Well, there's already a SHA-512. But none of the SHA family of hashes have ever been recommended for passwords, not because they are weak, but because they are

Well, there's already a SHA-512. But none of the SHA family of hashes have ever been recommended for passwords, not because they are weak, but because they are too fast. For other purposes, the logical successor to SHA-256/512 is SHA-3: https://en.wikipedia.org/wiki/SHA-3 https://en.wikipedia.org/wiki/SHA-3 But this is far from the only choice. Hashing algorithms are trendy right now, and there's plenty to choose from.