Paper 2010/474
Limitations on Transformations from Composite-Order to Prime-Order Groups: The Case of Round-Optimal Blind Signatures
Sarah Meiklejohn, Hovav Shacham, and David Mandell Freeman
Abstract
Beginning with the work of Groth and Sahai, there has been much interest in transforming pairing-based schemes in composite-order groups to equivalent ones in prime-order groups. A method for achieving such transformations has recently been proposed by Freeman, who identified two properties of pairings using composite-order groups--"cancelling" and "projecting"--on which many schemes rely, and showed how either of these properties can be obtained using prime-order groups. In this paper, we give evidence for the existence of limits to such transformations. Specifically, we show that a pairing generated in a natural way from the Decision Linear assumption in prime-order groups can be simultaneously cancelling and projecting only with negligible probability. As evidence that these properties can be helpful together as well as individually, we present a cryptosystem whose proof of security makes use of a pairing that is both cancelling and projecting. Our example cryptosystem is a simple round-optimal blind signature scheme that is secure in the common reference string model, without random oracles, and based on mild assumptions; it is of independent interest.
Note: Fixed a bug in the proof of Proposition 6.4.
Metadata
- Available format(s)
-
PDF
- Category
- Cryptographic protocols
- Publication info
- Published elsewhere. To appear at Asiacrypt 2010; this is the full version.
- Keywords
- blind signaturespairingscomposite-order groups
- Contact author(s)
- smeiklej @ cs ucsd edu
- History
- 2010-09-20: revised
- 2010-09-08: received
- See all versions
- Short URL
- https://ia.cr/2010/474
- License
-
CC BY
BibTeX
@misc{cryptoeprint:2010/474,
author = {Sarah Meiklejohn and Hovav Shacham and David Mandell Freeman},
title = {Limitations on Transformations from Composite-Order to Prime-Order Groups: The Case of Round-Optimal Blind Signatures},
howpublished = {Cryptology {ePrint} Archive, Paper 2010/474},
year = {2010},
url = {https://eprint.iacr.org/2010/474}
}
