A method includes a validation computer receiving an authorization request message comprising a user state and a user proof from a user device. The user state comprises first and second user state elements. The user proof comprises first, second, and third user proof elements. The validation computer computes a first verification value by multiplying the first user proof element raised to the power of the second user state element, and the second user proof element raised to the power of the first user state element. The computer computes a second verification value by raising the second user proof element to the power of the second user state element. The computer compares the first verification value to a first accumulated state element of an accumulated state. The compares the second verification value to a second accumulated state element. The validation computer authorizes the authorization request message based on the comparison steps.