Method to generate, verify and deny an undeniable signature

A method of confirming by a Verifier an undeniable signature (y1, . . . , yt) of a set of data (m) generated by a Signer taking into account a predefined security parameter of the confirmation protocol, this Signer having a public/secret key pair, this method comprising the following steps:

• obtaining a personal value (ρ) from the Signer, this personal value being part of the public key (G, H, d, ρ, (e1, . . . es)) of the Signer;
• extracting a first sequence of elements (e1, . . . es) from the public key,
• generating a second sequence of elements (g1, . . . gs) from the personal value (ρ),
• generating a third sequence of elements (x1, . . . , xt) from the set of data (m);
• randomly picking challenge parameters ri∈G and aij∈Zd for i=1, . . . , k and j=1, . . . , s+t and computing a challenge value ui=dri+ai1g1+ . . . aisgs+ais+1x1+ . . . +ais+txt;
• sending by the Verifier the challenge value uj to the Signer;
• receiving from the Signer a commitment value (<vi>), this commitment value (<vi>) being calculated by the Signer based on a response value vi=f(ui);
• sending by the Verifier the challenge parameters ri and aij to the Signer;
• verifying by the Signer whether ui=dri+ai1g1+ . . . aisgs+ais+1x1+ . . . +ais+txt, and in a positive event, opening by the Signer the commitment on the response value (vi);
• and
• verifying by the Verifier whether vi=ai1e1+ . . . aises+ais+1x1+ . . . +ais+txt.