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
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.
