Identity-Based Encryption Protocols Using Bilinear Pairing

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[31] Sanjit Chatterjee and Palash Sarkar. HIBE with Short Public Parameters Secure in the Full Model Without Random Oracle. Indian Statistical Institute, Technical Report No. ASD/2006/6, 2006. [32] Sanjit Chatterjee and Palash Sarkar. New Constructions of Constant Size Ciphertext HIBE Without Random Oracle. Indian Statistical Institute, Technical Report No. ASD/2006/7, 2006. [33] Sanjit Chatterjee, Palash Sarkar, and Rana Barua. Efficient Computation of Tate Pairing in Projective Coordinate over General Characteristic Fields. In Choonsik Park and Seongtaek Chee, editors, ICISC, volume 3506 of Lecture Notes in Computer Science, pages 168–181. Springer, 2004. [34] Clifford Cocks. An Identity Based Encryption Scheme Based on Quadratic Residues. In Bahram Honary, editor, IMA Int. Conf., volume 2260 of Lecture Notes in Computer Science, pages 360–363. Springer, 2001. [35] Jean-Sébastien Coron. On the exact security of full domain hash. In Mihir Bellare, editor, CRYPTO, volume 1880 of Lecture Notes in Computer Science, pages 229–235. Springer, 2000. [36] Ronald Cramer, editor. Advances in Cryptology - EUROCRYPT 2005, 24th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Aarhus, Denmark, May 22-26, 2005, Proceedings, volume 3494 of Lecture Notes in Computer Science. Springer, 2005. [37] Whitfield Diffie and Martin E. Hellman. New Directions in Cryptography. IEEE Tr. Inf. Th., 22:644–654, 1976. [38] Yevgeniy Dodis and Nelly Fazio. Public Key Broadcast Encryption for Stateless Receivers. In Joan Feigenbaum, editor, Digital Rights Management Workshop, volume 2696 of Lecture Notes in Computer Science, pages 61–80. Springer, 2002. [39] Iwan M. Duursma and Hyang-Sook Lee. Tate Pairing Implementation for Hyperelliptic Curves y 2 = x p −x+d. In Chi-Sung Laih, editor, ASIACRYPT, volume 2894 of Lecture Notes in Computer Science, pages 111–123. Springer, 2003. [40] Kirsten Eisenträger, Kristin Lauter, and Peter L. Montgomery. Fast Elliptic Curve Arithmetic and Improved Weil Pairing Evaluation. In Joye [59], pages 343–354. [41] Taher Elgamal. A Public Key Cryptosystem and a Signature Scheme Based on Discrete Logarithms. IEEE Transactions on Information Theory, 31(4):469–472, 1985. [42] Matthew K. Franklin, editor. Advances in Cryptology - CRYPTO 2004, 24th Annual International CryptologyConference, Santa Barbara, California, USA, August 15-19, 2004, Proceedings, volume 3152 of Lecture Notes in Computer Science. Springer, 2004. 132
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Page 1:
Construction of (Hierarchical) Iden
Page 5:
The scientist does not study nature
Page 9 and 10:
Contents 1 Introduction 1 1.1 Plan
Page 11:
7.4.1 HIBE H 1 . . . . . . . . . .
Page 14 and 15:
the public key. In this setting, an
Page 16 and 17:
adversary in distinguishing two mes
Page 18 and 19:
previous chapter. The second varian
Page 20 and 21:
as it is closer to the known exampl
Page 22 and 23:
Let P i = a i P . An algorithm A ha
Page 24 and 25:
Given the security parameter κ, th
Page 26 and 27:
the Key-Gen algorithm and C is the
Page 28 and 29:
Phase 2: A now issues additional qu
Page 30 and 31:
Chapter 3 Previous Works in Identit
Page 32 and 33:
Decrypt: Decrypt C = 〈U, V 〉 us
Page 34 and 35:
Game 2 Suppose B is given a BDH pro
Page 36 and 37:
Security of BasicHIBE against chose
Page 38 and 39:
BB-HIBE Here individual components
Page 40 and 41:
F i (v ∗ i ) = α i P , so C =
Page 42 and 43:
Key-Gen: Let v = (v 1 , . . . , v n
Page 44 and 45:
Composite HIBE Boneh, Boyen and Goh
Page 46 and 47:
Security Given an identity tuple v
Page 48 and 49:
Chapter 4 Tate Pairing in General C
Page 50 and 51:
order on the elliptic curve E(IF p
Page 52 and 53:
the best result. In [57] the author
Page 54 and 55:
Hence, we require 3[S] + 8[M] for E
Page 56 and 57:
Algorithm 2 (iterated doubling): In
Page 58 and 59:
Level 1 : t 1 = Y 2 1 ; t 4 = Z 2 1
Page 60 and 61:
Table 4.1: Cost Comparison. Note 1[
Page 62 and 63:
problem. - Our construction resembl
Page 64 and 65:
is equal to c 2 |IF a | 3 . Thus, t
Page 66 and 67:
aborts if F (v ∗ ) ≠ 0 and outp
Page 68 and 69:
DBDH problem over (G 1 , G 2 , e) i
Page 70 and 71:
these are respectively 2.4 kb and 2
Page 72 and 73:
Signing: Let M = (m 1 , m 2 , . . .
Page 74 and 75:
model without random oracles. Addit
Page 76 and 77:
6.2 Construction HIBE-spp The ident
Page 78 and 79:
Table 6.1: Comparison of HIBE Proto
Page 80 and 81:
For 1 ≤ j ≤ h, we define severa
Page 82 and 83:
establish the claim. We provide the
Page 84 and 85:
The probability is over the indepen
Page 86 and 87:
= ≥ ( ( 1 − Pr 1 − [( q∨ i=
Page 88 and 89:
of public parameters is significant
Page 90 and 91:
to be I ∗ . It can then ask for t
Page 92 and 93:
Phase 2: The adversary issues addit
Page 94 and 95: 7.3 Interpreting Security Models Th
Page 96 and 97: 7.4 Constructions We present severa
Page 98 and 99: 7.4.2 HIBE H 2 The description of H
Page 100 and 101: Since b 0,1 , . . . , b 0,h , b 1 ,
Page 102 and 103: For 1 ≤ i ≤ h, we have V i (y)
Page 104 and 105: 1. The encryption is converted into
Page 106 and 107: Chapter 8 Constant Size Ciphertext
Page 108 and 109: Let a private key for (v 1 , . . .
Page 110 and 111: Phase 1: Suppose a key extraction q
Page 112 and 113: = γ ( P 3 + ) u∑ V i . i=1 If th
Page 114 and 115: Encrypt: To encrypt a message M ∈
Page 116 and 117: and outputs a random bit if there i
Page 118 and 119: Chapter 9 Augmented Selective-ID Mo
Page 120 and 121: Phase 1 and Phase 2: As discussed i
Page 122 and 123: an adversary has to commit to an id
Page 124 and 125: Table 9.1: Comparison of BBG-HIBE a
Page 126 and 127: where ˜r = (r − αk F k ). Also
Page 128 and 129: The maximum height of the HIBE be h
Page 130 and 131: B declares the public parameters to
Page 132 and 133: So, the challenge ciphertext is ( C
Page 134 and 135: Choose a random r ∗ ∈ Z p and f
Page 136 and 137: The size of the private key in the
Page 138 and 139: generalisation and move on to addre
Page 140 and 141: Table 10.3: Comparison of HIBE prot
Page 142 and 143: [9] Paulo S. L. M. Barreto, Ben Lyn
Page 146 and 147: [55] Florian Hess, Nigel P. Smart,
Page 148: [81] Palash Sarkar. Head: Hybrid en
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