Certificateless Threshold Ring Signature Source: Information Sciences 179(2009) Author: Shuang Chang, Duncan S. Wong, Yi Mu, Zhenfeng Zhang Presenter: Chun-Yen Lee

Outline  Introduction  Definition  Proposed scheme

Ring signature Introduction

Ring signature Introduction Public Key Secret Key

Ring signature Introduction Public Key Secret Key

Ring signature Introduction Public Key Secret Key

Introduction  2001 Rivest et al. Ring signature  2002 Bresson et al. extended the notion of ring signature to threshold setting  2003 Al-Riyami and Paterson certificateless public key cryptography

Outline  Introduction  Definition  Proposed scheme

Definition  SetUp  MasterKeyGen  PartialKeyGen  UserKeyGen  Sign  Verify

Definition  SetUp System parameters (param)  MaterKeyGen master public key (mpk) master secret key (msk)

Definition  PartialKeyGen  UserKeyGen Master Public Key Master Secret Key params ID params ID user partial key (psk) user secret key (usk) user public key (upk)

Definition Public Key Secret Key Sign verify

Sign Definition Public Key Secret Key verify

Outline  Introduction  Definition  Proposed scheme

An efficient 1-out-of-n certificateless ring signature  SetUp Input: Output: param  MasterKeyGen Input: param Randomly pick a master secret key Master public key

An efficient 1-out-of-n certificateless ring signature  PartialKeyGen Input (param, msk, ID)  UserKeyGen Input (param, mpk, ID) Randomly pick a user secret key user public key

An efficient 1-out-of-n certificateless ring signature  Sign Input (param, mpk, R, S, m)   Randomly pick  Compute

An efficient 1-out-of-n certificateless ring signature  Compute  Compute  The signature is

An efficient 1-out-of-n certificateless ring signature  Verify Input (param, mpk, R, 1, S, m, σ) if