**EC Cryptography Tutorials - Herong's Tutorial Examples** - v1.00, by Dr. Herong Yang

Is ECDH Key Exchange Secure

This section discusses the question of: how secure is the ECDH (Elliptic Curve Diffie-Hellman) key exchange protocol?

**Is ECDH Key Exchange Protocol Secure?**
Yes, ECDH Key Exchange protocol is secure, if
both Alice and Bob select large private numbers, i and j.

If Eve gets a copy of
Q_{A} and Q_{B} by taking copies of messages
exchanged between Alice and Bob, Eve needs to perform the reverse operation
to find d_{A}, such that d_{A}*G = Q_{A};
or to find d_{B}, such that d_{B}*G = Q_{B}.

If d_{A} and d_{B} are both 256-bit integers,
Eve needs to perform about 2^{256} operations.
That is about 1.2239143543602674e+60 years on a laptop
with a 3 GHZ CPU doing 1 operation per CPU click.

Table of Contents

Geometric Introduction to Elliptic Curves

Algebraic Introduction to Elliptic Curves

Abelian Group and Elliptic Curves

Discrete Logarithm Problem (DLP)

Generators and Cyclic Subgroups

tinyec - Python Library for ECC

►ECDH (Elliptic Curve Diffie-Hellman) Key Exchange

ECDSA (Elliptic Curve Digital Signature Algorithm)