Security with Discrete Logarithms (and How to Break It)

A high-level overview of the Number Field Sieve approach used in the Logjam attack described in the "Imperfect Forward Secrecy" paper by Adrian et al., CCS 2015. We dive into Discrete Logarithms, why it is supposed to be a tough problem, and how the common practice of reusing the same finite fields to avoid weakening the security of Diffie-Hellman key exchange actually results in weakening the security of Diffie-Hellman key exchange. Continue learning: - The paper and more material: https://weakdh.org - Some criticism: https://nohats.ca/wordpress/blog/2015/10/17/66-of-vpns-are-not-in-fact-broken/ - Math is Fun has a great introduction to properties of logarithms: https://www.mathsisfun.com/algebra/logarithms.html - Find out what keys are common today: https://www.ssllabs.com/ssl-pulse/ - Learn all about primes: https://www.springer.com/gp/book/9780387252827 Bad Ideas - Silent Film Dark by Kevin MacLeod is licensed under a Creative Commons Attribution 4.0 licence. https://creativecommons.org/licenses/by/4.0/ Source: http://incompetech.com/music/royalty-free/index.html?isrc=USUAN1100489 Artist: http://incompetech.com/