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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 1699 (29 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.
The exact security of digital signatures: How to sign with RSA and Rabin
, 1996
"... We describe an RSAbased signing scheme called PSS which combines essentially optimal efficiency with attractive security properties. Signing takes one RSA decryption plus some hashing, verification takes one RSA encryption plus some hashing, and the size of the signature is the size of the modulus. ..."
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Cited by 393 (16 self)
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We describe an RSAbased signing scheme called PSS which combines essentially optimal efficiency with attractive security properties. Signing takes one RSA decryption plus some hashing, verification takes one RSA encryption plus some hashing, and the size of the signature is the size of the modulus. Assuming the underlying hash functions are ideal, our schemes are not only provably secure, but are so in a tight way — an ability to forge signatures with a certain amount of computational resources implies the ability to invert RSA (on the same size modulus) with about the same computational effort. Furthermore, we provide a second scheme which maintains all of the above features and in addition provides message recovery. These ideas extend to provide schemes for Rabin signatures with analogous properties; in particular their security can be tightly related to the hardness of factoring.
Short group signatures
 In proceedings of CRYPTO ’04, LNCS series
, 2004
"... Abstract. We construct a short group signature scheme. Signatures in our scheme are approximately the size of a standard RSA signature with the same security. Security of our group signature is based on the Strong DiffieHellman assumption and a new assumption in bilinear groups called the Decision ..."
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Cited by 382 (21 self)
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Abstract. We construct a short group signature scheme. Signatures in our scheme are approximately the size of a standard RSA signature with the same security. Security of our group signature is based on the Strong DiffieHellman assumption and a new assumption in bilinear groups called the Decision Linear assumption. We prove security of our system, in the random oracle model, using a variant of the security definition for group signatures recently given by Bellare, Micciancio, and Warinschi. 1
Security Arguments for Digital Signatures and Blind Signatures
 JOURNAL OF CRYPTOLOGY
, 2000
"... Since the appearance of publickey cryptography in the seminal DiffieHellman paper, many new schemes have been proposed and many have been broken. Thus, the ..."
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Cited by 374 (41 self)
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Since the appearance of publickey cryptography in the seminal DiffieHellman paper, many new schemes have been proposed and many have been broken. Thus, the
Universal OneWay Hash Functions and their Cryptographic Applications
, 1989
"... We define a Universal OneWay Hash Function family, a new primitive which enables the compression of elements in the function domain. The main property of this primitive is that given an element x in the domain, it is computationally hard to find a different domain element which collides with x. We ..."
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Cited by 357 (15 self)
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We define a Universal OneWay Hash Function family, a new primitive which enables the compression of elements in the function domain. The main property of this primitive is that given an element x in the domain, it is computationally hard to find a different domain element which collides with x. We prove constructively that universal oneway hash functions exist if any 11 oneway functions exist. Among the various applications of the primitive is a OneWay based Secure Digital Signature Scheme which is existentially secure against adoptive attacks. Previously, all provably secure signature schemes were based on the stronger mathematical assumption that trapdoor oneway functions exist. Key words. cryptography, randomized algorithms AMS subject classifications. 68M10, 68Q20, 68Q22, 68R05, 68R10 Part of this work was done while the authors were at the IBM Almaden Research Center. The first author was supported in part by NSF grant CCR88 13632. A preliminary version of this work app...
On the (im)possibility of obfuscating programs
 Lecture Notes in Computer Science
, 2001
"... Informally, an obfuscator O is an (efficient, probabilistic) “compiler ” that takes as input a program (or circuit) P and produces a new program O(P) that has the same functionality as P yet is “unintelligible ” in some sense. Obfuscators, if they exist, would have a wide variety of cryptographic an ..."
