FA5AE9F24117C4B1FE649286651ECE45B3D\
+            C2007CB8A163BF0598DA48361C55D39A69163FA8FD24CF5F\
+            83655D23DCA3AD961C62F356208552BB9ED529077096966D\
+            670C354E4ABC9804F1746C08CA18217C32905E462E36CE3B\
+            E39E772C180E86039B2783A2EC07A28FB5C55DF06F4C52C9\
+            DE2BCBF6955817183995497CEA956AE515D2261898FA0510\
+            15728E5A8AAAC42DAD33170D04507A33A85521ABDF1CBA64\
+            ECFB850458DBEF0A8AEA71575D060C7DB3970F85A6E1E4C7\
+            ABF5AE8CDB0933D71E8C94E04A25619DCEE3D2261AD2EE6B\
+            F12FFA06D98A0864D87602733EC86A64521F2B18177B200C\
+            BBE117577A615D6C770988C0BAD946E208E24FA074E5AB31\
+            43DB5BFCE0FD108E4B82D120A93AD2CAFFFFFFFFFFFFFFFF",
+            16
+        ).unwrap()
+    );
+    m.insert(
+    // 4096-bit
+    16,
+    BigUint::parse_bytes(
+            b"FFFFFFFFFFFFFFFFC90FDAA22168C234C4C6628B80DC1CD1\
+            29024E088A67CC74020BBEA63B139B22514A08798E3404DD\
+            EF9519B3CD3A431B302B0A6DF25F14374FE1356D6D51C245\
+            E485B576625E7EC6F44C42E9A637ED6B0BFF5CB6F406B7ED\
+            EE386BFB5A899FA5AE9F24117C4B1FE649286651ECE45B3D\
+            C2007CB8A163BF0598DA48361C55D39A69163FA8FD24CF5F\
+            83655D23DCA3AD961C62F356208552BB9ED529077096966D\
+            670C354E4ABC9804F1746C08CA18217C32905E462E36CE3B\
+            E39E772C180E86039B2783A2EC07A28FB5C55DF06F4C52C9\
+            DE2BCBF6955817183995497CEA956AE515D2261898FA0510\
+            15728E5A8AAAC42DAD33170D04507A33A85521ABDF1CBA64\
+            ECFB850458DBEF0A8AEA71575D060C7DB3970F85A6E1E4C7\
+            ABF5AE8CDB0933D71E8C94E04A25619DCEE3D2261AD2EE6B\
+            F12FFA06D98A0864D87602733EC86A64521F2B18177B200C\
+            BBE117577A615D6C770988C0BAD946E208E24FA074E5AB31\
+            43DB5BFCE0FD108E4B82D120A92108011A723C12A787E6D7\
+            88719A10BDBA5B2699C327186AF4E23C1A946834B6150BDA\
+            2583E9CA2AD44CE8DBBBC2DB04DE8EF92E8EFC141FBECAA6\
+            287C59474E6BC05D99B2964FA090C3A2233BA186515BE7ED\
+            1F612970CEE2D7AFB81BDD762170481CD0069127D5B05AA9\
+            93B4EA988D8FDDC186FFB7DC90A6C08F4DF435C934063199\
+            FFFFFFFFFFFFFFFF",
+            16
+        ).unwrap()
+    );
+    m.insert(
+    // 6144-bit
+    17,
+     BigUint::parse_bytes(
+            b"FFFFFFFFFFFFFFFFC90FDAA22168C234C4C6628B80DC1CD129024E08\
+             8A67CC74020BBEA63B139B22514A08798E3404DDEF9519B3CD3A431B\
+             302B0A6DF25F14374FE1356D6D51C245E485B576625E7EC6F44C42E9\
+             A637ED6B0BFF5CB6F406B7EDEE386BFB5A899FA5AE9F24117C4B1FE6\
+             49286651ECE45B3DC2007CB8A163BF0598DA48361C55D39A69163FA8\
+             FD24CF5F83655D23DCA3AD961C62F356208552BB9ED529077096966D\
+             670C354E4ABC9804F1746C08CA18217C32905E462E36CE3BE39E772C\
+             180E86039B2783A2EC07A28FB5C55DF06F4C52C9DE2BCBF695581718\
+             3995497CEA956AE515D2261898FA051015728E5A8AAAC42DAD33170D\
+             04507A33A85521ABDF1CBA64ECFB850458DBEF0A8AEA71575D060C7D\
+             B3970F85A6E1E4C7ABF5AE8CDB0933D71E8C94E04A25619DCEE3D226\
+             1AD2EE6BF12FFA06D98A0864D87602733EC86A64521F2B18177B200C\
+             BBE117577A615D6C770988C0BAD946E208E24FA074E5AB3143DB5BFC\
+             E0FD108E4B82D120A92108011A723C12A787E6D788719A10BDBA5B26\
+             99C327186AF4E23C1A946834B6150BDA2583E9CA2AD44CE8DBBBC2DB\
