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 QA and QB by taking copies of messages exchanged between Alice and Bob, Eve needs to perform the reverse operation to find dA, such that dA*G = QA; or to find dB, such that dB*G = QB.

If dA and dB are both 256-bit integers, Eve needs to perform about 2256 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

 About This Book

 Geometric Introduction to Elliptic Curves

 Algebraic Introduction to Elliptic Curves

 Abelian Group and Elliptic Curves

 Discrete Logarithm Problem (DLP)

 Finite Fields

 Generators and Cyclic Subgroups

 Reduced Elliptic Curve Groups

 Elliptic Curve Subgroups

 tinyec - Python Library for ECC

 EC (Elliptic Curve) Key Pair

ECDH (Elliptic Curve Diffie-Hellman) Key Exchange

 What Is ECDH Key Exchange

Is ECDH Key Exchange Secure

 ECDSA (Elliptic Curve Digital Signature Algorithm)

 ECES (Elliptic Curve Encryption Scheme)

 Terminology

 References

 Full Version in PDF/EPUB