XTR+: A Provable Secure Public Key Cryptosystem

The XTR is a very effective public key cryptosystem based on 3rd order LFSR sequence. But it has the parameter corresponding problem and it neglects the provable security property and the blind signature scheme. For overcoming these problems in this paper, the XTR is extended with 4-th order LFSR sequence to form a new cryptosystem called XTR⁺. An algorithm for computing the trace elements is proposed, which only depends on a 2 times 2 recursive matrix not as 4 times 4 so that the running time of the algorithm is much shorter than the algorithm for XTR which depends on a 3 times 3 recursive matrix. Over XTR⁺ the provable IND-CCA2 secure encryption/decryption protocol and the provable secure blind signature protocol are established. Compared with the traditional methods such as ECC, XTR⁺ is more simple in cipherkey and parameter selections and has more randomicity and faster algorithms. Under the same security requirements, the XTR⁺ can greatly reduce the overheads in parameter storage and communication and be suitable for bigger plaintext and ciphertext spaces