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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 1748 (28 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.
Publickey cryptosystems based on composite degree residuosity classes
 IN ADVANCES IN CRYPTOLOGY — EUROCRYPT 1999
, 1999
"... This paper investigates a novel computational problem, namely the Composite Residuosity Class Problem, and its applications to publickey cryptography. We propose a new trapdoor mechanism and derive from this technique three encryption schemes: a trapdoor permutation and two homomorphic probabilist ..."
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Cited by 1009 (4 self)
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This paper investigates a novel computational problem, namely the Composite Residuosity Class Problem, and its applications to publickey cryptography. We propose a new trapdoor mechanism and derive from this technique three encryption schemes: a trapdoor permutation and two homomorphic probabilistic encryption schemes computationally comparable to RSA. Our cryptosystems, based on usual modular arithmetics, are provably secure under appropriate assumptions in the standard model.
A Digital Signature Scheme Secure Against Adaptive ChosenMessage Attacks
, 1995
"... We present a digital signature scheme based on the computational diculty of integer factorization. The scheme possesses the novel property of being robust against an adaptive chosenmessage attack: an adversary who receives signatures for messages of his choice (where each message may be chosen in a ..."
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Cited by 959 (40 self)
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We present a digital signature scheme based on the computational diculty of integer factorization. The scheme possesses the novel property of being robust against an adaptive chosenmessage attack: an adversary who receives signatures for messages of his choice (where each message may be chosen in a way that depends on the signatures of previously chosen messages) can not later forge the signature of even a single additional message. This may be somewhat surprising, since the properties of having forgery being equivalent to factoring and being invulnerable to an adaptive chosenmessage attack were considered in the folklore to be contradictory. More generally, we show how to construct a signature scheme with such properties based on the existence of a "clawfree" pair of permutations  a potentially weaker assumption than the intractibility of integer factorization. The new scheme is potentially practical: signing and verifying signatures are reasonably fast, and signatures are compact.
Fully homomorphic encryption using ideal lattices
 In Proc. STOC
, 2009
"... We propose a fully homomorphic encryption scheme – i.e., a scheme that allows one to evaluate circuits over encrypted data without being able to decrypt. Our solution comes in three steps. First, we provide a general result – that, to construct an encryption scheme that permits evaluation of arbitra ..."
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Cited by 663 (17 self)
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We propose a fully homomorphic encryption scheme – i.e., a scheme that allows one to evaluate circuits over encrypted data without being able to decrypt. Our solution comes in three steps. First, we provide a general result – that, to construct an encryption scheme that permits evaluation of arbitrary circuits, it suffices to construct an encryption scheme that can evaluate (slightly augmented versions of) its own decryption circuit; we call a scheme that can evaluate its (augmented) decryption circuit bootstrappable. Next, we describe a public key encryption scheme using ideal lattices that is almost bootstrappable. Latticebased cryptosystems typically have decryption algorithms with low circuit complexity, often dominated by an inner product computation that is in NC1. Also, ideal lattices provide both additive and multiplicative homomorphisms (modulo a publickey ideal in a polynomial ring that is represented as a lattice), as needed to evaluate general circuits. Unfortunately, our initial scheme is not quite bootstrappable – i.e., the depth that the scheme can correctly evaluate can be logarithmic in the lattice dimension, just like the depth of the decryption circuit, but the latter is greater than the former. In the final step, we show how to modify the scheme to reduce the depth of the decryption circuit, and thereby obtain a bootstrappable encryption scheme, without reducing the depth that the scheme can evaluate. Abstractly, we accomplish this by enabling the encrypter to start the decryption process, leaving less work for the decrypter, much like the server leaves less work for the decrypter in a serveraided cryptosystem.
Guide to Elliptic Curve Cryptography
, 2004
"... Elliptic curves have been intensively studied in number theory and algebraic geometry for over 100 years and there is an enormous amount of literature on the subject. To quote the mathematician Serge Lang: It is possible to write endlessly on elliptic curves. (This is not a threat.) Elliptic curves ..."
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Cited by 610 (18 self)
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Elliptic curves have been intensively studied in number theory and algebraic geometry for over 100 years and there is an enormous amount of literature on the subject. To quote the mathematician Serge Lang: It is possible to write endlessly on elliptic curves. (This is not a threat.) Elliptic curves also figured prominently in the recent proof of Fermat's Last Theorem by Andrew Wiles. Originally pursued for purely aesthetic reasons, elliptic curves have recently been utilized in devising algorithms for factoring integers, primality proving, and in publickey cryptography. In this article, we aim to give the reader an introduction to elliptic curve cryptosystems, and to demonstrate why these systems provide relatively small block sizes, highspeed software and hardware implementations, and offer the highest strengthperkeybit of any known publickey scheme.
Encrypted Key Exchange: PasswordBased Protocols Secure Against Dictionary Attacks
 IEEE SYMPOSIUM ON RESEARCH IN SECURITY AND PRIVACY
, 1992
"... Classical cryptographic protocols based on userchosen keys allow an attacker to mount passwordguessing attacks. We introduce a novel combination of asymmetric (publickey) and symmetric (secretkey) cryptography that allow two parties sharing a common password to exchange confidential and authenti ..."
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Cited by 436 (5 self)
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Classical cryptographic protocols based on userchosen keys allow an attacker to mount passwordguessing attacks. We introduce a novel combination of asymmetric (publickey) and symmetric (secretkey) cryptography that allow two parties sharing a common password to exchange confidential and authenticated information over an insecure network. These protocols are secure against active attacks, and have the property that the password is protected against offline "dictionary" attacks. There are a number of other useful applications as well, including secure public telephones.
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 308 (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
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 308 (13 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.
Security Proofs for Signature Schemes
, 1996
"... In this paper, we address the question of providing security proofs for signature schemes in the socalled random oracle model [1]. In particular, we establish the generality of this technique against adaptively chosen message attacks. Our main application achieves such a security proof for a slight ..."
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Cited by 263 (25 self)
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In this paper, we address the question of providing security proofs for signature schemes in the socalled random oracle model [1]. In particular, we establish the generality of this technique against adaptively chosen message attacks. Our main application achieves such a security proof for a slight variant of the El Gamal signature scheme [3] where committed values are hashed together with the message. This is a rather surprising result since the original El Gamal is, as RSA [11], subject to existential forgery.