Possible situations

• C = Client , R = Remote service

• 1. C ìknowsî fC(x) and R provides fR(x).

  • E.g. Simple test case(easy to be computed by C itself). Matrix inverse operation. Comparing fC(x) and fR(x).
  • PAC Learning theory.

• 2. C ìknowsî fC(x) and R does not provide fR(x).

  • E.g. Fee-based service. R offers hashed results g(fR(x)), where g is a secure hash function. E.g. , y is a singular matrix. Comparing and .
  • Zero-Knowledge proofs.

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• Traditional Software testing

• Zero-knowledge proofs have been used to securely exchange information between corresponding parties without giving away any unnecessary knowledge.

• E.g. the challenge here would be to ìproveî that a service agent ìknowsî how to compute matrix inversion without giving away any information that could be useful to the client agent.