Key Escrow free Identity-based Cryptosystem
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1 Key Escrow free Manik Lal Das DA-IICT, Gandhinagar, India
2 About DA-IICT and Our Group DA-IICT is a private university, located in capital of Gujarat state in India. DA-IICT offers undergraduate and postgraduate programs in Information and Communication Technology.
3 About DA-IICT and Our Group Cyber Security Research Group in DA-IICT:
4 Outline
5 Authentication What is Authentication? Authentication is a process of confirming the (i) identity of an entity (entity authentication); and/or (ii) legitimacy of a document (data origin authentication).
6 Authentication Techniques Authentication Symmetric key crypto Keyed Hash Password based Token based Proxy Public key crypto Digital Multi-signature Ring
7 A is a 3-tuple (Key Generation, Encryption, Decryption) algorithm defined as:
8 A is a 3-tuple (Key Generation, Encryption, Decryption) algorithm defined as: Key Generation INPUT: a security parameter. OUTPUT: key(s) and public parameters.
9 A is a 3-tuple (Key Generation, Encryption, Decryption) algorithm defined as: Key Generation INPUT: a security parameter. OUTPUT: key(s) and public parameters. Encryption INPUT: key, message, public parameters. OUTPUT: ciphertext.
10 A is a 3-tuple (Key Generation, Encryption, Decryption) algorithm defined as: Key Generation INPUT: a security parameter. OUTPUT: key(s) and public parameters. Encryption INPUT: key, message, public parameters. OUTPUT: ciphertext. Decryption INPUT: key, ciphertext, public parameters. OUTPUT: message.
11 A is a 3-tuple (Key Generation, Encryption, Decryption) algorithm defined as: Key Generation INPUT: a security parameter. OUTPUT: key(s) and public parameters. Encryption INPUT: key, message, public parameters. OUTPUT: ciphertext. Decryption INPUT: key, ciphertext, public parameters. OUTPUT: message. Domain: Key space; Message space; Ciphertext space
12 (contd.) Symmetric key cryptosystem: One key is used for encryption and decryption. Limitation: Secret key distribution. Asymmetric key cryptosystem: Two keys are used for encryption (public key) and decryption (private key) Limitation: Public key management.
13 Public key is the user s identity or derived from the user s identity (e.g. ). User identity acts as the public key. Aim is to eliminate infrastructure for public key certification. A. Shamir. cryptosystems and signature schemes.in Proc. of Advances in Cryptology-CRYPTO 84, LNCS 196, Springer-Verlag, pp , IEEE Standard for identity-based cryptographic techniques using pairings (2013).
14 Interesting Properties of Elliptic Curve Let y 2 = x 3 + ax + b be an elliptic curve that forms an elliptic curve group, where a, b F q for a large prime q.
15 Bilinear Pairing Let G 1 be an additive group of order a prime q, P be a generator of G 1, and G 2 be a multiplicative group of order prime q. A bilinear pairing is a map e : G 1 G 1 G 2 that satisfies the following properties. Properties of Bilinear Pairing 1) e(ap, bq) = e(p, Q) ab, for all P, Q G 1 and a, b Z q. 2) There exist P, Q G 1 such that e(p, Q) 1. 3) There exists an efficient algorithm to compute e(p, Q).
16 Computational Hardness Assumptions Elliptic curve discrete logarithm problem Given P, Q(= xp), finding x is computationally infeasible. Computational Diffie-Hellman problem Given P, ap, bp, finding abp is computationally infeasible. There are many other variants...
17 Pairing-based Authenticated Key Exchange+ Scenario: Mobile communications
18 Pairing-based Authenticated Key Exchange+ Scenario: Wireless Sensor Networks
19 (IDS) Scheme IDS is defined by the 4-tuple (Setup, KeyGen, Sign, Verify)
20 (IDS) Scheme IDS is defined by the 4-tuple (Setup, KeyGen, Sign, Verify) System keys Setup(1 k ) Inputs a security parameter k; Outputs system secret and public keys.
21 (IDS) Scheme IDS is defined by the 4-tuple (Setup, KeyGen, Sign, Verify) System keys Setup(1 k ) Inputs a security parameter k; Outputs system secret and public keys. User private key KeyGen(user ID, system keys) Inputs user ID; Outputs user private key.
22 (IDS) Scheme IDS is defined by the 4-tuple (Setup, KeyGen, Sign, Verify) System keys Setup(1 k ) Inputs a security parameter k; Outputs system secret and public keys. User private key KeyGen(user ID, system keys) Inputs user ID; Outputs user private key. σ Sign(m, user private key, public parameter) Inputs message m and user private key; Outputs signature σ.
23 (IDS) Scheme IDS is defined by the 4-tuple (Setup, KeyGen, Sign, Verify) System keys Setup(1 k ) Inputs a security parameter k; Outputs system secret and public keys. User private key KeyGen(user ID, system keys) Inputs user ID; Outputs user private key. σ Sign(m, user private key, public parameter) Inputs message m and user private key; Outputs signature σ. Accept/Reject Verify(user ID, m, σ, public parameter) Inputs signature σ, message m, user ID, public parameters; Outputs Accept or Reject.
