# Verifiable Encryption of a Pedersen Commitment

Can the Verifiable Encryption of a Discrete Logarithm scheme of the paper https://www.shoup.net/papers/verenc.pdf (page 19) be used to verify that a ciphertext encrypts the same value committed in a Pedersen Commitment?

Yes. Say the message is $$m$$ and the commitment is $$C$$ such that $$C = g^mh^r$$. Since you can use verifiable encryption to prove that a given ciphertext encrypts $$m$$ in relation $$g^m = y$$ where $$g$$ and $$y$$ are also public knowledge, using the Schnorr protocol you can prove that the $$m$$ in relation $$g^m = y$$ is same as the $$m$$ in $$C$$