Pairing-Based Cryptography – Pairing 2012: 5th International by Xusheng Zhang, Kunpeng Wang, Dongdai Lin (auth.), Michel

By Xusheng Zhang, Kunpeng Wang, Dongdai Lin (auth.), Michel Abdalla, Tanja Lange (eds.)

This e-book constitutes the refereed complaints of the fifth overseas convention on Pairing-Based Cryptography, Pairing 2012, held in Cologne, Germany, in may well 2012.
The 17 complete papers for presentation on the educational song and three complete papers for presentation on the business music have been rigorously reviewed and chosen from forty nine submissions. those papers are provided including 6 invited talks. The contributions are geared up in topical sections on: algorithms for pairing computation, safeguard versions for encryption, practical encryption, implementations in and software program, tune, houses of pairings, and signature schemes and applications.

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Pairing-Based Cryptography – Pairing 2012: 5th International Conference, Cologne, Germany, May 16-18, 2012, Revised Selected Papers

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Additional info for Pairing-Based Cryptography – Pairing 2012: 5th International Conference, Cologne, Germany, May 16-18, 2012, Revised Selected Papers

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Most cryptosystems use not only exponentiation but also multiplication. The existing trace representation is not useful because of lack of multiplication. Our Contributions. We propose factor-4 and 6 decompressible trace representation with additional information for characteristics 2 and 3, respectively. We construct decompression maps for the trace representation by adding extra information. Our decompression maps are efficient. Since our representation permits decompression, we are able to introduce multiplication in the trace representation for the first time.

Factor-6 decompression D Input: (i, T r6/1 (g)) Output: the T2 affine representation 1: 2: 3: 4: 5: 6: 7: 8: 9: 10: 11: −2 f +z m f +z p , f = δ1 y + δ2 y p −1 m + δ3 y (p m 2 ) for g −1 A−1 0 , A1 + 1] for A and obtain solutions solve A = −[{T r6/1 (g)} if i1 = 1 then with ai = 1 for the least nonzero trit ai in the vector representation select A−1 1 else if i1 = 0 then with ai = 2 for the least nonzero trit ai in the vector representation select A−1 0 end if 2 +1 + 1) = 0 and obtain a solution β with the least trit i2 solve β 3 − β − ( A At+3 t−2 2 +1 β ← −A{( A + 1) β1 + 1 − A−2 } At+3 −2 tb ← −(1 + A )A−t − A−1 tc ← A2 − Atb + A−1 tb − t2b − A−4 (1−A−2 )β 2 +tb β−tc γ ← −A −1 β 2 +(1−A−2 )β Factor-4 and 6 (De)Compression for Values of Pairings Using Trace Maps Lemma 5.

The place is the same for the least nonzero trit of c. The compression map C described by eq. (14) costs I3 + M3 to calculate α/β = a + bw + cw2 , a, b, c ∈ Fpm from α, β ∈ F(pm )3 . The decompression map D described by eq. (15) costs I1 + 7M1 + 2S1 to calculate D(c) = 2(c3t+3 + c2t + 1) c3t+3 34 T. Yonemura et al. and to solve the following degree-1 polynomial P2 (x) = x + 2b2t+3 + 2b2t c3 + bt ct+3 + c2t+3 + 2ct ∈ Fpm [x]. We recall an estimation of exponentiation cost [13]. We determine the widthw radix-3 NAF representation of the power r, and then it contains on average 2 log3 r/(2w + 1) nonzero digits.

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