+             04DE8EF92E8EFC141FBECAA6287C59474E6BC05D99B2964FA090C3A2\
+             233BA186515BE7ED1F612970CEE2D7AFB81BDD762170481CD0069127\
+             D5B05AA993B4EA988D8FDDC186FFB7DC90A6C08F4DF435C934028492\
+             36C3FAB4D27C7026C1D4DCB2602646DEC9751E763DBA37BDF8FF9406\
+             AD9E530EE5DB382F413001AEB06A53ED9027D831179727B0865A8918\
+             DA3EDBEBCF9B14ED44CE6CBACED4BB1BDB7F1447E6CC254B33205151\
+             2BD7AF426FB8F401378CD2BF5983CA01C64B92ECF032EA15D1721D03\
+             F482D7CE6E74FEF6D55E702F46980C82B5A84031900B1C9E59E7C97F\
+             BEC7E8F323A97A7E36CC88BE0F1D45B7FF585AC54BD407B22B4154AA\
+             CC8F6D7EBF48E1D814CC5ED20F8037E0A79715EEF29BE32806A1D58B\
+             B7C5DA76F550AA3D8A1FBFF0EB19CCB1A313D55CDA56C9EC2EF29632\
+             387FE8D76E3C0468043E8F663F4860EE12BF2D5B0B7474D6E694F91E\
+             6DCC4024FFFFFFFFFFFFFFFF",
+            16
+        ).unwrap()
+    );
+
+    m.insert(
+    // 8192-bit
+    18,
+    BigUint::parse_bytes(
+             b"FFFFFFFFFFFFFFFFC90FDAA22168C234C4C6628B80DC1CD1\
+               29024E088A67CC74020BBEA63B139B22514A08798E3404DD\
+               EF9519B3CD3A431B302B0A6DF25F14374FE1356D6D51C245\
+               E485B576625E7EC6F44C42E9A637ED6B0BFF5CB6F406B7ED\
+               EE386BFB5A899FA5AE9F24117C4B1FE649286651ECE45B3D\
+               C2007CB8A163BF0598DA48361C55D39A69163FA8FD24CF5F\
+               83655D23DCA3AD961C62F356208552BB9ED529077096966D\
+               670C354E4ABC9804F1746C08CA18217C32905E462E36CE3B\
+               E39E772C180E86039B2783A2EC07A28FB5C55DF06F4C52C9\
+               DE2BCBF6955817183995497CEA956AE515D2261898FA0510\
+               15728E5A8AAAC42DAD33170D04507A33A85521ABDF1CBA64\
+               ECFB850458DBEF0A8AEA71575D060C7DB3970F85A6E1E4C7\
+               ABF5AE8CDB0933D71E8C94E04A25619DCEE3D2261AD2EE6B\
+               F12FFA06D98A0864D87602733EC86A64521F2B18177B200C\
+               BBE117577A615D6C770988C0BAD946E208E24FA074E5AB31\
+               43DB5BFCE0FD108E4B82D120A92108011A723C12A787E6D7\
+               88719A10BDBA5B2699C327186AF4E23C1A946834B6150BDA\
+               2583E9CA2AD44CE8DBBBC2DB04DE8EF92E8EFC141FBECAA6\
+               287C59474E6BC05D99B2964FA090C3A2233BA186515BE7ED\
+               1F612970CEE2D7AFB81BDD762170481CD0069127D5B05AA9\
+               93B4EA988D8FDDC186FFB7DC90A6C08F4DF435C934028492\
+               36C3FAB4D27C7026C1D4DCB2602646DEC9751E763DBA37BD\
+               F8FF9406AD9E530EE5DB382F413001AEB06A53ED9027D831\
+               179727B0865A8918DA3EDBEBCF9B14ED44CE6CBACED4BB1B\
+               DB7F1447E6CC254B332051512BD7AF426FB8F401378CD2BF\
+               5983CA01C64B92ECF032EA15D1721D03F482D7CE6E74FEF6\
+               D55E702F46980C82B5A84031900B1C9E59E7C97FBEC7E8F3\
+               23A97A7E36CC88BE0F1D45B7FF585AC54BD407B22B4154AA\
+               CC8F6D7EBF48E1D814CC5ED20F8037E0A79715EEF29BE328\
+               06A1D58BB7C5DA76F550AA3D8A1FBFF0EB19CCB1A313D55C\
+               DA56C9EC2EF29632387FE8D76E3C0468043E8F663F4860EE\
+               12BF2D5B0B7474D6E694F91E6DBE115974A3926F12FEE5E4\
+               38777CB6A932DF8CD8BEC4D073B931BA3BC832B68D9DD300\
+               741FA7BF8AFC47ED2576F6936BA424663AAB639C5AE4F568\
+               3423B4742BF1C978238F16CBE39D652DE3FDB8BEFC848AD9\
+               22222E04A4037C0713EB57A81A23F0C73473FC646CEA306B\
+               4BCBC8862F8385DDFA9D4B7FA2C087E879683303ED5BDD3A\
