Undeniable signatures are classic digital signatures which arenot universally verifiable and can only be verified with the help of thesigner. Its extended version, convertible undeniable signatures, equipsthe signer with the additional ability to make his undeniable signaturesuniversally verifiable whenever required. A selectively-convertible undeniablesignature scheme allows the signer to convert a single signatureinto a universally verifiable signature by releasing a selective proof in alater time, while universally-convertible refers to the case where thesigner has the additional ability to generate a universal proof whichcan finally convert all his undeniable signatures into universally verifiablesignatures. In this paper, we propose a generic construction foruniversally-convertible undeniable signatures. Our construction is basedon three building blocks: a strongly unforgeable classic signature scheme,a selectively-convertible undeniable signature scheme and a collisionresistanthash function. Formal proofs guarantee that our constructionhas a tight security reduction to the underlying security assumptions. Asone of the applications of our generic construction, one can obtain thefirst provable secure universally-convertible undeniable signature schemein the standard model.