The aim of this coursework assignment is to show evidence of understanding of the Elliptic curve Diffie-Hellman (ECDH) key exchange protocol, which allows two parties, each having an elliptic curve public-private key pair, to establish a shared secret over an insecure channel. This shared secret may be directly used as a key, or to derive another key which can then be used to encrypt subsequent communications using a symmetric key cipher. It is a variant of the Diffie-Hellman protocol using elliptic curve cryptography.
Protocol
The following example will illustrate how a key establishment is made. Suppose Alice wants to establish a shared key with Bob, but the only channel available for them may be eavesdropped by a third party. Initially, the domain parameters, which are k, a, b, and G, must be agreed upon;
a and b determine the curve;
k restricts the curve to a prime field Fk;
G is a generator, a point in the field.
Also, each party must have a key pair suitable for elliptic curve cryptography, consisting of a private key d (a randomly selected integer in the interval (1, n-1], where n is the order of the field) and a public key Q (where Q = dG, that is, the result of adding G together d times). Let Alice's key pair be (dA, QA) and Bob's key pair be (dB, QB). Each party must know the other party's public key prior to execution of the protocol.
Alice computes (xk, yk) = dAQB. Bob computes (xk, yk) = dBQA. The shared secret is xk (the x coordinate of the point).
Report - Please write a report using the following skeleton:
1. Show in detail all the steps of the key exchange protocol, with the calculation expanded using the numbers you were given. For the private keys (dA and dB) you may choose any number in the [11, n-1], where n is the order of the field.
2. How do Alice and Bob arrive at the same shared secret?
3. If Carol is intercepting the communication and captures QA and QB, can she compute Alice's and Bob's private keys?
4. A more sophisticated attack by Carol involves generating (dC, QC) for use as a reset value, using the same values of a, b, k and G that Alice and Bob are using. Explain how this would work.
5. Write a brief discussion (two paragraphs) on the comparison of ECC (Elliptic Curve Cryptography) and RSA, focusing on the advantages and disadvantages of each.
6. Include key snippets of your code. NOTE: as you are doing modulo multiplications with figures greater than 10 on an elliptic curve, your work will most probably involve some programming. You may choose a programming language of your liking, whatever you are most comfortable with. The snippet should be the fragment dealing with modular multiplication on the elliptic curve.
Attachment:- Assignment File.rar