11.3 One-way functions
In Chapter 4, Encryption and Decryption, we learned that the notion of computational security is built on the concept of pseudorandomness, the idea that bit strings can look completely random even though they are not. In fact, pseudorandom generators, functions, and permutations form the basis of modern symmetric key cryptography. As being one-way is also one of the defining properties of a cryptographic hash function, we chose to include a more formal discussion of this property in this section, even though it is fundamental for the whole of cryptography.
This is because mathematicians have proved that pseudorandom generators, functions, and permutations can be constructed from one-way functions.
As a result, the existence of one-way functions is equivalent to the existence of any non-trivial symmetric-key cryptography [97]. This means, if we can find functions that we can prove to be one-way, we can use them to construct symmetric-key cryptographic schemes...