+               062B3CF5B3A278A66D2A13F83F44F82DDF310EE074AB6A36\
+               4597E899A0255DC164F31CC50846851DF9AB48195DED7EA1\
+               B1D510BD7EE74D73FAF36BC31ECFA268359046F4EB879F92\
+               4009438B481C6CD7889A002ED5EE382BC9190DA6FC026E47\
+               9558E4475677E9AA9E3050E2765694DFC81F56E880B96E71\
+               60C980DD98EDD3DFFFFFFFFFFFFFFFFF",
+            16
+        ).unwrap()
+    );
+    m
+    };
+}
+
+/// Generating random number, should use num_bigint::RandomBits if possible.
+fn rand() -> usize {
+    SystemTime::now()
+        .duration_since(UNIX_EPOCH)
+        .unwrap()
+        .subsec_nanos() as usize
+}
+
+pub struct DiffieHellman {
+    prime: BigUint,
+    private_key: BigUint,
+    public_key: BigUint,
+    generator: u8,
+}
+
+impl DiffieHellman {
+    // Diffie-Hellman key exchange algorithm is based on the following mathematical concepts:
+
+    //  - A large prime number p (known as the prime modulus) is chosen and shared by both parties.
+
+    //  - A base number g (known as the generator) is chosen and shared by both parties.
+
+    //  - Each party generates a private key a or b (which are secret and only known to that party) and calculates a corresponding public key A or B using the following formulas:
+    //          - A = g^a mod p
+    //          - B = g^b mod p
+
+    //  - Each party then exchanges their public keys with each other.
+
+    //  - Each party then calculates the shared secret key s using the following formula:
+    //          - s = B^a mod p or s = A^b mod p
+
+    // Both parties now have the same shared secret key s which can be used for encryption or authentication.
+
+    pub fn new(group: Option<u8>) -> Self {
+        let mut _group: u8 = 14;
+        if let Some(x) = group {
+            _group = x;
+        }
+
+        if !PRIMES.contains_key(&_group) {
+            panic!("group not in primes")
+        }
+
+        // generate private key
+        let private_key: BigUint = BigUint::from(rand());
+
+        Self {
+            prime: PRIMES[&_group].clone(),
+            private_key,
+            generator: 2, // the generator is 2 for all the primes if this would not be the case it can be added to hashmap
+            public_key: BigUint::default(),
+        }
+    }
+
+    /// get private key as hexadecimal String
+    pub fn get_private_key(&self) -> String {
+        self.private_key.to_str_radix(16)
+    }
+
+    /// Generate public key A = g**a mod p
+    pub fn generate_public_key(&mut self) -> String {
+        self.public_key = BigUint::from(self.generator).modpow(&self.private_key, &self.prime);
+        self.public_key.to_str_radix(16)
+    }
+
+    pub fn is_valid_public_key(&self, key_str: &str) -> bool {
+        // the unwrap_or_else will make sure it is false, because 2 <= 0 and therefor False is returned
+        let key = BigUint::from_str_radix(key_str, 16)
+            .unwrap_or_else(|_| BigUint::parse_bytes(b"0", 16).unwrap());
+
+        // Check if the other public key is valid based on NIST SP800-56
+        if BigUint::from(2_u8) <= key
+            && key <= &self.prime - BigUint::from(2_u8)
+            && !key
+                .modpow(
+                    &((&self.prime - BigUint::from(1_u8)) / BigUint::from(2_u8)),
+                    &self.prime,
+                )
+                .is_zero()
