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...ieties are proposed by Rubin and Silverberg [39]. We note that both encryption and decryption in FullIdent can be made faster by using the Tate pairing on elliptic curves rather than the Weil pairing =-=[19, 1]-=-. Asymmetric pairings. Our IBE system can use slightly more general bilinear maps, namely maps of the form ê : G0 × G1 → G2 where G0, G1, G2 are three groups of prime order q. Using the notation of Se...

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...G1 is a cyclic group. We note that the Weil and Tate pairings associated with supersingular elliptic curves or abelian varieties can be modified to create such bilinear maps, as in [13,5,7]; see also =-=[14,2]-=-. BDH Parameter Generator: As in [5], we say that a randomized algorithm IG is a BDH parameter generator if IG takes a security parameter K > 0, runs in time polynomial in K, and outputs the descripti...

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...prehensive overview). There has been a lot of work on efficient implementation of pairings on elliptic curves. Supersingular curves lead to more efficient implementations in terms of processing speed =-=[2, 8,5]-=- and bandwidth requirements [15,9] than the best available algorithms for ordinary curves [3]. Pairings on hyperelliptic curves have received considerably less attention than their elliptic counterpar...

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...mentation of thesniteseld arithmetic. Section 10 contains some of our timing results. We must note that in thesnal stages of preparing this paper we became aware of the work of Barreto, Kim and Scott =-=[1]-=- which also provides an excellent solution to the problem of eÆcient computation of the Tate pairing. 2 The Tate pairing The Weil pairing wassrst introduced into cryptography by Menezes, Okamoto and V...

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...ing a “multi-pairing” approach [21], which is similar to multi-exponentiation. One can also exploit the fact that all the k··· are fixed for a given recipient to perform advantageous pre-computations =-=[3]-=-. 6 Consistency and Security The following theorems state that extracted and delegated private keys are identically distributed, and that extraction, encryption, and decryption, are consistent. We rem...

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...1. By taking degrees, it is easy to see that Ker([ξk d ]−1) ⊂ E[d], with E[d] the d-torsion points on E. However, a more detailed analysis shows that (3) holds if and only if: – d = 2, 4: E(F q d) ∩ E=-=[2]-=- = O – d = 3: E(F q d) ∩ Ker([ξ3] − 1) = O with Ker([ξ3] − 1) � E[3] 10s– d = 6: E(F q d) ∩ E[2] = O and E(F q d) ∩ Ker([ξ3] − 1) = O Furthermore, translating these conditions back to E(Fq), we get th...

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...the string we want to map, and then generate a pseudorandom point in E(Fp)[q]. The bilinear map ê we used is the Tate pairing, with some of the modifications and performance improvements described in=-= [3, 6]-=-. 6.3. Measurements We ran our 100% Java implementation on a 1.8GHz Pentium 4. The table below shows the handshake times for various parameter values, alongside RSA key sizes that are believed to deli...

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...r ring signature scheme can be performed with supersingular elliptic curves or hyperelliptic curves. The essential operation in our ID-based signature schemes is to compute a bilinear pairing. Due to =-=[3]-=- and [10], the computation of a bilinear pairing becomes efficient. Furthermore, the length of signature can be reduced by a factor of 2 using compression technique. Since our scheme is based on ident...