**EC Cryptography Tutorials - Herong's Tutorial Examples** - Version 1.00, 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.

Last update: 2019.

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)