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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 278 (35 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
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 209 (24 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.
Numbertheoretic constructions of efficient pseudorandom functions
 In 38th Annual Symposium on Foundations of Computer Science
, 1997
"... ..."
The Security of Cipher Block Chaining
, 1994
"... The Cipher Block Chaining  Message Authentication Code (CBC MAC) specifies that a message x = x 1 \Delta \Delta \Delta xm be authenticated among parties who share a secret key a by tagging x with a prefix of f (m) a (x) def = f a (f a (\Delta \Delta \Delta f a (f a (x 1 )\Phix 2 )\Phi \Delta ..."
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Cited by 144 (26 self)
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The Cipher Block Chaining  Message Authentication Code (CBC MAC) specifies that a message x = x 1 \Delta \Delta \Delta xm be authenticated among parties who share a secret key a by tagging x with a prefix of f (m) a (x) def = f a (f a (\Delta \Delta \Delta f a (f a (x 1 )\Phix 2 )\Phi \Delta \Delta \Delta \Phix m\Gamma1 )\Phix m ) ; where f is some underlying block cipher (eg. f = DES). This method is a pervasively used international and U.S. standard. We provide its first formal justification, showing the following general lemma: that cipher block chaining a pseudorandom function gives a pseudorandom function. Underlying our results is a technical lemma of independent interest, bounding the success probability of a computationally unbounded adversary in distinguishing between a random mlbit to lbit function and the CBC MAC of a random lbit to lbit function. Advanced Networking Laboratory, IBM T.J. Watson Research Center, PO Box 704, Yorktown Heights, NY 10598, USA. em...
Publicly Verifiable Secret Sharing
, 1996
"... . A secret sharing scheme allows to share a secret among several participants such that only certain groups of them can recover it. Verifiable secret sharing has been proposed to achieve security against cheating participants. Its first realization had the special property that everybody, not only t ..."
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Cited by 119 (1 self)
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. A secret sharing scheme allows to share a secret among several participants such that only certain groups of them can recover it. Verifiable secret sharing has been proposed to achieve security against cheating participants. Its first realization had the special property that everybody, not only the participants, can verify that the shares are correctly distributed. We will call such schemes publicly verifiable secret sharing schemes, we discuss new applications to escrow cryptosystems and to payment systems with revocable anonymity, and we present two new realizations based on ElGamal's cryptosystem. 1 Introduction A secret sharing scheme [20, 2] allows to split a secret into different pieces, called shares, which are given to the participants, such that only certain groups of them can recover the secret. The first secret sharing schemes have been threshold schemes, where only groups of more than a certain number of participants can recover the secret. Verifiable secret sharing (V...
Robustness Principles for Public Key Protocols
, 1995
"... : We present a number of attacks, some new, on public key protocols. We also advance a number of principles which may help designers avoid many of the pitfalls, and help attackers spot errors which can be exploited. 1 Introduction Cryptographic protocols are typically used to identify a user to a co ..."
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Cited by 116 (9 self)
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: We present a number of attacks, some new, on public key protocols. We also advance a number of principles which may help designers avoid many of the pitfalls, and help attackers spot errors which can be exploited. 1 Introduction Cryptographic protocols are typically used to identify a user to a computer system, to authenticate a transaction, or to set up a key. They typically involve the exchange of about 25 messages, and they are very easy to get wrong: bugs have been found in well known protocols years after they were first published. This is quite remarkable; after all, a protocol is a kind of program, and one would expect to get any other program of this size right by staring at it for a while. A number of remedies have been proposed. One approach is formal mathematical proof, and can range from systematic protocol verification techniques such as the BAN logic [BAN89] to the casebycase reduction of security claims to the intractability of some problem such as factoring. Anot...
Incremental Cryptography: The Case of Hashing and Signing
 In CRYPTO
, 1994
"... Abstract. We initiate the investigation of a new kind of efficiency for cryptographic transformations. The idea is that having once applied the transformation to some document M, the time to update the result upon modification of M should be “proportional ” to the “amount of modification” done to M. ..."
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Cited by 74 (4 self)
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Abstract. We initiate the investigation of a new kind of efficiency for cryptographic transformations. The idea is that having once applied the transformation to some document M, the time to update the result upon modification of M should be “proportional ” to the “amount of modification” done to M. Thereby one obtains much faster cryptographic primitives for environments where closely related documents are undergoing the same cryptographic transformations. We provide some basic definitions enabling treatment of the new notion. We then exemplify our approach by suggesting incremental schemes for hashing and signing which are efficient according to our new measure. 1
Sharing decryption in the context of voting or lotteries
, 2000
"... Several public key cryptosystems with additional homomorphic properties have been proposed so far. They allow to perform computation with encrypted data without the knowledge of any secret information. In many applications, the ability to perform decryption, i.e. the knowledge of the secret key, giv ..."
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Cited by 72 (6 self)
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Several public key cryptosystems with additional homomorphic properties have been proposed so far. They allow to perform computation with encrypted data without the knowledge of any secret information. In many applications, the ability to perform decryption, i.e. the knowledge of the secret key, gives a huge power. A classical way to reduce the trust in such a secret owner, and consequently to increase the security, is to share the secret between many entities in such a way that cooperation between them is necessary to decrypt. In this paper, we propose a distributed version of the Paillier cryptosystem presented at Eurocrypt ’99. This shared scheme can for example be used in an electronic voting scheme or in a lottery where a random number related to the winning ticket has to be jointly chosen by all participants.
Towards the Equivalence of Breaking the DiffieHellman Protocol and Computing Discrete Logarithms
, 1994
"... Let G be an arbitrary cyclic group with generator g and order jGj with known factorization. G could be the subgroup generated by g within a larger group H. Based on an assumption about the existence of smooth numbers in short intervals, we prove that breaking the DiffieHellman protocol for G and ..."
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Cited by 69 (6 self)
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Let G be an arbitrary cyclic group with generator g and order jGj with known factorization. G could be the subgroup generated by g within a larger group H. Based on an assumption about the existence of smooth numbers in short intervals, we prove that breaking the DiffieHellman protocol for G and base g is equivalent to computing discrete logarithms in G to the base g when a certain side information string S of length 2 log jGj is given, where S depends only on jGj but not on the definition of G and appears to be of no help for computing discrete logarithms in G. If every prime factor p of jGj is such that one of a list of expressions in p, including p \Gamma 1 and p + 1, is smooth for an appropriate smoothness bound, then S can efficiently be constructed and therefore breaking the DiffieHellman protocol is equivalent to computing discrete logarithms.
Provably Secure Blind Signature Schemes
, 1996
"... In this paper, we give a provably secure design for blind signatures, the most important ingredient for anonymity in offline electronic cash systems. Previous examples of blind signature schemes were constructed from traditional signature schemes with only the additional proof of blindness. The des ..."
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Cited by 68 (10 self)
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In this paper, we give a provably secure design for blind signatures, the most important ingredient for anonymity in offline electronic cash systems. Previous examples of blind signature schemes were constructed from traditional signature schemes with only the additional proof of blindness. The design of some of the underlying signature schemes can be validated by a proof in the socalled random oracle model, but the security of the original signature scheme does not, by itself, imply the security of the blind version. In this paper, we first propose a definition of security for blind signatures, with application to electronic cash. Next, we focus on a specific example which can be successfully transformed in a provably secure blind signature scheme.