ECC CALCULATOR FOR EXAM

You will get the complete calculator for ecc on https://graui.de/code/elliptic2/

But the above code will use if you want stepwise calculation.

1. ecc_calculator is use for the finding all the points lies on the ecc.
2. point_sum is use for the find the sum of two point P+Q.
3. findNalpha is use for the value of , Where n is {1,2,...p}.
4. Find public key if private key is given: where is public key.
5. Find Encryption of for random number k is: = { , }. where is cipher text.
6. Decrypt cipher text(Recover from ): . Now consider after solving and is { , } - { , } is equal to { , } + { , }.

Note: In Code you will get x_1 which is equal to , and x__i is equal to . is generator(also called G).

Assignment:

1. Consider the elliptic curve (1, 6); that is, the curve defined by with modulus of p = 11.

   (i) Find all points.

   (ii) If public key assuming private key is 2.

   (iii) Assume k = 3, find ciphertext.

   (iv) Decrypt ciphertext.

2. Find the sum of three points on an elliptic curve that lie on straight line?.