PointProofs, Revisited

Benoît Libert (1) , Alain Passelègue (1, 2) , Mahshid Riahinia (1)

1 LIP - Laboratoire de l'Informatique du Parallélisme
2 ARIC - Arithmétiques des ordinateurs, méthodes formelles, génération de code

Vector commitments allow a user to commit to a vector of length n using a constant-size commitment while being able to locally open the commitment to individual vector coordinates. Importantly, the size of position-wise openings should be independent of the dimension n. Gorbunov, Reyzin, Wee, and Zhang recently proposed PointProofs (CCS 2020), a vector commitment scheme that supports non-interactive aggregation of proofs across multiple commitments, allowing to drastically reduce the cost of block propagation in blockchain smart contracts. Gorbunov et al. provide a security analysis combining the algebraic group model and the random oracle model, under the weak n-bilinear Diffie-Hellman Exponent assumption (n-wBDHE) assumption. In this work, we propose a novel analysis that does not rely on the algebraic group model. We prove the security in the random oracle model under the n-Diffie-Hellman Exponent (n-DHE) assumption, which is implied by the n-wBDHE assumption considered by Gorbunov et al. We further note that we do not modify their scheme (and thus preserve its efficiency) nor introduce any additional assumption. Instead, we prove the security of the scheme as it is via a strictly improved analysis.

Keywords: cryptography; Vector commitments; provable security

Domains: Cryptography and Security [cs.CR]

Benoît Libert, Alain Passelègue, Mahshid Riahinia. PointProofs, Revisited. Asiacrypt 2022 - International Conference on the Theory and Application of Cryptology and Information Security, Dec 2022, Taipei, Taiwan. ⟨hal-03903981⟩