Verifiable computation on signed data
One of the many verifiable computation schemes would be the way to go.

Something like zkSNARKs would allow a prover, Alice in this case, to prove that she performed a computation correctly without revealing the inputs to her function. These schemes require Alice to initially send a commitment of her input to the verifier. In your setup, the chunk of data Victor signs may be a commitment to the original data he sent.

To learn more about zkSNARKs, I recommend the already linked Winter School, as well as the following primer provided by Zcash: https://z.cash/blog/snark-explain.html. 

Edit Just encountered this work that is relevant: ADSNARK: Nearly Practical and Privacy-Preserving Proofs on Authenticated Data (https://eprint.iacr.org/2014/617)