#pragma once
#include "prelude/basic.mpv"
#include "prelude/bits.mpv"
#include "crypto/key.mpv"
#include "crypto/setup.mpv"
@module kem

type kem_sk.
type kem_pk.

fun kem_pub(kem_sk) : kem_pk.
fun kem_enc(kem_pk, key) : bits.
fun kem_dec(kem_sk, bits) : key
  reduc forall sk:kem_sk, shk:key;
    kem_dec(sk, kem_enc(kem_pub(sk), shk)) = shk.

fun kem_pk2b(kem_pk) : bits [typeConverter].

const kem_sk0:kem_sk.
letfun kem_pk0 = kem_pub(kem_sk0).

#if FULL_MODEL
fun kem_keyeq(bits, bits) : bool
  reduc forall k:kem_pk, pt1:key, pt2:key;
    kem_keyeq(kem_enc(k, pt1), kem_enc(k, pt2)) = true
  otherwise forall k1:kem_pk, pt1:key, k2:kem_pk, pt2:key;
    kem_keyeq(kem_enc(k1, pt1), kem_enc(k2, pt2)) = false.
#endif