Elliptic Curve Cryptography + JAVA

download source code @ https://sites.fastspring.com/prototypeprj/instant/crypto

• Public Key Cryptography + JAVA (prototype project 08) - ECC

  • find all points that satisfy elliptic curve equation

  • show cyclic behavior of a generator point in a small group

  • use double and add algorithm for fast point hopping

  • quick intro to elliptic curves

  • singular versus nonsingular elliptic curves

  • why use elliptic curve in cryptography

  • equations for elliptic curve point addition and doubling

  • what is a field

  • elliptic curve group operations

  • associativity proof for elliptic curve point addition

  • elliptic curve over prime fields

  • implement checking if curve to be instantiated is singular

  • implement point addition and doubling

  • imlement finding all points that satisfy elliptic curve equation

  • implement checking if 2 points are inverse of each other

  • explain elliptic curve order, subgroup size n, and cofactor h

  • implement double and add algorithm

  • what does 'Points on elliptic curve + O have cyclic subgroups' mean

  • when do all points on an elliptic curve form a cyclic group

• Public Key Cryptography + JAVA (prototype project 09) - ECDH #01

  • ECDH - Elliptic Curve Diffie–Hellman key exchange

  • Demo (using small cyclic group)

  • Write, & Test Run (using secp256k1 the curve used by bitcoin)

• Elliptic Curve Diffie–Hellman key exchange + P2P - ECDH #02

  public version (demo only) | members-only version (demo, write, and test run)

  • Refactor Public Key Cryptography prototype project 09 (ECDH #01)

  • Add Peer-to-peer functionality

• Public Key Cryptography + JAVA (prototype project 10) - ECDSA #01

  • Elliptic Curve Digital Signature Algorithm (ECDSA)

  • Write, & Test Run w/ secp256k1 (used by bitcoin) & secp384r1 curves

• Elliptic Curve Digital Signature Algorithm+P2P - ECDSA #02

  public version (demo only) | members-only version (demo, write, and test run)

  • Refactor Elliptic Curve Digital Signature Algorithm Prototype Project 01

  • Write, & Test Run w/ secp256k1 (used by bitcoin) & secp384r1 curves

• P2P + multi-peers exchange signed messages+ECDSA #03

  public version (demo only) | members-only version (demo, write, and test run)

  • Refactor Elliptic Curve Digital Signature Algorithm Prototype Project 02

  • Multi-peers communicating w/ signed messages (using secp256k1 & secp384r1)