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I'm working for a professor to build a platform for students to take midterms and finals online. The student downloads the test during class (when the professor makes the test available on the server or passes out the paper copy). However, because of unreliable internet service, we'd like for students to be able to submit their finals later, when they can find a reliable connection. What I need is a way for a server to check that the student has not modified their answers to the exam in the intermittent period. How can I do this?

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This is exactly the scenario that the Timestamp Protocol has been created for.

You need to provide your students with access to a trusted timestamping authority (TSA). This could be you yourself or someone else (like a CA offering that service). The TSA signes the hash of the document (the test with all answers) alongside the current date and if your student passes that timestamp along to you, you have the guarantee, that the answers were not created later than the signed timestamp says.

Pleas note that while this solution does not require your students to be able to connect to your servers, it does require a short online communication to the TSA server. This requirements holds true for any other alternatives that I am aware of (like tweeting the test's hash or storing the hash in a public blockchain), I do not believe that a completely offline solution exists for your problem.

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