Twin-Schnorr: A Security Upgrade for the Schnorr Identity-Based Identification Scheme

Algorithm 4

Description of the Simulator solving an instance of the discrete logarithm problem with the help of impersonator as subroutine.

SETUP

(1)  ;

(2)  ;

(3)  ; ;

(4)  , ; ;

(5)  ;

(6)  

(7)  :

 (i) ;

 (ii) , ;

 (iii) , , ;

 (iv) ;

 (v) ;

 (vi) ;

 (vii) ;

 (viii) ;

 (ix) ;

(8)  :

 (i) ;

 (ii) ;

 (iii) ;

(9)  :

 (i) ;

 (ii) ;

 (iii) ;

 (iv) ,

 (v)

 (vi)

 (vii) , , , ;

 (viii)

 (ix)

 (x) ;

Phase 1

(10)  : , , ;

Phase 2

(11)  ;

(12)  , : , , ;

(13)  RESET CP;

(14)  , : , , ;

(15)  ;

(16)  ;

(17)  ;

(18)  ;

(19)   ;

(20)  ;

(21)  ;