Researchers warn that many 1,024-bit keys used to secure communications on the internet today might be based on prime numbers that have been intentionally backdoored in an undetectable way.
Many public-key cryptography algorithms that are used to secure web, email, VPN, SSH and other types of connections on the internet derive their strength from the mathematical complexity of discrete logarithms — computing discrete logarithms for groups of large prime numbers cannot be efficiently done using classical methods. This is what makes cracking strong encryption computationally impractical.
