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

Box 2

The description of the proposed generic construction. In the concrete instantiation, denotes a tuple consisting of all group elements that appear in the bracket, and the operator is the component-wise group multiplication. The noninteractive proof system is for demonstrating the existence of a satisfying assignment of (5).

:

 For all :

 Output .

GSig():

 Parse as

 Parse as

 Output .

GVf():

 Parse as

 Parse as

 If

 and

then Output

 Else Output .

Td():

 Parse as

 Output .

Open():

 Parse as

 Parse as

 If or

then Output

 If

 and and

then Output

 Else Output .