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Identity Based Encryption Schemes : a Survey

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Identity Based Encryption Schemes : a Survey International Journal for Research in Engineering Application & Management (IJREAM) ISSN : 2454-9150 Vol-04, Issue-10, Jan 2019 Identity Based Encryption Schemes : A Survey Khaleda Afroaz, Assistant Professor, Department of CS&IT, MANUU, Hyderabad, Telangana & India,[email protected] ABSTRACT- Identity Based Encryption is an alternate to public key encryption, as it removes the necessity of digital certificates. Identity based encryption(IBE) is one of public key encryption scheme in which identity of a receiver is used as public key. Therefore, it eliminates the authentication of public key by digital certificates. In this paper we explain various IBE schemes such as IBE based on the quadratic residues, IBE based on weil pairing and Hierarchical IBE . IBE includes the applications such as give assistance to the deployment of public key encryption, public key revocation and decryption key delegation. Keywords : Identity Based Encryption, IBE, Public Key Encryption and Hierarchical Identity Based Encryption I. INTRODUCTION Identity Based Encryption In public key encryption if Alice wants to convey a The model for Identity Based Encryption composed of a message to Bob in an encrypted form he needs the public private key generator that generates a pmsi(system key of Bob. Digital certificates are used for the parameters) and a master secret key mski [5]. authenticity of that public key. Digital certificates are This scheme is specified by four polynomial time generated by Certificate Authorities(CAs), who are trusted probabilistic algorithms[15,16]. and implement the process as follows: When Bob creates a 1.Setup(1k) key pair he presents PKB and some valid identity to the CA. Then, CA generates a signature, under its verification Input :k is the security parameter Output : System parameters pmsi, master secret key mski. key VKCA which Bob appends to its public key. Here, signature is a sign of authentication to Bob's public key 2.Extract(pmsi,mski,ID) provided by CA[9,11]. Later, Alice can verify the Input : System parameters pmsi, master secret key mski, * signature of CA by using VKCA . If it matches, he can gain ID {0,1} is an IDentity of the receiver the confidence that the key really belongs to Bob. Output: skID secret key of the identity ID However, in order to verify the signature Alice requires to 3. Encryption (pms , ID ,x) know the true public key of CA[12,13]n . To make it i Input : System parameters pms , identity of the receiver ID, practically possible there should be less number of CAs i message to be encrypted xϵ M with wide publicity of their public keys. Though, the entire Output : Cipher text yϵ C process is difficult, as all new public keys should be registered with CA[5]. 4. Decryption (skID ,y) Input : Secret key corresponding to that identity ID, In Identity Based Encryption, Alice can send encrypted cipher text yϵ C data to Bob, by using any one of his identity, such as email Output : Message xϵ M id, name , finger print etc., After receiving the encrypted data Bob generates the private key of that identity with II. IBE BASED ON THE QUADRATIC RESIDUES the help of private key generator[2,3,4]. Here, no need for Alice to get the public key or certificate. Here, notice that Suppose q is a prime which is greater than 2 and b is an the private key generator has the knowledge of the private integer then b is a quadratic residue modulo q if b ≢ 0 2 keys and it should be a trusted party[5]. (mod q) and the congruence l ≡b(mod q) has a solution lϵZq. Here, the first practical IBE scheme was In 1984 Shamir has raised a problem for a public key implemented by using quadratic residues. The security of encryption scheme where an arbitrary string can be used as this scheme is a dependant on the hardness of the quadratic a public key. Since the problem was raised many IBE residue problem. It consists of the following schemes were proposed. Here, we want to discuss various algorithms[6,2]. schemes[1]. In section 2, we give basic definition of IBE scheme. We 1. Setup() then give an overview of various proposed schemes. The PKG generates a private key by using the following inputs. 