Type 1 pairing + DLIN ⇒ Structure-preserving signatures, tightly (Hofheinz–Jager)

Standard model · HJ12 · security loss: tight: independent of the number of signing queries

Statement

If DLIN holds in a symmetric bilinear group, there is a structure-preserving signature scheme with a tight security reduction, whose loss does not depend on the number of signing queries — HJ12. Combined with Groth–Sahai proofs, it yields a tightly simulation-sound NIZK proof system for group equations and, through Naor–Yung double encryption, tightly IND-CCA public-key encryption from DLIN — HJ12.