Efficient computation of Tate pairing is a crucial factor for practical applications of pairing-based cryptosystems(PBC).Recently,there have been many improvements for the computation of Tate pairing,which focuses on ...Efficient computation of Tate pairing is a crucial factor for practical applications of pairing-based cryptosystems(PBC).Recently,there have been many improvements for the computation of Tate pairing,which focuses on the arithmetical operations above the finite field.In this paper,we analyze the structure of Miller’s algorithm firstly,which is used to implement Tate pairing.Based on the characteristics that Miller’s algorithm will be improved tremendous if the order of the subgroup of elliptic curve group is low hamming prime,a new method for generating parameters for PBC is put forward,which enable it feasible that there is certain some subgroup of low hamming prime order in the elliptic curve group generated.Finally,we analyze the computation efficiency of Tate pairing using the new parameters for PBC and give the test result.It is clear that the computation of Tate pairing above the elliptic curve group generating by our method can be improved tremendously.展开更多
Tate pairings over elliptic curves are important in cryptography since they can be. used to construct efficient identity-based cryptosystems, and their implementation dominantly determines the efficiencies of the cryp...Tate pairings over elliptic curves are important in cryptography since they can be. used to construct efficient identity-based cryptosystems, and their implementation dominantly determines the efficiencies of the cryptosystems. In this paper, the implementation of a cryptosystem is provided based on the Tate. pairing over a supersingular elliptic curve of MOV degree 3. The implementation is primarily designed to re-use low-level codes developed in implementation of usual elliptic curve cryptosystems. The paper studies how to construct the underlying ground field and its extension to accelerate the finite field arithmetic, and presents a technique to speedup the time-consuming powering in the Tate pairing algorithm.展开更多
Pairing-based cryptosystems have developed very fast in the last few years. The efficiencies of these cryptosystems depend on the computation of the bilinear pairings, In this paper, a new efficient algorithm based on...Pairing-based cryptosystems have developed very fast in the last few years. The efficiencies of these cryptosystems depend on the computation of the bilinear pairings, In this paper, a new efficient algorithm based on double-base chains for computing the Tate pairing is proposed for odd characteristic p 〉 3. The inherent sparseness of double-base number system reduces the computational cost for computing the Tate pairing evidently. The new algorithm is 9% faster than the previous fastest method for the embedding degree k = 6.展开更多
基金Acknowledgments This research is supported by National Nature Science Foundation of China under Grant No. 60873107 to G.M. Dai, Nature Science Foundation CD2008438B to G.M. Dai and in Hubei under Grant No. Special Funds to Finance Operating Expenses for Basic Scientific Research of Central Colleges in China under Grant No. CUGL090241 to M.C. Wang.
文摘Efficient computation of Tate pairing is a crucial factor for practical applications of pairing-based cryptosystems(PBC).Recently,there have been many improvements for the computation of Tate pairing,which focuses on the arithmetical operations above the finite field.In this paper,we analyze the structure of Miller’s algorithm firstly,which is used to implement Tate pairing.Based on the characteristics that Miller’s algorithm will be improved tremendous if the order of the subgroup of elliptic curve group is low hamming prime,a new method for generating parameters for PBC is put forward,which enable it feasible that there is certain some subgroup of low hamming prime order in the elliptic curve group generated.Finally,we analyze the computation efficiency of Tate pairing using the new parameters for PBC and give the test result.It is clear that the computation of Tate pairing above the elliptic curve group generating by our method can be improved tremendously.
文摘Tate pairings over elliptic curves are important in cryptography since they can be. used to construct efficient identity-based cryptosystems, and their implementation dominantly determines the efficiencies of the cryptosystems. In this paper, the implementation of a cryptosystem is provided based on the Tate. pairing over a supersingular elliptic curve of MOV degree 3. The implementation is primarily designed to re-use low-level codes developed in implementation of usual elliptic curve cryptosystems. The paper studies how to construct the underlying ground field and its extension to accelerate the finite field arithmetic, and presents a technique to speedup the time-consuming powering in the Tate pairing algorithm.
基金the National Natural Science Foundation of China(Grant Nos.60403007 and 60633030)the Major State Basic Research Development Program of China(973 Program)(Grant No.2006CB303104)
文摘Pairing-based cryptosystems have developed very fast in the last few years. The efficiencies of these cryptosystems depend on the computation of the bilinear pairings, In this paper, a new efficient algorithm based on double-base chains for computing the Tate pairing is proposed for odd characteristic p 〉 3. The inherent sparseness of double-base number system reduces the computational cost for computing the Tate pairing evidently. The new algorithm is 9% faster than the previous fastest method for the embedding degree k = 6.
