Statement proof and verification

A computer implemented method of verifying that a secret that is committed in a batched commitment is a discrete logarithm of a public element of a finite group of data elements, the method performed on a computing device and comprising:

• obtaining the batched commitment, wherein the batched commitment is a commitment to a first vector comprising n components and one of the n components of the first vector is the secret and is at a position in the first vector;
• receiving a further batched commitment from a proving computing device, wherein the further batched commitment is a commitment to a second vector comprising n components, wherein a component of the second vector, at a predetermined position corresponding to the position in the first vector, is set to zero;
• in response to receiving the further batched commitment generating a random challenge and transmitting the random challenge to the proving computing device;
• receiving a response to the random challenge from the proving computing device;
• and
• verifying that the secret is the discrete logarithm of the public element using the response, the batched commitment, the further batched commitment, and the random challenge.

A non-transitory computer readable storage medium comprising computer readable instructions that, when executed by a computing device, cause the computing device to perform a method of proving that a secret that is committed in a batched commitment is a discrete logarithm of a public element of a finite group of data elements, the method performed on a computing device and comprising:

• obtaining a first vector used to generate the batched commitment, the first vector comprising n components, wherein the secret is one of the n components of the first vector at a position in the first vector;
• generating a second vector comprising n components, wherein a component of the second vector, at a predetermined position corresponding to the position in the first vector, is set to zero;
• generating a further batched commitment to the second vector;
• transmitting the further batched commitment to a verifying computing device;
• receiving a random challenge from the verifying computing device;
• generating a response to the random challenge using the first vector, the second vector and the random challenge;
• and
• transmitting the response to the verifying computing device to prove that the secret is the discrete logarithm of the public element.