Identity-Based Encryption Protocols Using Bilinear Pairing

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Table 10.3: Comparison of HIBE protocols Secure in Generalised Selective-ID Model. protocol id public max pvt decryption comp. parameter key size subkey size H 1 Z p n + h + 3 h + 1 h + 1 H 2 Z p 3 + (n + 1)h h + 1 h + 1 ccHIBE Z ∗ p 4 + nh 2 + n(h − 1) 2 G 2 Z p 3 + (n + 1)h h + 1 + n(h − 1) 2 protocol ciphertext encryption decryption security expansion efficiency efficiency model H 1 h + 1 h(n + 1) + 1 h + 1 M 1 H 2 h + 1 h(n + 1) + 1 h + 1 M 2 ccHIBE 2 nh + 2 2 M 2 G 2 2 nh + 2 2 M + 2 For a HIBE of maximum height h, the columns for public parameter, max pvt key size, decryption subkey size and ciphertext expansion denote the number of elements of G 1 , encryption efficiency denotes the number of scalar multiplications in G 1 and decryption efficiency denotes the number of pairing computations. 128
Bibliography [1] Michel Abdalla, Mihir Bellare, Dario Catalano, Eike Kiltz, Tadayoshi Kohno, Tanja Lange, John Malone-Lee, Gregory Neven, Pascal Paillier, and Haixia Shi. Searchable Encryption Revisited: Consistency Properties, Relation to Anonymous IBE, and Extensions. In Victor Shoup, editor, CRYPTO, volume 3621 of Lecture Notes in Computer Science, pages 205–222. Springer, 2005. [2] Michel Abdalla, Mihir Bellare, and Phillip Rogaway. The Oracle Diffie-Hellman Assumptions and an Analysis of DHIES. In David Naccache, editor, CT-RSA, volume 2020 of Lecture Notes in Computer Science, pages 143–158. Springer, 2001. [3] Nuttapong Attrapadung, Benoit Chevallier-Mames, Jun Furukawa, Takeshi Gomi, Goichiro Hanaoka, Hideki Imai, and Rui Zhang. Efficient Identity-Based Encryption with Tight Security Reduction. Cryptology ePrint Archive, Report 2005/320, 2005. http://eprint.iacr.org/. [4] Joonsang Baek, Reihaneh Safavi-Naini, and Willy Susilo. Efficient Multi-receiver Identity-Based Encryption and Its Application to Broadcast Encryption. In Serge Vaudenay, editor, Public Key Cryptography, volume 3386 of Lecture Notes in Computer Science, pages 380–397. Springer, 2005. [5] Joonsang Baek and Yuliang Zheng. Identity-Based Threshold Decryption. In Feng Bao, Robert H. Deng, and Jianying Zhou, editors, Public Key Cryptography, volume 2947 of Lecture Notes in Computer Science, pages 262–276. Springer, 2004. [6] Paulo S. L. M. Barreto. Pairing-Based Crypto Lounge – A compendium of bilinear pairing related works . Available at: http://paginas.terra.com.br/informatica/paulobarreto/pblounge.html. [7] Paulo S. L. M. Barreto, Steven Galbraith, Colm O hEigeartaigh, and Michael Scott. Efficient Pairing Computation on Supersingular Abelian Varieties. Cryptology ePrint Archive, Report 2004/375, 2004. http://eprint.iacr.org/. [8] Paulo S. L. M. Barreto, Hae Yong Kim, Ben Lynn, and Michael Scott. Efficient Algorithms for Pairing-Based Cryptosystems. In Moti Yung, editor, CRYPTO, volume 2442 of Lecture Notes in Computer Science, pages 354–368. Springer, 2002. 129
Page 1:
Construction of (Hierarchical) Iden
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The scientist does not study nature
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Contents 1 Introduction 1 1.1 Plan
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7.4.1 HIBE H 1 . . . . . . . . . .
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the public key. In this setting, an
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adversary in distinguishing two mes
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previous chapter. The second varian
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as it is closer to the known exampl
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Let P i = a i P . An algorithm A ha
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Given the security parameter κ, th
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the Key-Gen algorithm and C is the
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Phase 2: A now issues additional qu
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Chapter 3 Previous Works in Identit
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Decrypt: Decrypt C = 〈U, V 〉 us
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Game 2 Suppose B is given a BDH pro
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Security of BasicHIBE against chose
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BB-HIBE Here individual components
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F i (v ∗ i ) = α i P , so C =
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Key-Gen: Let v = (v 1 , . . . , v n
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Composite HIBE Boneh, Boyen and Goh
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Security Given an identity tuple v
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Chapter 4 Tate Pairing in General C
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order on the elliptic curve E(IF p
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the best result. In [57] the author
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Hence, we require 3[S] + 8[M] for E
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Algorithm 2 (iterated doubling): In
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Level 1 : t 1 = Y 2 1 ; t 4 = Z 2 1
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Table 4.1: Cost Comparison. Note 1[
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problem. - Our construction resembl
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is equal to c 2 |IF a | 3 . Thus, t
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aborts if F (v ∗ ) ≠ 0 and outp
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DBDH problem over (G 1 , G 2 , e) i
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these are respectively 2.4 kb and 2
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Signing: Let M = (m 1 , m 2 , . . .
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model without random oracles. Addit
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6.2 Construction HIBE-spp The ident
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Table 6.1: Comparison of HIBE Proto
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For 1 ≤ j ≤ h, we define severa
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establish the claim. We provide the
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The probability is over the indepen
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= ≥ ( ( 1 − Pr 1 − [( q∨ i=
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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 142 and 143: [9] Paulo S. L. M. Barreto, Ben Lyn
Page 144 and 145: [31] Sanjit Chatterjee and Palash S
Page 146 and 147: [55] Florian Hess, Nigel P. Smart,
Page 148: [81] Palash Sarkar. Head: Hybrid en
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Identity-Based Encryption Protocols Using Bilinear Pairing

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