EllipticCurveofDiffieHellman

psuedocode of elliptic curve of diffie helman for code written in python

ECDH (Elliptic curve of Diffie Hellman) – Key Exchange Algorithm

The system was established in 1976 by Whitfield Diffie and Martin Hellman , it is a scheme that consist of key agreement, key agreement refers to which indicates that when two or more parties uses a protocol that will safely exchange a consequent key value. It suggested that the Diffie-Hellman key exchange is established on the idea of that it is quite difficult to compute a discrete logarithm above a finite field. It utilized the modular exponentiation so it could yield exchange data encryption key so all the sides communication will exchange it. By multiplying points, Neal Koblits and VS Miller used this method of Elliptic curve over a finite field to yield the data that both parties would share. The user to keys used to access the cloud data is generated the following way, nominating a point 𝑃 on the curve and a number assume it will be 𝑑 𝑤ℎ𝑒𝑟𝑒 (1 ≤ 𝑑 ≥ 𝑛 − 1), then we will be calculating 𝑄 which is the Public key by the equation, 𝑑 which the private key. 𝑄 = 𝑑 ∗ 𝑃 The receiver decrypts the encrypted message sent by the sender using the saved public key. He uses his own private key.

Algorithm of the code

The algorithm of the code we are implementing is Diffie Helman key exchange, and we will state the algorithm in this section. The steps of the algorithm as:

1. Alice will start by producing a random pair of Keys by the formula a. {PrivateKeyOfAlice, PublicKeyOfAlice = PrivateKeyOfAlice *G}
2. Bob will start by producing a random pair of keys by the formula a. {PrivateKeyOfBob, PublicKeyOfBob = PrivateKeyOfBob *G}
3. Then both Alice along Bob will exchange each other’s public key through an insecure channel.
4. Then Alice and Bob will calculate the shared key between them by the formulas a. Alice, Shared Key = PublicKeyOfBob * PrivateKeyOfAlice b. Bob, Shared Key = PublicKeyOfAlice * PrivateKeyOfBob
5. For now, both Alice and Bob will possess the shared key were this formula proves it a. Shared Key == PublicKeyOfBob * PrivateKeyOfAlice == PublicKeyOfAlice * PrivateKeyOfBob

Pseudocode of ECDH

A point in the group and the order of the group (in this case the number of points on the elliptic curve) are public knowledge. Bob chooses a secret message (a number b with 0 < b < n). Alice chooses a secret message (a number a with 0 < a < n).