Simple improvements to Harn´s digital signature for Diffie-Hellman public keys

To integrate authentication into the Diffie-Hellman public key distribution scheme, Harn proposed digital signature schemes that did not involve the use of one-way functions. However, such schemes cannot withstand the Nyberg-Rueppel attack. To ensure that the Nyberg-Rueppel attack could not be used, an improvement was proposed by He and Wu. However, the computational cost caused by the improvement is too high. Therefore, some efficient improvements are proposed such that the size of signatures is the same