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1. (WO2015118160) SIGNING METHODS FOR DELIVERING PARTIAL SIGNATURES, AND/OR THRESHOLD SIGNATURES, CORRESPONDING VERIFICATION METHODS, AND CORRESPONDING ELECTRONIC DEVICES

Pub. No.:    WO/2015/118160    International Application No.:    PCT/EP2015/052681
Publication Date: Fri Aug 14 01:59:59 CEST 2015 International Filing Date: Wed Feb 11 00:59:59 CET 2015
IPC: H04L 9/32
Applicants: THOMSON LICENSING
Inventors: JOYE, Marc
LIBERT, Benoit
Title: SIGNING METHODS FOR DELIVERING PARTIAL SIGNATURES, AND/OR THRESHOLD SIGNATURES, CORRESPONDING VERIFICATION METHODS, AND CORRESPONDING ELECTRONIC DEVICES
Abstract:
In one embodiment, it is proposed a signing method delivering a partial signature associated with a message, said partial signature being used in a threshold signing method, the signing method being executed on an electronic device. The signing method is remarkable in that it comprises: - obtaining a partial secret key SKi being obtained from an output of a secret sharing scheme, said partial secret key SKi being equal to {u1 (i), uK+1 (i)}, where elements uj (i) ∈ Zp for all j ∈ {1,..., K + 1}, with p being a prime number, and K being an integer greater or equal to one; - determining from said partial key, K elements tj = g-uj(i), with j ∈ {1,...,K + 1} and g being a generator of a group G, said group G being part of a bilinear group (G, Ĝ, GT) with Ĝ being a group and GT being a target group; - determining from said message a vector so as to define a Groth-Sahai common reference string; - determining Groth-Sahai commitments on said K + 1 elements tj with j ∈ {1,...,Κ + 1} from said Groth-Sahai common reference string, said Groth-Sahai commitments belonging to said group G; and - determining a non-interactive witness indistinguishable proof comprising K(K + 1) elements, all the K(K + 1) elements belonging to said group Ĝ, said proof guarantying that said K + 1 elements tj verify K pairing equations; - delivering said partial signature associated with said message, said partial signature comprising said Groth-Sahai commitments, and said non-interactive witness indistinguishable proof.