Group Signatures with Message-Dependent Opening: Formal Definitions and Constructions

Box 3

The proposed construction in the random oracle model. The functions and are cryptographic hash functions and , which are modeled as random oracles in the security proof. is the parameter generation algorithm, which is defined in Section 2.5.

GKg:

 , ,

 , , , ,

 ; ; ;

 For :

 For :

 Output .

GSig:

 , , ,

 , , , , , , , ,

 ;

 ;

 ;

 ;

 Output .

GVf:

 If

Output

 Else output .

Td:

 Output .

Open:

 If

Output

 If :

 Output ;

 Else output .