What are the cryptographic assumptions underlying modern encryption algorithms such as RSA and elliptic curve cryptography, and what are the implications of potential breakthroughs in cryptanalysis for cybersecurity?

Modern encryption algorithms rely on mathematical problems such as integer factorization and discrete logarithm, which are believed to be computationally hard to solve. Breakthroughs in cryptanalysis, such as the development of quantum computers or new mathematical techniques, could potentially compromise the security of encrypted communications and data.