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205
IdentityBased Encryption from the Weil Pairing
, 2001
"... We propose a fully functional identitybased encryption scheme (IBE). The scheme has chosen ciphertext security in the random oracle model assuming an elliptic curve variant of the computational DiffieHellman problem. Our system is based on bilinear maps between groups. The Weil pairing on elliptic ..."
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Cited by 1123 (24 self)
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We propose a fully functional identitybased encryption scheme (IBE). The scheme has chosen ciphertext security in the random oracle model assuming an elliptic curve variant of the computational DiffieHellman problem. Our system is based on bilinear maps between groups. The Weil pairing on elliptic curves is an example of such a map. We give precise definitions for secure identity based encryption schemes and give several applications for such systems.
Short signatures from the Weil pairing
, 2001
"... Abstract. We introduce a short signature scheme based on the Computational DiffieHellman assumption on certain elliptic and hyperelliptic curves. The signature length is half the size of a DSA signature for a similar level of security. Our short signature scheme is designed for systems where signa ..."
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Cited by 560 (31 self)
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Abstract. We introduce a short signature scheme based on the Computational DiffieHellman assumption on certain elliptic and hyperelliptic curves. The signature length is half the size of a DSA signature for a similar level of security. Our short signature scheme is designed for systems where signatures are typed in by a human or signatures are sent over a lowbandwidth channel. 1
Selecting Cryptographic Key Sizes
 TO APPEAR IN THE JOURNAL OF CRYPTOLOGY, SPRINGERVERLAG
, 2001
"... In this article we offer guidelines for the determination of key sizes for symmetric cryptosystems, RSA, and discrete logarithm based cryptosystems both over finite fields and over groups of elliptic curves over prime fields. Our recommendations are based on a set of explicitly formulated parameter ..."
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Cited by 253 (6 self)
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In this article we offer guidelines for the determination of key sizes for symmetric cryptosystems, RSA, and discrete logarithm based cryptosystems both over finite fields and over groups of elliptic curves over prime fields. Our recommendations are based on a set of explicitly formulated parameter settings, combined with existing data points about the cryptosystems.
Aggregate and Verifiably Encrypted Signatures from Bilinear Maps
, 2002
"... An aggregate signature scheme is a digital signature that supports aggregation: Given n signatures on n distinct messages from n distinct users, it is possible to aggregate all these signatures into a single short signature. This single signature (and the n original messages) will convince the verif ..."
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Cited by 237 (14 self)
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An aggregate signature scheme is a digital signature that supports aggregation: Given n signatures on n distinct messages from n distinct users, it is possible to aggregate all these signatures into a single short signature. This single signature (and the n original messages) will convince the verifier that the n users did indeed sign the n original messages (i.e., user i signed message M i for i = 1; : : : ; n). In this paper we introduce the concept of an aggregate signature scheme, present security models for such signatures, and give several applications for aggregate signatures. We construct an efficient aggregate signature from a recent short signature scheme based on bilinear maps due to Boneh, Lynn, and Shacham. Aggregate signatures are useful for reducing the size of certificate chains (by aggregating all signatures in the chain) and for reducing message size in secure routing protocols such as SBGP. We also show that aggregate signatures give rise to verifiably encrypted signatures. Such signatures enable the verifier to test that a given ciphertext C is the encryption of a signature on a given message M . Verifiably encrypted signatures are used in contractsigning protocols. Finally, we show that similar ideas can be used to extend the short signature scheme to give simple ring signatures.
Hierarchical IDBased Cryptography
, 2002
"... We present hierarchical identitybased encryption schemes and signature schemes that have total collusion resistance on an arbitrary number of levels and that have chosen ciphertext security in the random oracle model assuming the difficulty of the Bilinear DiffieHellman problem. ..."
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Cited by 184 (3 self)
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We present hierarchical identitybased encryption schemes and signature schemes that have total collusion resistance on an arbitrary number of levels and that have chosen ciphertext security in the random oracle model assuming the difficulty of the Bilinear DiffieHellman problem.
