Statistical ZAPs from Group-Based Assumptions - Archive ouverte HAL Accéder directement au contenu
Communication Dans Un Congrès Année : 2021

Statistical ZAPs from Group-Based Assumptions

Geoffroy Couteau
Shuichi Katsumata
  • Fonction : Auteur
  • PersonId : 1113018
Elahe Sadeghi
  • Fonction : Auteur
  • PersonId : 1113102
Bogdan Ursu
  • Fonction : Auteur
  • PersonId : 1084656

Résumé

We put forth a template for constructing statistical ZAPs for NP. Our template compiles NIZKs for NP in the hidden-bit model (which exist unconditionally) into statistical ZAPs using a new notion of interactive hidden-bit generator (IHBG), which adapts the notion of hidden-bit generator to the plain model by building upon the recent notion of statistically-hiding extractable commitments. We provide a construction of IHBG from the explicit hardness of the decision Diffie-Hellman assumption (where explicit refers to requiring an explicit upper bound on the advantage of any polynomial-time adversary against the assumption) and the existence of statistical ZAPs for a specific simple language, building upon the recent construction of dual-mode hidden-bit generator from (Libert et al., EUROCRYPT 2020). We provide two instantiations of the underlying simple ZAP:-Using the recent statistical ZAP for the Diffie-Hellman language of (Couteau and Hartmann, CRYPTO 2020), we obtain statistical ZAPs for NP assuming (the explicit hardness of) DDH in G1 and kernel-DH in G2 (a search assumption which is weaker than DDH), where (G1, G2) are groups equipped with an asymmetric pairing. This improves over the recent work of (Lombardi et al., EUROCRYPT 2020) which achieved a relaxed variant of statistical ZAP for NP, under a stronger assumption.-Using the recent work of (Couteau et al., EUROCRYPT 2020), we obtain statistical ZAPs for NP assuming the explicit hardness of DDH, together with the assumption that no efficient adversary can break the key-dependent message one-wayness of ElGamal with respect to efficient functions over groups of size 2 λ with probability better than poly(λ)/2 (c+o(1))•λ , denoted 2 −cλ-OW-KDM, for a constant c = 1/2, in pairing-free groups. Note that the latter is a search discrete-log-style falsifiable assumption, incomparable to DDH (in particular, it is not known to imply public-key encryption).
Fichier principal
Vignette du fichier
2021-688.pdf (774.64 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-03374562 , version 1 (12-10-2021)

Identifiants

  • HAL Id : hal-03374562 , version 1

Citer

Geoffroy Couteau, Shuichi Katsumata, Elahe Sadeghi, Bogdan Ursu. Statistical ZAPs from Group-Based Assumptions. TCC 2021 - Theory of Cryptography Conference, Nov 2021, Raleigh, United States. ⟨hal-03374562⟩
18 Consultations
57 Téléchargements

Partager

Gmail Facebook X LinkedIn More