We propose a convertible undeniable signature scheme without
random oracles. Our construction is based on Waters and Kurosawa
and Hengs schemes that were proposed in Eurocrypt 2005. The security
of our scheme is based on the CDH and the decision linear assumption.
Comparing only the part of undeniable signatures, our scheme uses more
standard assumptions than the existing undeniable signatures without
random oracles due to Laguillamie and Vergnaud.