理想格上可证明安全的不经意传输协议

Ideal lattice-based oblivious transfer protocol of provably secure

针对理想格相比一般格可以在不降低安全性的基础上减少密钥量、缩短密钥长度、降低运行开销的优点,将理想格上的优势与一般格上的不经意传输协议结合,把2012年欧密会上Peiker提出的格上陷门函数生成算法扩展到理想格上,提出基于理想格上的1-out-of-n不经意传输协议方案。利用理想格上的基于错误学习问题的陷门单向函数,保证了协议发送方和接收方的隐私性,并证明了协议的完备性和安全性。效率方面,协议中使用的计算是小整数的模乘和模加,有很高的计算效率;并且使用理想格有效地限制明密文长度和密钥量,减少了通信成本。

There were some advantages in the ideal lattices which can decrease the keys, shorten the length of key and reduce the cost without reducing the safety. By combining the merits of ideal lattices with the oblivious transfer protocol on general lattices and expanding the general lattices＇ trapdoors generation algorithm presented by Peiker on the EUROCRYPT 2012 to the ideal lattices, this paper presented an ideal lattice-based 1-out-of-n oblivious transfer protocol. Using the trapdoor one-way function based learning with errors on ideal lattice ensures the privacy of submitter and receiver, in addition proved the completeness and security. In terms of efficiency, since using merely modular addition and modular multiplication operations, the protocol was efficient. Besides, it restricted the size of key the length of plaintext and ciphertext effectively and reduced the communication cost significantly.