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# 数学代写|密码学代写Cryptography Theory代考|CS255

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## 数学代写|密码学代写Cryptography Theory代考|Arbitrated digital signature schemes

The first case arises when there exists a trusted third party, the arbitrator, who participates in the transfer of data and generates evidence which can be used to settle any disputes. Both the signer and verifier trust the arbitrator. Disputes are settled based on the premise that a statement is true if the arbitrator says it is true.

An example of an arbitrated digital signature scheme is illustrated in Figure 7.1. Prior to using the scheme in Figure 7.1, we assume all the parties involved have agreed upon a method for computing MACs. Further, the signer and the arbitrator share a symmetric MAC key $K S$, and the verifier and the arbitrator share a symmetric MAC key $K V$. To generate a digital signature on some data:

1. The signer computes a MAC on the message using key $K S$. The sender then sends the message and the MAC to the arbitrator. (This message includes an indication of the identities of the signer and the intended verifier.)
2. The arbitrator uses key $K S$ to verify the correctness of the MAC received from the signer. If it is correct, then the arbitrator continues, otherwise the process is aborted.
3. The arbitrator computes a new MAC on all the data received from the signer. In other words, the MAC is computed using key $K V$ on both the message and the MAC computed by the signer using $K S$. The arbitrator then forwards everything sent by the signer, plus this new MAC, to the verifier.
4. The verifier uses key $K V$ to verify the correctness of the MAC received from the arbitrator. If it is correct, then the verifier accepts this as a ‘digital signature’ on the message, otherwise the verifier rejects the signature. Although the verifier cannot check the first MAC, there is no need for the verifier to do so since the arbitrator has already verified this MAC for them.

## 数学代写|密码学与系统安全代写Cryptography and System Security代考|Data origin authentication

Data origin authentication. The second MAC (computed using $K V$ ) provides the verifier with data origin authentication of the message passed on by the arbitrator. The first MAC (computed using $K S$ ) provides the arbitrator with data origin authentication of the message from the signer. The verifier trusts the arbitrator to behave honestly. Therefore, the verifier has assurance through the second MAC that the arbitrator, who is trusted, had assurance through the first MAC that the message came from the signer. Under the trust assumptions of this model, the verifier does indeed have data origin authentication of the signer.

Non-repudiation. Suppose a dispute arises at a later date and the signer falsely denies digitally signing the message. The verifier can present the full data received from the arbitrator as evidence of the data exchange. The presence of the valid MACs essentially states that the verifier received the message from the arbitrator, who vouched it came from the signer. While the verifier could have forged the second MAC (computed using $K V$ ), the verifier could certainly not have forged the first MAC (computed using $K S$ ) because the verifier does not know key $K S$. The arbitrator (or indeed any judicator who is given access to the appropriate MAC keys) will rule in favour of the verifier in this case.

## Matlab代写

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