+        {
+            return true;
+        }
+        false
+    }
+
+    /// Generate the shared key
+    pub fn generate_shared_key(self, other_key_str: &str) -> Option<String> {
+        let other_key = BigUint::from_str_radix(other_key_str, 16)
+            .unwrap_or_else(|_| BigUint::parse_bytes(b"0", 16).unwrap());
+        if !self.is_valid_public_key(&other_key.to_str_radix(16)) {
+            return None;
+        }
+
+        let shared_key = other_key.modpow(&self.private_key, &self.prime);
+        Some(shared_key.to_str_radix(16))
+    }
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+
+    #[test]
+    fn verify_invalid_pub_key() {
+        let diffie = DiffieHellman::new(Some(14));
+        assert_eq!(diffie.is_valid_public_key("0000"), false);
+    }
+
+    #[test]
+    fn verify_valid_pub_key() {
+        let diffie = DiffieHellman::new(Some(14));
+        assert_eq!(
+            diffie.is_valid_public_key("EF9519B3CD3A431B302B0A6DF25F14374FE1356D6D51C245"),
+            true
+        );
+    }
+
+    #[test]
+    fn verify_invalid_pub_key_same_as_prime() {
+        let diffie = DiffieHellman::new(Some(14));
+        assert_eq!(
+            diffie.is_valid_public_key(
+                "FFFFFFFFFFFFFFFFC90FDAA22168C234C4C6628B80DC1CD1\
+        29024E088A67CC74020BBEA63B139B22514A08798E3404DD\
+        EF9519B3CD3A431B302B0A6DF25F14374FE1356D6D51C245\
+        E485B576625E7EC6F44C42E9A637ED6B0BFF5CB6F406B7ED\
+        EE386BFB5A899FA5AE9F24117C4B1FE649286651ECE45B3D\
+        C2007CB8A163BF0598DA48361C55D39A69163FA8FD24CF5F\
+        83655D23DCA3AD961C62F356208552BB9ED529077096966D\
+        670C354E4ABC9804F1746C08CA18217C32905E462E36CE3B\
+        E39E772C180E86039B2783A2EC07A28FB5C55DF06F4C52C9\
+        DE2BCBF6955817183995497CEA956AE515D2261898FA0510\
+        15728E5A8AACAA68FFFFFFFFFFFFFFFF"
+            ),
+            false
+        );
+    }
+
+    #[test]
+    fn verify_key_exchange() {
+        let mut alice = DiffieHellman::new(Some(16));
+        let mut bob = DiffieHellman::new(Some(16));
+
+        // Private key not used, showed for illustrative purpose
+        let _alice_private = alice.get_private_key();
+        let alice_public = alice.generate_public_key();
+
+        // Private key not used, showed for illustrative purpose
+        let _bob_private = bob.get_private_key();
+        let bob_public = bob.generate_public_key();
+
+        // generating shared key using the struct implemenations
+        let alice_shared = alice.generate_shared_key(bob_public.as_str()).unwrap();
+        let bob_shared = bob.generate_shared_key(alice_public.as_str()).unwrap();
+        assert_eq!(alice_shared, bob_shared);
+    }
+}
diff --git a/src/ciphers/mod.rs b/src/ciphers/mod.rs
@@ -3,6 +3,7 @@ mod another_rot13;
 mod base64;
 mod caesar;
 mod chacha;
+mod diffie_hellman;
 mod hashing_traits;
 mod kerninghan;
 mod morse_code;
@@ -21,6 +22,7 @@ pub use self::another_rot13::another_rot13;
 pub use self::base64::{base64_decode, base64_encode};
 pub use self::caesar::caesar;
 pub use self::chacha::chacha20;
+pub use self::diffie_hellman::DiffieHellman;
 pub use self::hashing_traits::Hasher;
 pub use self::hashing_traits::HMAC;
 pub use self::kerninghan::kerninghan;

diff --git a/src/lib.rs b/src/lib.rs
@@ -1,3 +1,5 @@
+#[macro_use]
+extern crate lazy_static;
 pub mod backtracking;
 pub mod big_integer;
 pub mod ciphers;