Leios.VRF

This module defines the Verifiable Random Function (VRF) interface and its use in the Leios protocol. It specifies the types and operations for VRF evaluation, verification, and key management, as well as predicates for block and vote eligibility based on VRF outputs. The module also provides the Leios-specific VRF abstraction and utility functions for protocol slot leader selection.

open import Leios.Prelude
open import Leios.Abstract
 
module Leios.VRF
  (a : LeiosAbstract) (open LeiosAbstract a) where
 
record VRF (Dom Range PubKey : Type) : Type₁ where
  field isKeyPair : PubKey → PrivKey → Type
        eval      : PrivKey → Dom → Range × VrfPf
        verify    : PubKey → Dom → Range → VrfPf → Type
        verify?   : (pk : PubKey) → (d : Dom) → (r : Range) → (pf : VrfPf) → Dec (verify pk d r pf)
 
record LeiosVRF : Type₁ where
  field PubKey     : Type
        poolID     : PubKey → PoolID
        verifySig  : PubKey → Sig → Type
        verifySig? : (pk : PubKey) → (sig : Sig) → Dec (verifySig pk sig)
 
        vrf : VRF ℕ ℕ PubKey
 
  open VRF vrf public
 
  -- transforming slot numbers into VRF seeds
  field genIBInput genEBInput genVInput genV1Input genV2Input : ℕ → ℕ
 
  canProduceIB : ℕ → PrivKey → ℕ → VrfPf → Type
  canProduceIB slot k stake π = let (val , pf) = eval k (genIBInput slot) in val < stake × pf ≡ π
 
  Dec-canProduceIB : ∀ {slot k stake} → (∃[ π ] canProduceIB slot k stake π) ⊎ (∀ π → ¬ canProduceIB slot k stake π)
  Dec-canProduceIB {slot} {k} {stake} with eval k (genIBInput slot)
  ... | (val , pf) = case ¿ val < stake ¿ of λ where
    (yes p) → inj₁ (pf , p , refl)
    (no ¬p) → inj₂ (λ π (h , _) → ¬p h)
 
  canProduceIBPub : ℕ → ℕ → PubKey → VrfPf → ℕ → Type
  canProduceIBPub slot val k pf stake = verify k (genIBInput slot) val pf × val < stake
 
  canProduceEB : ℕ → PrivKey → ℕ → VrfPf → Type
  canProduceEB slot k stake π = let (val , pf) = eval k (genEBInput slot) in val < stake × pf ≡ π
 
  Dec-canProduceEB : ∀ {slot k stake} → (∃[ π ] canProduceEB slot k stake π) ⊎ (∀ π → ¬ canProduceEB slot k stake π)
  Dec-canProduceEB {slot} {k} {stake} with eval k (genEBInput slot)
  ... | (val , pf) = case ¿ val < stake ¿ of λ where
    (yes p) → inj₁ (pf , p , refl)
    (no ¬p) → inj₂ (λ π (h , _) → ¬p h)
 
  canProduceEBPub : ℕ → ℕ → PubKey → VrfPf → ℕ → Type
  canProduceEBPub slot val k pf stake = verify k (genEBInput slot) val pf × val < stake
 
  canProduceV : ℕ → PrivKey → ℕ → Type
  canProduceV slot k stake = proj₁ (eval k (genVInput slot)) < stake
 
  Dec-canProduceV : ∀ {slot k stake} → Dec (canProduceV slot k stake)
  Dec-canProduceV {slot} {k} {stake} with eval k (genVInput slot)
  ... | (val , pf) = ¿ val < stake ¿
 
  canProduceV1 : ℕ → PrivKey → ℕ → Type
  canProduceV1 slot k stake = proj₁ (eval k (genV1Input slot)) < stake
 
  Dec-canProduceV1 : ∀ {slot k stake} → Dec (canProduceV1 slot k stake)
  Dec-canProduceV1 {slot} {k} {stake} with eval k (genV1Input slot)
  ... | (val , pf) = ¿ val < stake ¿
 
  canProduceV2 : ℕ → PrivKey → ℕ → Type
  canProduceV2 slot k stake = proj₁ (eval k (genV2Input slot)) < stake
 
  Dec-canProduceV2 : ∀ {slot k stake} → Dec (canProduceV2 slot k stake)
  Dec-canProduceV2 {slot} {k} {stake} with eval k (genV2Input slot)
  ... | (val , pf) = ¿ val < stake ¿