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Cited by 341 (24 self)
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Informally, an obfuscator O is an (efficient, probabilistic) “compiler ” that takes as input a program (or circuit) P and produces a new program O(P) that has the same functionality as P yet is “unintelligible ” in some sense. Obfuscators, if they exist, would have a wide variety of cryptographic and complexitytheoretic applications, ranging from software protection to homomorphic encryption to complexitytheoretic analogues of Rice’s theorem. Most of these applications are based on an interpretation of the “unintelligibility ” condition in obfuscation as meaning that O(P) is a “virtual black box, ” in the sense that anything one can efficiently compute given O(P), one could also efficiently compute given oracle access to P. In this work, we initiate a theoretical investigation of obfuscation. Our main result is that, even under very weak formalizations of the above intuition, obfuscation is impossible. We prove this by constructing a family of efficient programs P that are unobfuscatable in the sense that (a) given any efficient program P ′ that computes the same function as a program P ∈ P, the “source code ” P can be efficiently reconstructed, yet (b) given oracle access to a (randomly selected) program P ∈ P, no efficient algorithm can reconstruct P (or even distinguish a certain bit in the code from random) except with negligible probability. We extend our impossibility result in a number of ways, including even obfuscators that (a) are not necessarily computable in polynomial time, (b) only approximately preserve the functionality, and (c) only need to work for very restricted models of computation (TC 0). We also rule out several potential applications of obfuscators, by constructing “unobfuscatable” signature schemes, encryption schemes, and pseudorandom function families.
An efficient system for nontransferable anonymous credentials with optional anonymity revocation
, 2001
"... A credential system is a system in which users can obtain credentials from organizations and demonstrate possession of these credentials. Such a system is anonymous when transactions carried out by the same user cannot be linked. An anonymous credential system is of significant practical relevance ..."
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Cited by 312 (14 self)
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A credential system is a system in which users can obtain credentials from organizations and demonstrate possession of these credentials. Such a system is anonymous when transactions carried out by the same user cannot be linked. An anonymous credential system is of significant practical relevance because it is the best means of providing privacy for users. In this paper we propose a practical anonymous credential system that is based on the strong RSA assumption and the decisional DiffieHellman assumption modulo a safe prime product and is considerably superior to existing ones: (1) We give the first practical solution that allows a user to unlinkably demonstrate possession of a credential as many times as necessary without involving the issuing organization. (2) To prevent misuse of anonymity, our scheme is the first to offer optional anonymity revocation for particular transactions. (3) Our scheme offers separability: all organizations can choose their cryptographic keys independently of each other. Moreover, we suggest more effective means of preventing users from sharing their credentials, by introducing allornothing sharing: a user who allows a friend to use one of her credentials once, gives him the ability to use all of her credentials, i.e., taking over her identity. This is implemented by a new primitive, called circular encryption, which is of independent interest, and can be realized from any semantically secure cryptosystem in the random oracle model.
A Secure and Optimally Efficient MultiAuthority Election Scheme
, 1997
"... Abstract. In this paper we present a new multiauthority secretballot election scheme that guarantees privacy, universal verifiability, and robustness. It is the first scheme for which the performance is optimal in the sense that time and communication complexity is minimal both for the individual ..."
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Cited by 300 (6 self)
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Abstract. In this paper we present a new multiauthority secretballot election scheme that guarantees privacy, universal verifiability, and robustness. It is the first scheme for which the performance is optimal in the sense that time and communication complexity is minimal both for the individual voters and the authorities. An interesting property of the scheme is that the time and communication complexity for the voter is independent of the number of authorities. A voter simply posts a single encrypted message accompanied by a compact proof that it contains a valid vote. Our result is complementary to the result by Cramer, Franklin, Schoenmakers, and Yung in the sense that in their scheme the work for voters is linear in the number of authorities but can be instantiated to yield informationtheoretic privacy, while in our scheme the voter’s effort is independent of the number of authorities but always provides computational privacyprotection. We will also point out that the majority of proposed voting schemes provide computational privacy only (often without even considering the lack of informationtheoretic privacy), and that our new scheme is by far superior to those schemes. 1