""" Implémentation DKG Feldman VSS pour le PoC PKI-MPC-ZKP Génération de clés distribuée avec vérification publique """ import hashlib import secrets from typing import List, Tuple, Dict from dataclasses import dataclass from cryptography.hazmat.primitives.asymmetric import ec from cryptography.hazmat.primitives import hashes import json @dataclass class FeldmanVSSShare: """Représente une part dans le schéma Feldman VSS""" participant_id: int share_value: int verification_commitments: List[int] @dataclass class DKGNode: """Nœud participant au processus DKG""" node_id: int private_polynomial: List[int] # Coefficients du polynôme secret public_commitments: List[ec.EllipticCurvePoint] # Engagements publics received_shares: Dict[int, int] # Parts reçues des autres nœuds class FeldmanVSSDKG: """ Implémentation du protocole DKG basé sur Feldman VSS Seuil (t,n) où t parts sont nécessaires pour reconstruire la clé """ def __init__(self, threshold: int, num_participants: int, curve=ec.SECP256K1()): self.threshold = threshold self.num_participants = num_participants self.curve = curve self.field_order = curve.generator.curve.field_size self.generator = curve.generator self.nodes: Dict[int, DKGNode] = {} def generate_polynomial(self, secret: int = None) -> List[int]: """Génère un polynôme aléatoire de degré t-1 avec le secret comme terme constant""" if secret is None: secret = secrets.randbelow(self.field_order) polynomial = [secret] # a0 = secret for _ in range(self.threshold - 1): polynomial.append(secrets.randbelow(self.field_order)) return polynomial def evaluate_polynomial(self, polynomial: List[int], x: int) -> int: """Évalue le polynôme en x""" result = 0 for i, coeff in enumerate(polynomial): result = (result + coeff * pow(x, i, self.field_order)) % self.field_order return result def generate_commitments(self, polynomial: List[int]) -> List[ec.EllipticCurvePoint]: """Génère les engagements publics g^ai pour chaque coefficient""" commitments = [] for coeff in polynomial: # Point = coeff * generator commitment = self._scalar_mult(self.generator, coeff) commitments.append(commitment) return commitments def _scalar_mult(self, point: ec.EllipticCurvePoint, scalar: int) -> ec.EllipticCurvePoint: """Multiplication scalaire sur courbe elliptique""" # Implémentation simplifiée - en production utiliser cryptography # Cette fonction devrait utiliser les primitives de la librairie cryptography return point # Placeholder def verify_share(self, share_value: int, participant_id: int, commitments: List[ec.EllipticCurvePoint]) -> bool: """Vérifie qu'une part est cohérente avec les engagements publics""" # Calcul de sum(commitments[i] * participant_id^i) expected_commitment = commitments[0] # C0 for i in range(1, len(commitments)): # expected_commitment += commitments[i] * participant_id^i term = self._scalar_mult(commitments[i], pow(participant_id, i, self.field_order)) expected_commitment = self._point_add(expected_commitment, term) # Vérifier que share_value * G == expected_commitment actual_commitment = self._scalar_mult(self.generator, share_value) return self._points_equal(actual_commitment, expected_commitment) def _point_add(self, p1: ec.EllipticCurvePoint, p2: ec.EllipticCurvePoint) -> ec.EllipticCurvePoint: """Addition de points sur courbe elliptique""" return p1 # Placeholder def _points_equal(self, p1: ec.EllipticCurvePoint, p2: ec.EllipticCurvePoint) -> bool: """Comparaison de points sur courbe elliptique""" return True # Placeholder def initialize_node(self, node_id: int) -> DKGNode: """Initialise un nœud participant""" polynomial = self.generate_polynomial() commitments = self.generate_commitments(polynomial) node = DKGNode( node_id=node_id, private_polynomial=polynomial, public_commitments=commitments, received_shares={} ) self.nodes[node_id] = node return node def phase1_share_distribution(self) -> Dict[int, Dict[int, FeldmanVSSShare]]: """Phase 1: Chaque nœud distribue ses parts aux autres""" shares_distribution = {} for sender_id, sender_node in self.nodes.items(): shares_distribution[sender_id] = {} for receiver_id in range(1, self.num_participants + 1): if receiver_id != sender_id: # Calcul de la part pour le receiver_id share_value = self.evaluate_polynomial( sender_node.private_polynomial, receiver_id ) share = FeldmanVSSShare( participant_id=receiver_id, share_value=share_value, verification_commitments=sender_node.public_commitments ) shares_distribution[sender_id][receiver_id] = share return shares_distribution def phase2_verification(self, shares_distribution: Dict[int, Dict[int, FeldmanVSSShare]]) -> bool: """Phase 2: Vérification des parts reçues""" verification_results = {} for receiver_id in range(1, self.num_participants + 1): verification_results[receiver_id] = {} for sender_id, sender_shares in shares_distribution.items(): if receiver_id in sender_shares: share = sender_shares[receiver_id] is_valid = self.verify_share( share.share_value, receiver_id, share.verification_commitments ) verification_results[receiver_id][sender_id] = is_valid # Stocker la part si elle est valide if is_valid and receiver_id in self.nodes: self.nodes[receiver_id].received_shares[sender_id] = share.share_value # Retourner True si toutes les vérifications passent return all( all(results.values()) for results in verification_results.values() ) def phase3_key_derivation(self) -> Dict[int, Tuple[int, ec.EllipticCurvePoint]]: """Phase 3: Dérivation des clés finales""" final_shares = {} for node_id, node in self.nodes.items(): # La part finale est la somme de toutes les parts reçues + sa propre part final_share = node.private_polynomial[0] # Sa propre part for sender_id, received_share in node.received_shares.items(): final_share = (final_share + received_share) % self.field_order # Calcul de la clé publique correspondante public_key = self._scalar_mult(self.generator, final_share) final_shares[node_id] = (final_share, public_key) return final_shares def execute_dkg(self) -> Dict[int, Tuple[int, ec.EllipticCurvePoint]]: """Exécute le protocole DKG complet""" print(f"🔄 Démarrage DKG avec seuil ({self.threshold}, {self.num_participants})") # Initialisation des nœuds for i in range(1, self.num_participants + 1): self.initialize_node(i) print(f"✅ {self.num_participants} nœuds initialisés") # Phase 1: Distribution des parts shares_dist = self.phase1_share_distribution() print("✅ Phase 1: Distribution des parts terminée") # Phase 2: Vérification verification_success = self.phase2_verification(shares_dist) if not verification_success: raise ValueError("❌ Échec de la vérification des parts") print("✅ Phase 2: Vérification réussie") # Phase 3: Dérivation finale final_keys = self.phase3_key_derivation() print("✅ Phase 3: Clés distribuées générées") return final_keys # Exemple d'utilisation if __name__ == "__main__": # Configuration pour un schéma (3,5) dkg = FeldmanVSSDKG(threshold=3, num_participants=5) try: distributed_keys = dkg.execute_dkg() print("\n🎉 DKG terminé avec succès!") print(f"Parts générées pour {len(distributed_keys)} nœuds") # Affichage des résultats (en production, ne jamais logger les clés privées) for node_id, (private_share, public_key) in distributed_keys.items(): print(f"Nœud {node_id}: Part privée générée (length: {len(str(private_share))})") except Exception as e: print(f"❌ Erreur DKG: {e}")