Verify secret shares

With Pedersen verifiable secret sharing the sharing and the reconstruction of any secret can be verified.

• in the sharing phase each Shareholder can verify that the secret shares that he has received are valid

• in the reconstruction phase the Dealer can verify that the secret shares received from the shareholders are valid.

Before you can verify any secret shares, you have to configure a cyclic group to be used for Pedersen operations as is shown in Configure a cyclic group.

In the following examples a $(t, n)$-threshold scheme of $(t, n) = ($ schemeThreshold , schemeParts $)$ is assumed.

Shareholder verification

When a shareholder privately receives a secret part and the corresponding broadcast secret commitments he can verify the part in the following way.

import (
    "github.com/matteoarella/pedersen"
)

schemeParts := 5
schemeThreshold := 3
group := /* cyclic group */
x := /* abscissa related to the shareholder part */
share := /* secret share received from the dealer */
commitments := /* commitments broadcast from the dealer */

p, err := pedersen.NewPedersen(schemeParts, schemeThreshold, pedersen.CyclicGroup(group))
if err != nil {
    panic(err)
}

err = p.Verify(x, share, commitments)
if err != nil {
    panic(err)
}

Dealer verification

When a dealer receives a secret part from a shareholder he can verify the part in the same way as shown in Shareholder verification.

import (
    "github.com/matteoarella/pedersen"
)

schemeParts := 5
schemeThreshold := 3
group := /* cyclic group */
x := /* abscissa related to the shareholder part */
share := /* secret share received from the dealer */
commitments := /* commitments broadcast from the dealer */

p, err := pedersen.NewPedersen(schemeParts, schemeThreshold, pedersen.CyclicGroup(group))
if err != nil {
    panic(err)
}

err = p.Verify(x, share, commitments)
if err != nil {
    panic(err)
}

Additionally, the dealer can also collect every secret shares and then verify all of them in a single step as is shown here:

import (
    "github.com/matteoarella/pedersen"
)

schemeParts := 5
schemeThreshold := 3
group := /* cyclic group */
shares := /* secret shares assembled from every secret parts */

p, err := pedersen.NewPedersen(schemeParts, schemeThreshold, pedersen.CyclicGroup(group))
if err != nil {
    panic(err)
}

err = p.VerifyShares(shares)
if err != nil {
    panic(err)
}