可完全验证的双线性对运算外包算法

New algorithms for verifiable outsourcing of bilinear pairings

双线性对运算是基于对的密码学中最昂贵的运算.基于两个不可信的服务器,本文首先提出了单个双线性对运算的外包计算方案.用户不需要执行任何复杂度高的运算,如标量乘、模乘运算等.本文还提出了多个双线性对运算的外包方案,效率远远高于调用单个对运算外包方案.在所提的两个算法中,如果服务器不诚实,用户均能以概率1检测到错误.基于两个算法,本文还提出了可外包解密的基于身份匿名加密方案和签名外包验证的基于身份签名方案.

It is well known that the computation of bilinear pairing is the most expensive operation in pairingbased cryptography. In this paper, we first propose a secure verifiable outsourcing algorithm of single bilinear pairing based on two servers in the one-malicious model. The outsourcer need not execute any expensive operations, such as scalar multiplication or modular exponentiation. We also present another verifiable outsourcing algorithm for multiple bilinear pairings. This algorithm is much more efficient than the repeated invocation of the outsourcing algorithm of single bilinear pairing. Both of the proposed algorithms enable the outsourcer to detect any failure with a probability of 1 if one of the servers misbehaves. Finally, we utilize the proposed algorithms as two subroutines to achieve an anonymous identity-based encryption（AIBE） scheme with outsourced decryption and an identity-based signature（IBS） scheme with outsourced verification.