Elliptic Curve Cryptography + JAVA - Public Key Cryptography (Prototype Project 08)
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00:05 demo prebuilt version of the application
01:05 find all points that satisfy elliptic curve equation
03:05 show cyclic behavior of a generator point in a small group
04:05 use double and add algorithm for fast point hopping
04:45 quick intro to elliptic curves
05:20 singular versus nonsingular elliptic curves
06:00 why use elliptic curve in cryptography
09:55 equations for elliptic curve point addition and doubling
12:02 what is a field
13:35 elliptic curve group operations
14:02 associativity proof for elliptic curve point addition
15:30 elliptic curve over prime fields
16:35 code the application
19:46 check if curve to be instantiated is singular
24:06 implement point addition and doubling
25:59 find all points that satisfy elliptic curve equation
28:00 check if 2 points are inverse of each other
29:15 explain elliptic curve order, subgroup size n, and cofactor h
32:53 implement double and add algorithm
35:09 test run the application
40:20 what does 'Points on elliptic curve + O have cyclic subgroups' mean
40:45 when do all points on an elliptic curve form a cyclic group
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