Algorithm testing

A signature is received from the recipient s entity and tested with the same algorithm test that entities of recipients use in authentication. ... 

Fixed recipient or one recipient per initialization. With all existing fail-stop signature schemes, what one gains by this restriction is efficiency in authentication, in particular, in the algorithm test, because the recipient s entity can store information from previous signatures. On the other hand, this implies that a court s entity cannot use the same test for a signature as the recipient s entity, i.e., disputes are not constructed as above. 

The structure of disputes in standard fail-stop signature schemes was almost completely described in Section 6.1.2 (Subsection Number of Recipients and Complexity of Tests ) by the actions of the court s entity In Step 1, the court s entity tests the signature with the algorithm test defined above. (Now test is memory-less anyway, i.e., no special case is needed.) In Step 2, this signature is sent to the signer s entity, which can answer with a string called a proof of forgery. In Step 3, the court s entity verifies this proof... 

Arbitrary transferability is easy to achieve as a consequence of the existence of public keys and non-interactive authentication The entity of the former recipient of a signed message can simply pass the signature on, and the entity of the new recipient tests it with the normal algorithm test. (Signatures had to be stored anyway in case of disputes.) The effectiveness of transfers, i.e., the requirement that the new recipient should accept the signature, is guaranteed information-theoretically without error probability because both entities have the same public key. 

Test The input to the algorithm test is a triple (pk, m, s) with pk = j and 5 = (Si)isidsj. g Each part of the signature is tested with the correspohchng part of the pumic Key, and all parts must be correct. Hence the result acc is true iff... 

Shor factorization algorithm tested in a 7-qubit molecule... 

Typically, minimization algorithms test for a sufficiently small gradient norm, i.e.. 

---