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Questions What is the general form of all elliptic curve equations?

Elliptic Curve Cryptography. General Equation for Elliptic Curves :. Finite Field Elliptic Curves: Elliptic Curve “Point” Algebra : if x 1 != x 2 , if x 1 == x 2 , x 3 = y 3 = . Key Generation : Agree on the following (public): Curve parameters (a, b) The modulus p

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Questions What is the general form of all elliptic curve equations?

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  1. Elliptic Curve Cryptography General Equation for Elliptic Curves: Finite Field Elliptic Curves: Elliptic Curve “Point” Algebra: if x1 != x2, if x1 == x2, x3 = y3 = Key Generation: Agree on the following (public): Curve parameters (a, b) The modulus p Base point G (on the curve) Pick a random integer n as private key Calculate public key P = n*G Questions What is the general form of all elliptic curve equations? What is the sum of two points that form a vertical line? Why is ECC stronger than RSA? What is the name of the best known algorithm for attacking ECC? When will ECC likely be available and implemented for public use?

  2. Answers • What is the general form of all elliptic curve equations? • What is the sum of two points that form a vertical line?The point-at-infinity, O • Why is ECC stronger than RSA?The new algebra doesn’t have the same weaknesses that traditional algebra (and thereby RSA) does.orThe best attack on ECC runs in full exponential time, whereas the best attack on RSA runs in sub-exponential time. • What is the name of the best known algorithm for attacking ECC?Pollard’s Rho • When will ECC likely be available and implemented for public use?~2020

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