Diffie-Hellman Security

Cryptography · Axiom Academy

LESSON Diffie-Hellman Security Understanding the security assumptions, vulnerabilities, and best practices for the Diffie-Hellman key exchange protocol 1. Computational Diffie-Hellman (CDH) Assumption The security of the Diffie-Hellman key exchange fundamentally relies on the Computational Diffie-Hellman (CDH) problem . An eavesdropper Eve observes the public values transmitted during key exchange: The generator g and prime modulus p Alice's public key: A = g a mod p Bob's public key: B = g b mod p To recover the shared secret K = g ab mod p, Eve must solve the CDH problem. The CDH assumption states that this is computationally infeasible for properly chosen parameters. 2. Decisional Diffie-Hellman (DDH) Assumption A stronger assumption than CDH is the Decisional Diffie-Hellman (DDH) problem , which states that DH outputs are indistinguishable from random. The DDH assumption is crucial for protocols requiring semantic security : An observer cannot distinguish (g, g a , g b , g ab ) from (g, g a , g b , g r ) where r is random This ensures the shared key reveals no information about the private keys DDH is believed to be harder than CDH (if you can solve DDH, you can solve CDH, but not necessarily vice versa) 3. Man-in-the-Middle (MITM) Attack The most critical vulnerability in basic Diffie-Hellman is the lack of authentication , enabling man-in-the-middle attacks. Step 1: Alice sends A = g a to Bob, but Eve intercepts it

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