Breaking an ID-based encryption based on discrete logarithm and factorization problems

Identity-based (ID-based) cryptography is very useful as it can simplify the certificate management in public key cryptosystem. Since 2001, researchers have introduced various practical and efficient ID-based encryption schemes. Most of them are based on pairings, under the Diffie-Hellman assumptions. Recently, Meshram [1] proposed a new ID-based encryption scheme which was not based on pairing-based cryptography. He proved that his scheme was secure against adaptive chosen plaintext attack, as its security was based on the difficulty of discrete logarithm and integer factorization problems. However, in this paper, we show that this new ID-based encryption scheme is insecure by presenting a method to recover the secret master key.