81 | IJREAMV04I1046029 DOI : 10.18231/2454-9150.2018.1289 © 2019, IJREAM All Rights Reserved. International Journal for Research in Engineering Application & Management (IJREAM) ISSN : 2454-9150 Vol-04, Issue-10, Jan 2019 i. An RSA module n1 = rs, where n1 is a Blum hard. One of the examples for such map is Weil pairing on integer which means r, s are two private distinct the elliptic curve. In this scheme admissible bilinear map prime numbers which satisfy r ≡ s ≡ 3 (mod 4) is used. The following properties are satisfied by an ii. A message space is indicated by M = {−1, 1} and admissible bilinear map [5,8,9,] . a cipher text space C = Zn a) Bilinear: The bilinear map is a map, if iii. A secure common hash mapping h1: {0, 1} * → e(cR,dS)=e(R,S)cd for all R,S ϵ G1 and all c,d ϵZ. Zn b) Non-Degenerate: The map does not send all the pairs in G1 X G1 to the identity in G2. 2. Extract (pms,msk,id) c) Computable: There is an efficient algorithm to Input: parameters that are generated by Setup() and generate the mapping. an arbitrary string ID This scheme composed of the following four algorithms. Output: the secret key skid l 1. Setup (1 ) i. Generate b such that ( )= 1 by a Input: l is the security parameter deterministic procedure ID. Output: System parameters pmsi, master secret key mski. l 2 i. Run G(1 ). G will generate a prime q and two ii. Let sk = mod n1 such that sk = id id groups G1,G2 of order q and a bilinear map ±b mod n1. which is admissible e:G1XG2→G2 ii. Select a random generator gr ϵ G1 3. Encryption (pms,id,x) * iii. Choose a random rmϵ Zq Input: parameters that are generated by Setup (), ID of the iv. Jp= rm gr sender and a message x v. Select a hash function f1:{0,1}*→G1*,which is Output: Corresponding cipher text C cryptographic i. Choose a random q such that x =( ), where x is vi. Select a hash function f2:G2→{0,1}n which is an arbitrary bit of x. cryptographic for some n ii. Let y1 = q + bq−1 mod n1 and y2 = q - bq−1 mod vii. Output pmsi=<q,G1,G2,e,n, gr, Jp,f1,f2> n1. viii. mski=rm iii. Send y = ⟨y1, y2⟩ to the recipient. 2. Extract (pmsi, mski, ID) 4.Decry Input : System parameters pmsi, master secret * Key mski, IDϵ {0,1} is an identity of the receiver ption (skid,y) Input : Secret key corresponding to that identity id, Output: skid secret key of the identity ID. * cipher text yϵ C i. Compute RID=f1(ID) ϵ G1 Output : Message xϵ M ii. Set eID= rm RID 2 i. Let β = y1 + 2skid if skid = b, otherwise 3. Encryption (pmsi, ID ,x) β = y2 + 2skid . Input: System parameters pmsi, Identity of the receiver ID, ii. Return m =( ) message to be encrypted xϵ M Correctness: Output: Cipher text yϵC * Since, β = y1 + 2skid i. Compute RID=f1(ID) ϵ G1 -1 * =(q+bq )+2skid ii. Choose a random t ϵ Zq -2 -1 =q(1+bq +2skidq ) iii. vID=e(RID,Jp)ϵ G2 2 -2 -1 t =q(1+skid q +2skidq ) iv. y=<tgr,x⊕f2(vID )> -1 2 =q(1+skidq ) ( ) 4. Decryption ( sky ,y) Take, ( ) = ( ) ID Input : Secret key corresponding to that identity ID, = ( ) cipher text yϵ C Output : Message xϵ M = x i. Let y=<W,U> ϵ C III. IBE BASED ON THE WEIL PAIRING ii. Compute x=U⊕ f2(e(eID,W)) This IBE scheme can be constructed from any bilinear Correctness: map e:G1XG1→G2 where G1,G2 are two groups of order q,as the Bilinear Diffie-Hellman problem( Though Take, <P,iP,jP,kP> is given, it is difficult to compute e(P,P)ijk, * e(eID,W) = e(rmRID,tgr) where P be the generator in G1 and I,j,k ϵ Zq ) in G1 is = e 82 | IJREAMV04I1046029 DOI : 10.18231/2454-9150.2018.1289 © 2019, IJREAM All Rights Reserved. International Journal for Research in Engineering Application & Management (IJREAM) ISSN : 2454-9150 Vol-04, Issue-10, Jan 2019 t ∑ = e(rmRID,Jp) =( ) t ∏ = vID s = e(U0, F1) Take,U f2(e(e ,W)) ⊕ ID s t =h =x⊕ vID ⊕f2(e(eID,W)) t t =x⊕ vID ⊕ vID Take, W⊕ ( ) ∏ =x s IV. HIERARCHICAL IDENTITY BASED =x⊕ h ⊕ ( ) ∏ ENCRYPTION (H-IBE) = x⊕ hs ⊕ hs The Hierarchical IBE scheme is an expansion of IBE scheme based upon weil pairing. In H-IBE, every =x user consists of an n-tuple ID in the hierarchy tree[14]. V. CONCLUSION The n-tuple ID contains IDs of the user itself and its Here we have discussed three basic identity based ancestors. The root is at level 0[7 8,10]. H-IBE contains encryption schemes. In addition to algorithms, this paper following five algorithms: – clearly depicts the step by step correctness of each scheme. 1. Root Setup() REFERENCES i. Based on l which is a security parameter l, [1]. A. Shamir. Identity-based cryptosystems and signature generate a prime q using IG (BDH Parameter schemes. In G. Blakley and D. Chaum, editors, Proceedings Generator). of Crypto 1984, volume 196 of LNCS, pages 47–53.
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