In this post, we’ll talk about permutations, sponge functions, and duplexes–what they are, how they’re built, what makes them secure, and how they’re used. We’ll use a sponge function to build our own hash function, calculate message authentication codes, generate pseudo-random data, and make a stream cipher. We’ll use a duplex to do authenticated encryption, make cryptographic transcripts, create digital signatures, and build an authenticated public key encryption scheme (a.k.a. signcryption). We’ll even design our own authenticated session encryption protocol with only a duplex and an elliptic curve.