Enhanced STS using Check Equation

We propose solutions to the problems which has been left in the Enhanced STS, which was proposed in the PQCrypto 2010. Enhanced STS signature scheme is defined as the public key with the Complementary STS structure, in which two STS public keys are symmetrically joined together. Or, the complementary STS is the public key where simply two STS public keys are joined together, without the protection with Check Equation. We discuss the following issues left in the Enhanced STS, which was prosented in the PQCrypt2010: (i) We implied that there may exist a way to cryptanalyze the Complementary STS structure. Although it has been proposed that the system be protected by Check Equations [35][37], in order to cope with an unknown attack, we did not show the concrete procedure. We show the actual procedure to cryptanalyze it and forge a signature. (ii) We assumed that the Check Equation should be changed every time a document is signed. This practice is not always allowed. We improved this matter. The Check Equation which was proposed in the PQCrypto 2010 defined the valid life as a function of the number of times the documents are signed, because the secret key of Check Equation is analyzed by collecting valid signatures. Now we propose a new method of integrating the Check Equation into the secret key and eliminate the risk of the hidden information drawn from the existing signature.