DiffieHellmam Algorithm in C++The DiffieHellman algorithm is an effective method for exchanging cryptographic keys over a public channel. It was one of the first publickey protocols. The Diffiehellman key exchange was invented by Ralph Merkle and named for Whitfield Diffie and Martin Hellman. DH (DiffieHellman) is the first instance of public key exchange in the realm of cryptography. This work introduced the concept of a corresponding pair of public and private keys for the first time to the general public. In general, secure encrypted communication between two parties necessitates exchanging keys by tangible and secure means, such as paper key lists that a reputable and secured courier delivers. By using the DH key exchange mechanism, two parties with no prior knowledge of one another can establish a shared secret through an unsecured (public) channel. This key can then be used to encrypt the communication using a symmetrickey cypher. DiffieHellman key exchange creates a secret that is shared by the two parties in order to exchange data in secret communication across a public network. Several Internetrelated services are developed using DiffieHellman. However, the research from October 2015 reveals that the DiffieHellman settings in use at the time were insufficient to defend against wellfunded attackers like the security service agents of some countries. Although DH key agreement is a nonauthentication keyagreement protocol, it serves as the foundation for many authenticated protocols and is employed to provide forward secrecy in the ephemeral modes of transport layer security. DiffieHellman AlgorithmThe algorithm's description:Publickey cryptography is addressed by the acronym ECC (Elliptic Curve Cryptography). It is based on the elliptical curves over finite fields' algebraic structure. When compared to nonElliptic Curve encryption, Elliptic Curve Cryptography requires a smaller key to give identical security (a 256bit ECC security is equivalent to 3072bit RSA encryption). Using this elliptic curve to generate points and the parameters to derive the secret key, the DiffieHellman algorithm is used to establish a shared secret that may be utilized for secret communication while transferring data over a public channel. StepbyStep DescriptionLet's consider four variables for a simple and practical implementation of the algorithm: a prime number P, a primitive root of P called Q (if for a prime number n, the primitive root of n is r and it lies within range [1,n1] such that all the values of rx(modn), where x lies within range [0,n2] are all different, and two private values called a and b. Both P and G are publicly available numbers. Users (let's say Alen and Roy) choose two private values, b and a, and then produce a key and publicly trade it. A secret key is generated when the other person receives the key.
Keys generated are exchanged
Algebraically, it is demonstrable that: ka = kb Users can now encrypt data with a symmetric secret key. Some examples:
Implementation:C++ code: Output: Value of Ps is: 32 Value of Gs is: 5 Private key g is: 6 Private key h is: 2 Alen's Secret key is: 17 Roy's Secret key is: 17 Other Uses EncryptionA public key encryption system based on a DiffieHellman key exchange has been proposed. The original such system is ElGamal encryption. Another contemporary variation is Integrated Encryption Scheme. Initial SecrecyForwardsecret protocols generate fresh key pairs for each session and destroy them at the end the session. The DiffieHellman key exchange is a viable option for such protocols due to its quick key generation. Agreement for passwordauthenticated keysWhen Joy and Allen share a password, they can protect themselves from maninthemiddle attacks by using DH's passwordauthenticated key agreement. A straightforward method involves comparing the generated password to the hash of s (where's' is the shared secret), which has been independently concatenated on both ends of the channel. These methods have the advantage that an attacker can only test one password with the other party at a time, providing strong security even with weak passwords. The method employed by the G.hn home networking standard is detailed in ITUT recommendation X.1035. One such protocol is the Secure Remote Password protocol. Conclusion
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