Efficient SelectiveID Secure IdentityBased Encryption Without Random Oracles., in Cachin and Camenisch [13
 6. , Secure Identity Based Encryption Without Random Oracles., in Franklin [20
"... Abstract. We construct two efficient Identity Based Encryption (IBE) systems that are selective identity secure without the random oracle model. Selective identity secure IBE is a slightly weaker security model than the standard security model for IBE. In this model the adversary must commit ahead o ..."
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Cited by 141 (8 self)
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Abstract. We construct two efficient Identity Based Encryption (IBE) systems that are selective identity secure without the random oracle model. Selective identity secure IBE is a slightly weaker security model than the standard security model for IBE. In this model the adversary must commit ahead of time to the identity that it intends to attack, whereas in the standard model the adversary is allowed to choose this identity adaptively. Our first secure IBE system extends to give a selective identity Hierarchical IBE secure without random oracles. 1
Efficient Identity Based Signature Schemes Based on Pairings
 SAC 2002, LNCS 2595
, 2002
"... We develop an efficient identity based signature scheme based on pairings whose security relies on the hardness of the DiffieHellman problem in the random oracle model. We describe how this scheme is obtained as a special version of a more general generic scheme which yields further new provably se ..."
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Cited by 138 (2 self)
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We develop an efficient identity based signature scheme based on pairings whose security relies on the hardness of the DiffieHellman problem in the random oracle model. We describe how this scheme is obtained as a special version of a more general generic scheme which yields further new provably secure identity based signature schemes if pairings are used. The generic scheme also includes traditional public key signature schemes. We further discuss issues of key escrow and the distribution of keys to multiple trust authorities. The appendix contains a brief description of the relevant properties of supersingular elliptic curves and the Weil and Tate pairings.
Collusion resistant broadcast encryption with short ciphertexts and private keys. Cryptology ePrint Archive, Report 2005/018, 2005. Full version of current paper
"... Abstract. We describe two new public key broadcast encryption systems for stateless receivers. Both systems are fully secure against any number of colluders. In our first construction both ciphertexts and private keys are of constant size (only two group elements), for any subset of receivers. The p ..."
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Cited by 119 (13 self)
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Abstract. We describe two new public key broadcast encryption systems for stateless receivers. Both systems are fully secure against any number of colluders. In our first construction both ciphertexts and private keys are of constant size (only two group elements), for any subset of receivers. The public key size in this system is linear in the total number of receivers. Our second system is a generalization of the first that provides a tradeoff between ciphertext size and public key size. For example, we achieve a collusion resistant broadcast system for n users where both ciphertexts and public keys are of size O ( √ n) for any subset of receivers. We discuss several applications of these systems. 1
Towards hierarchical identitybased encryption
 In Proceedings of Asiacrypt 2002, LNCS 2501
, 2002
"... Abstract. We introduce the concept of hierarchical identitybased encryption (HIBE) schemes, give precise definitions of their security and mention some applications. A twolevel HIBE (2HIBE) scheme consists of a root private key generator (PKG), domain PKGs and users, all of which are associated w ..."
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Cited by 109 (0 self)
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Abstract. We introduce the concept of hierarchical identitybased encryption (HIBE) schemes, give precise definitions of their security and mention some applications. A twolevel HIBE (2HIBE) scheme consists of a root private key generator (PKG), domain PKGs and users, all of which are associated with primitive IDs (PIDs) that are arbitrary strings. A user’s public key consists of their PID and their domain’s PID (in whole called an address). In a regular IBE (which corresponds to a 1HIBE) scheme, there is only one PKG that distributes private keys to each user (whose public keys are their PID). In a 2HIBE, users retrieve their private key from their domain PKG. Domain PKGs can compute the private key of any user in their domain, provided they have previously requested their domain secret key from the root PKG (who possesses a master secret). We can go beyond two levels by adding subdomains, subsubdomains, and so on. We present a twolevel system with total collusion resistance at the upper (domain) level and partial collusion resistance at the lower (user) level, which has chosenciphertext security in the randomoracle model. 1