RSA is one of the most important encryption/signature schemes which breaks if FACTORING is in P. However, there are many more. Several (but not all) of them are based on the assumption that distinguishing squares and non-squares modulo a composite number is hard:

1. Rabin's signature scheme
2. Rabin's oblivious transfer
3. Goldwasser–Micali semanticly-secure cryptosystem
4. Blum-Blum-Shub pseudorandom generator
5. Feige-Fiat-Shamir identification scheme

And many other schemes. However, note that schemes based on the hardness of discrete log (say, the Diffie-Helmann protocol or Elgamal encryption/signature scheme) will continue to be secure.

RSA is one of the most important encryption/signature schemes which breaks if FACTORING is in P. However, there are many more. Several (but not all) of them are based on the assumption that distinguishing squares and non-squares modulo a composite number is hard:

1. Rabin's signature scheme
2. Rabin's oblivious transfer
3. Goldwasser–Micali semantically-secure cryptosystem
4. Blum-Blum-Shub pseudorandom generator
5. Feige-Fiat-Shamir identification scheme

And many other schemes. However, note that schemes based on the hardness of discrete log (say, the Diffie-Helmann protocol or Elgamal encryption/signature scheme) will continue to be secure.