Conclusion
New factorization and discrete logarithm record computations

RSA and Diffie-Hellman algorithms are at the heart of modern communication protocols. According to ICSI Certificate Notary ( https://notary.icsi.berkeley.edu/ ), 90% of certificates used for encrypted exchanges on the Internet in July 2020 used RSA keys, and Diffie-Hellman key exchange is required for SSH (secure shell), TLS 1.3 (the latest version of the SSL/TLS protocol for encrypting e-mail and Internet exchanges), and IPsec (for virtual private networks).

Setting new records for factoring and discrete logarithm calculation is the best way to encourage users of these protocols to update key sizes in favor of more secure values. While official recommendations since 2010 are at least 2,048 bits for RSA and Diffie-Hellman keys, many sites still use smaller keys: Qualys...