External verifiability

Level of verification or assurance to be used - while few companies engage external verifiers to verify their first reports, it is helpful to engage stakeholders in the reporting process from the outset to identify their expectations for the report... 

Figure 8.11. Does your company issue a Sustainability Report If so, is the report externally verified in whole or in part If not, do you expect that your company will issue a report (Question 9). (Source PricewaterhouseCoopers, LLP.)...

The body turns a reddish hue as the Kundalini is aroused. There will also be a concentration of heat in the region of the awakened chakra, as Woodroffe also attests to in The Serpent Power. "There is one simple test whether the Shakti is actually aroused. When she is aroused intense heat is felt at that spot but when she leaves a particular centre that part so left becomes as cold and apparently lifeless as a corpse. The progress upwards may thus be externally verified by others. When the Shakti (Power) has reached the upper-brain (Sahasrara) the whole body is cold and corpse-like except the top of the skull, where some warmth is felt, this being the place where the static and kinetic aspects of Consciousness unite." At this point the body appears pale, cool, and glows with a soft lustre. 

This is the only disputable decision of this type Authentication is deliberately required to be a 2-party transaction (see Section 1.3) additional transactions can have arbitrary participants and new participants can be added to initialization and disputes if they do not influence the results for the original participants (e.g., the observers in Section 5.2.11, External Verifiability of the Behaviour of Participants ). 

External verifiability of the behaviour of participants in a transaction essentially means that there is a variant of this transaction where additional parties can observe the original participants and decide whether they behave correctly. Such a property has not been required explicitiy in any previous definition of signature schemes, but it can easily be fulfilled with some types of schemes and may be needed in some applications. The same property will be needed for other types of schemes in Sections 7.3 and 7.5.2 (zero-knowledge proofs and multi-party function evaluation), and the need for it may become clearer there. 

Generally. External verifiability of an output o of a transaction type trans is defined as follows One or more additional users, called observers, take part in the extended transaction. 

Usually, consistency of observations is also required, i.e., all honest observers should obtain identical results. However, this will be a consequence of a general structural requirement, see Section 5.3.2, Stracture for External Verifiability . 

Authentication. For the output acc in authentication, external verifiability means that each observer inputs a command observe authentication with the parameters m, ids, R,sign- Each observer receives an output acc observed according to the following requirements (where the latter is derived from the effectiveness of authentication) ... 

Dispute. External verifiability of the output acc of the court in a dispute corresponds to the informal requirement made in Section 1.3, Assessment by the Public . It means If the court is honest, the observing public obtains the same result as the court. Otherwise, each of them either catches the court cheating within the dispute transaction or knows that the output acc of the court s correct entity (which they cannot see, and which a dishonest court may have manipulated) must be equal to her own observed value. Thus, if the court announces a different decision, the observers also know that the court is cheating. 

This problem can also be handled outside the signature scheme e.g., the same court who might later have to decide whether the signer must pay the money back is now informed of the disagreement and settles the potential dispute in advance. However, the solution with external verifiability is more flexible. 

An extension of external verifiability is distributed variants of transactions, e.g., a variant of authentication where several recipients take part and either all of them accept the message as authenticated or none does. In contrast to observers, all these recipients should be able to win disputes about the message. 

If external verifiability of the behaviour of participants is required (see Section 5.2.11), a structural requirement is usually made, too The entities of the observers should only observe the messages between the original entities, and not send any messages themselves. For this purpose, the channels used in the normal implementation of the transaction are extended to broadcast channels including the observers entities as receivers. Moreover, it is required that the decisions of the observers are deterministic. This ensures the consistency of observations. 

External verifiability of both authentication and disputes can be added without modifying the original programs. 

External verifiability of authentication is easy to achieve because authentication is non-interactive, public keys exist, and test is deterministic and memory-less restr If the message exchange during authentication, i.e., sending the signature, takes place on a reliable broadcast channel (as it is standard when external verifiability is considered), all entities that took part in initialization can test the signature with the same public key. 

Definition 7.25 (Zero-knowledge proof scheme with generation algorithm, goodness predicate, and external verifiability). Let a pair (CorrFam, GoodFam) be given where... 

The components of a zero-knowledge proof scheme with generation algorithm and external verifiability for the pair CorrFam, GoodFam) are an algorithm gen and a triple ZKP = (P, V, Obs) with the following stmcture (see Figure 7.2 at the end of this definition) ... 

External verifiability requirement of the prover. For all probabilistic interactive functions V, all parameters par = ( 1 1 , and all values (K, aux) e [gen(par )] and auxy i The observer s output acc observed in all executions of ZKPp yipar, K, aux, auxyj ) is either TRUE or cheating , i.e., the observer either thinks that the verifier should be convinced or catches the verifier cheating. 

Figure 7.2. Components of a zero-knowledge proof scheme with generation algorithm and external verifiability, and their parameters in a correct execution...

Proof. Correct generation follows from the precondition on gen. Effectiveness of proofs follows immediately from the precondition [Corr, c Goodj fj. Soundness is just the definition of V. Zero-knowledge is clear because P does not send anything, hence it cannot divulge anything formally, one can use Sim = V. The external verifiability requirement of the prover is shown like the effectiveness of proofs, and the external verifiability requirement of the verifier is fulfilled because Obs = V and both are deterministic. ... 

It is now shown that the probability of this event is at most 2 ° By the definition of res, this implies acc observed = TRUE and with the external verifiability requirement of the verifier on the proof scheme, acc = true, too. The soundness of the proof scheme means that for any bad prekey and any auxiliary value aux that B might choose, the probability that acc = TRUE after the zero-knowledge proof is at most 2 . Hence the overall probability that B chooses a bad prekey and that this prekey is accepted in the zero-knowledge proof is at most 2 , too, as required. 

An algorithm res is needed that the entities of recipients and courts can execute, too. They do not take part in the multi-party function evaluation actively, but they observe the complete protocol execution, which is performed on broadcast channels anyway. (The following means that the protocol from [ChDG88] can easily be equipped with external verifiability as defined in Section 5.2.11.)... 

One can easily see that the scheme in [GrPe88] offers external verifiability. However, one must take care that the coin-flipping protocol used offers external verifiability, too. 

External verification there is no evidence that the CER has been externally verified. 

External verification the environmental report has not been externally verified. 

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