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New Efficient Searchable Encryption Schemes from Bilinear Pairings

New Efficient Searchable Encryption Schemes from Bilinear Pairings. Author:Chunxiang Gu and Yuefei Zhu International Journal of Network Security, 2007. Presenter: 李宗諺. Outline. Introduction Preliminaries PEKS IND-CKA A New PEKS Scheme from Pairing Conclusion. Introduction. Outline.

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New Efficient Searchable Encryption Schemes from Bilinear Pairings

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  1. New Efficient Searchable Encryption Schemes from Bilinear Pairings Author:Chunxiang Gu and Yuefei Zhu International Journal of Network Security, 2007 Presenter:李宗諺

  2. Outline • Introduction • Preliminaries • PEKS • IND-CKA • A New PEKS Scheme from Pairing • Conclusion

  3. Introduction

  4. Outline • Introduction • Preliminaries • PEKS • IND-CKA • A New PEKS Scheme from Pairing • Conclusion

  5. Preliminaries (1/4) • In 2004, Boneh et.al • Public Key Encryption with Keyword Search • four polynomial-time algorithms: • KeyGen • Trapdoor • PEKS • Test

  6. Preliminaries (2/4) • KeyGen : • Take as input a security parameterλ, generate a public/private key pair (pk,sk). • (pk,sk)=KeyGen(λ) • Trapdoor : • Take as input the receiver’s private key skand a word W , produce a trapdoorTw. • Tw=Trapdoor(sk,W)

  7. Preliminaries (3/4) • PEKS: • Take as input the receiver’s public keypk and a wordW, produce a searchable encryption ofW. • C = PEKS( pk , W) • Test: • Take as input the receiver’s public key pk, a searchable encryption C = PEKS(pk,W’), and a trapdoor Tw = Trapdoor(sk,W), output 1 (“yes”) if W = W’ and 0 (“no”) otherwise. • Test( pk ,PEKS(pk,W) ,Tw )=1

  8. (pk,sk) 1.λ KeyGan Preliminaries (4/4) Tw 加密過的訊息 傳回使用者 所需的文件 Bob Alice Sever 2.C=PEKS( Apk ,W ) 3.Tw= Trapdoor(Ask，W) 4. Test(Apk，C，Tw) ?= 1

  9. Outline • Introduction • Preliminaries • PEKS • IND-CKA • A New PEKS Scheme from Pairing • Conclusion

  10. Preliminaries • Indistinguishability of PEKS against chosen keyword attack (IND-CKA) • KeyGen • Phase 1 • Challenge • Phase 2 • Guess

  11. λ KeyGen (pk,sk) pk IND-CKA (1/6) • KeyGen • The challenger runs the KeyGen(λ) algorithm to generate(pk,sk). It gives pk to the attacker. challenger attacker

  12. IND-CKA (2/6) • Phase 1 • The attacker ask the challengger for the trapdoor Tw for any keyword W ∈{0,1}* • Challenge • The attacker A sends thechallenger two wordsW0 ,W1. • The challenger picks a random b∈{0,1} and gives the attacker C = PEKS( pk , W)

  13. λ KeyGen (pk,sk) IND-CKA (3/6) challenger attacker pk W0 ,W1 b∈{0,1} C = PEKS( pk , Wb)

  14. IND-CKA (4/6) • Phase 2 • The attacker can continue to ask for trapdoors Tw for any keyword W of his choice as long as W≠W0,W1 • Guess • The attacker A outputs b’∈{0,1} and wins the game if b = b’

  15. λ KeyGen (pk,sk) IND-CKA (5/6) challenger attacker pk W0 ,W1 b ∈{0,1} C = PEKS( pk , Wb) b‘∈{0,1} b’ b?=b’

  16. Preliminaries ( G1 , + ) and ( G2 ,‧) be two cyclic groups of prime order q e : G1 × G1→G2 be a map which satisfies the following properties • Bilinear Pairings • Bilinear: • Non-degenerate: • If P is a generator of G1 ,then e(P,P) is a generator of G2 • Computable: • There is an efficient algorithm to compute e(P,Q) for any P,Q∈ G1

  17. Preliminaries • BDH problem: • P,aP,bP,cP ∈ G1 • P,aP,bP,cP = e(P,P)abc • k – BDHI problem:

  18. Outline • Introduction • Preliminaries • PEKS • IND-CKA • A New PEKS Scheme from Pairing • Conclusion

  19. A New PEKS Scheme from Pairings (1/5) • The Scheme • ( G1 , + ) and ( G2 ,‧) be two cyclic groups of prime order q • e : G1 × G1→G2 be an admissible bilinear pairing • H1:{0,1}* → Zq* and H2: G2 →{0,1}log q • P is a generator of G1 • μ = e ( p , p )

  20. A New PEKS Scheme from Pairings (2/5) • KeyGen : • Pick a randomx ∈ Zq* • compute X = xP • Output pk =X and sk = x.

  21. A New PEKS Scheme from Pairings (3/5) • Trapdoor: • Take as input secret key x and keyword W • Output Tw = (H1(W)+x)-1P • PEKS : • Take as input public key X and a keyword W • Select randomly r∈ Zq* • compute U = rH1(W)P+rX , c = H2(μr) • Output (U,c)

  22. A New PEKS Scheme from Pairings (4/5) • Test • Input public key X , searchable encryption cipher-text(U,c) and trapdoor Tw • Test if H2(e(Tw,U)) = c • If so ,output 1 • Otherwise ,out put 0.

  23. A New PEKS Scheme from Pairings (5/5) • Consistency • H2(e(Tw,U)) = H2(e((H1(W)+x)-1P, rH1(W)P+rX)) • = H2(e((H1(W)+x)-1P, r(H1(W)+x)P) • = H2(e((P,P)r) • = c Tw = (H1(W)+x)-1P U = rH1(W)P+rX X = xP μ = e ( p , p ) c = H2(μr)

  24. Outline • Introduction • Preliminaries • PEKS • IND-CKA • A New PEKS Scheme from Pairing • Conclusion

  25. Conclusion • In this paper, we propose a new PEKS scheme based on bilinear pairings. • There is no pairing operation involved in the encryption, so new PEKS scheme is more efficient than the scheme of Boneh et.al.

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