24 Scheme (Setup, KeyGen, Sign, Verify) System keys Setup(1 k ) G 1 is an additive group of order prime q; G 2 is a multiplicative group of order prime q; P is a generator of G 1 ; e : G 1 G 1 G 2 is a bilinear map; H, h are cryptographic hash function. The system selects s Zq as the master secret key and computes its public key PK KGC = s P. The KGC publishes the public parameters params = < G 1, G 2, P, e, H, h, q, PK KGC >. s 1 k master secret Setup params: public parameters < G 1, G 2, P, e, H, h, q, PK KGC >
25 Scheme (Setup, KeyGen, Sign, Verify) SK U KeyGen(params, s, ID U ) KGC generates user private key SK U = s.pk U, where user public key PK U = H(ID U ). params s KeyGen SK U = s PK U user private key ID U KGC sends the private key SK U to the user securely.
26 Problems in user private key generation KGC generates user private key and sends it to the user securely. (1) User s private key is known to the KGC Key-escrow problem. (2) Sending user private key requires secure channel.
27 Proposed Solution: Binding-Blinding Technique User chooses two secret blinding factors, calculates the binding parameters and sends the parameters to the KGC over a public channel for his partial key. KGC gets a confirmation from the user about his request for the partial key, and then KGC proceeds to the next step. After validating the user s binding parameters, the KGC computes user partial key and sends it to the user over a public channel.
28 Proposed Solution: Binding-Blinding Technique User chooses two secret blinding factors, calculates the binding parameters and sends the parameters to the KGC over a public channel for his partial key. KGC gets a confirmation from the user about his request for the partial key, and then KGC proceeds to the next step. After validating the user s binding parameters, the KGC computes user partial key and sends it to the user over a public channel. No key escrow and no secure channel for user private key generation.
29 Scheme (Setup, KeyGen, Sign, Verify) Binding parameters with user secret blinding factor. Binding Parameters KeyGen(params, ID U, a, b) User selects secret blinding factors a, b Z q and computes X = a PK U, Y = a b PK U, Z = b P, W = a b P. User sends the binding parameters (X, Y, Z, W, ID U ) to KGC over a public channel. params a, b ID U KeyGen X = a PK U Y = a b PK U Z = b P W = a b P
30 Scheme (Setup, KeyGen, Sign, Verify) User Partial Key generation. D ID KeyGen(params, s, ID U, Binding parameters) KGC checks whether e(y, P) = e(x, Z) = e(pk U, W ). If the above holds, KGC computes the user partial key D ID = s Y and creates a registration-token R ID = s Z. Then, KGC publishes < R ID, ID U > in a public directory and sends D ID to the user over a public channel. params s X, Y, Z, W ID U KeyGen D ID = s Y user partial key R ID = s Z
31 Scheme (Setup, KeyGen, Sign, Verify) Unblinding Partial Key User Private Key. SK U KeyGen(params, a, D ID ) User checks whether e(d ID, P) = e(y, PK KGC ). If it holds, user unblinds his partial key and generates his private key SK U as SK U = a 1 D ID = b s PK U. params a KeyGen SK U = s b PK U user private key D ID
32 Scheme (Setup, KeyGen, Sign, Verify) Generation. (σ, c, m) Sign(params, t, m, SK U ) To sign a message m, the signer does the following: - Pick a random t Zq - Compute r = e(p, P) t and c = h(m, r, R ID ) - Compute σ = c SK U + t P. The signature on message m is (σ, c, m). params t m SK U Sign c σ
33 Scheme (Setup, KeyGen, Sign, Verify) Verification. Accept/Reject Verify(params, ID U, R ID, m, c, σ) - Compute ˆr = e(σ, P) e(pk U, R ID ) c - Accept the signature if c = h(m, ˆr, R ID ). params ID U R ID m c σ Verify Accept/Reject
34 : Merit and Limitation of the proposed solution The proposed technique provides solution to key escrow problem in ID-based construction. The proposed technique eiminates the use of secure channel in ID-based construction. User Registration identity needs to be managed, which is a bottleneck of the suggested solution. Manik Lal Das. Key-escrow free multi-signature scheme using bilinear pairings. Groups-Complexity-Cryptology, 7(1):47-57, Manik Lal Das. A key escrow-free identity-based signature scheme without using secure channel. Cryptologia, 35(1): 58-72, 2011.
35 : Merit and Limitation of the proposed solution The proposed technique provides solution to key escrow problem in ID-based construction. The proposed technique eiminates the use of secure channel in ID-based construction. User Registration identity needs to be managed, which is a bottleneck of the suggested solution. Manik Lal Das. Key-escrow free multi-signature scheme using bilinear pairings. Groups-Complexity-Cryptology, 7(1):47-57, Manik Lal Das. A key escrow-free identity-based signature scheme without using secure channel. Cryptologia, 35(1): 58-72, Thanks!
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ISSN (Online) : 2319-8753 ISSN (Print) : 2347-6710 International Journal of Innovative Research in Science, Engineering and Technology Volume 3, Special Issue 3, March 2014 2014 International Conference