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A practical public key cryptosystem provably secure against adaptive chosen ciphertext attack
 CRYPTO '98
, 1998
"... A new public key cryptosystem is proposed and analyzed. The scheme is quite practical, and is provably secure against adaptive chosen ciphertext attack under standard intractability assumptions. There appears to be no previous cryptosystem in the literature that enjoys both of these properties simu ..."
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Cited by 482 (16 self)
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A new public key cryptosystem is proposed and analyzed. The scheme is quite practical, and is provably secure against adaptive chosen ciphertext attack under standard intractability assumptions. There appears to be no previous cryptosystem in the literature that enjoys both of these properties simultaneously.
Optimal Asymmetric Encryption – How to Encrypt with RSA
, 1995
"... Given an arbitrary kbit to kbit trapdoor permutation f and a hash function, we exhibit an encryption scheme for which (i) any string x of length slightly less than k bits can be encrypted as f(rx), where rx is a simple probabilistic encoding of x depending on the hash function; and (ii) the scheme ..."
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Cited by 216 (19 self)
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Given an arbitrary kbit to kbit trapdoor permutation f and a hash function, we exhibit an encryption scheme for which (i) any string x of length slightly less than k bits can be encrypted as f(rx), where rx is a simple probabilistic encoding of x depending on the hash function; and (ii) the scheme can be proven semantically secure assuming the hash function is \ideal. &quot; Moreover, a slightly enhanced scheme is shown to have the property that the adversary can create ciphertexts only of strings for which she \knows &quot; the corresponding plaintextssuch ascheme is not only semantically secure but also nonmalleable and secure against chosenciphertext attack.
Design and Analysis of Practical PublicKey Encryption Schemes Secure against Adaptive Chosen Ciphertext Attack
 SIAM Journal on Computing
, 2001
"... A new public key encryption scheme, along with several variants, is proposed and analyzed. The scheme and its variants are quite practical, and are proved secure against adaptive chosen ciphertext attack under standard intractability assumptions. These appear to be the first publickey encryption sc ..."
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Cited by 205 (11 self)
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A new public key encryption scheme, along with several variants, is proposed and analyzed. The scheme and its variants are quite practical, and are proved secure against adaptive chosen ciphertext attack under standard intractability assumptions. These appear to be the first publickey encryption schemes in the literature that are simultaneously practical and provably secure.
Securing Threshold Cryptosystems against Chosen Ciphertext Attack
 JOURNAL OF CRYPTOLOGY
, 1998
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The knowledgeofexponent assumptions and 3round zeroknowledge protocols
, 2004
"... Abstract. Hada and Tanaka [11, 12] showed the existence of 3round, negligibleerror zeroknowledge arguments for NP based on a pair of nonstandard assumptions, here called KEA1 and KEA2. In this paper we show that KEA2 is false. This renders vacuous the results of [11, 12]. We recover these result ..."
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Cited by 59 (1 self)
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Abstract. Hada and Tanaka [11, 12] showed the existence of 3round, negligibleerror zeroknowledge arguments for NP based on a pair of nonstandard assumptions, here called KEA1 and KEA2. In this paper we show that KEA2 is false. This renders vacuous the results of [11, 12]. We recover these results, however, under a suitably modified new assumption called KEA3. What we believe is most interesting is that we show that it is possible to “falsify ” assumptions like KEA2 that, due to their nature and quantifierstructure, do not lend themselves easily to “efficient falsification ” (Naor [15]). 1
Lower bounds for nonblackbox zero knowledge
 In 44th FOCS
, 2003
"... We show new lower bounds and impossibility results for general (possibly nonblackbox) zeroknowledge proofs and arguments. Our main results are that, under reasonable complexity assumptions: 1. There does not exist a tworound zeroknowledge proof system with perfect completeness for an NPcomplet ..."
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Cited by 36 (8 self)
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We show new lower bounds and impossibility results for general (possibly nonblackbox) zeroknowledge proofs and arguments. Our main results are that, under reasonable complexity assumptions: 1. There does not exist a tworound zeroknowledge proof system with perfect completeness for an NPcomplete language. The previous impossibility result for tworound zero knowledge, by Goldreich and Oren (J. Cryptology, 1994) was only for the case of auxiliaryinput zeroknowledge proofs and arguments. 2. There does not exist a constantround zeroknowledge strong proof or argument of knowledge (as defined by Goldreich (2001)) for a nontrivial language. 3. There does not exist a constantround publiccoin proof system for a nontrivial language that is resettable zero knowledge. This result also extends to boundedresettable zero knowledge, in which the number of resets is a priori bounded by a polynomial in the input length and provertoverifier communication.
Why Chosen Ciphertext Security Matters
, 1998
"... This article motivates the importance of publickey cryptosystems that are secure against chosen ciphertext attack, and of rigorous security proofs. It also discusses the new cryptosystem developed by Cramer and Shoup, and its relevance in this regard. ..."
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Cited by 30 (2 self)
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This article motivates the importance of publickey cryptosystems that are secure against chosen ciphertext attack, and of rigorous security proofs. It also discusses the new cryptosystem developed by Cramer and Shoup, and its relevance in this regard.
Perfect nizk with adaptive soundness
 In proceedings of TCC ’07, LNCS series
, 2007
"... Abstract. The notion of noninteractive zeroknowledge (NIZK) is of fundamental importance in cryptography. Despite the vast attention the concept of NIZK has attracted since its introduction, one question has remained very resistant: Is it possible to construct NIZK schemes for any NPlanguage with ..."
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Cited by 28 (0 self)
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Abstract. The notion of noninteractive zeroknowledge (NIZK) is of fundamental importance in cryptography. Despite the vast attention the concept of NIZK has attracted since its introduction, one question has remained very resistant: Is it possible to construct NIZK schemes for any NPlanguage with statistical or even perfect ZK? Groth, Ostrovsky and Sahai recently answered this question in the affirmative. However, in order to achieve adaptive soundness, i.e., soundness against dishonest provers who may choose the target statement depending on the common reference string (CRS), their schemes require some restriction to be put upon the statements to be proven, e.g. an apriori bound on its size. In this work, we first present a very simple and efficient adaptivelysound perfect NIZK argument system for any NPlanguage. Besides being the first adaptivelysound statistical NIZK argument for all NP that does not pose any restriction on the statements to be proven, it enjoys a number of additional desirable properties: it allows to reuse the CRS, it can handle arithmetic circuits, and the CRS can be setup very efficiently without the need for an honest party. We then show an application of our techniques in constructing efficient NIZK schemes for proving arithmetic relations among committed secrets, whereas previous methods required expensive generic NPreductions. The security of the proposed schemes is based on a strong nonstandard assumption, an extended version of the socalled KnowledgeofExponent Assumption (KEA) over bilinear groups. We give some justification for using such an assumption by showing that the commonlyused approach for proving NIZK arguments sound does not allow for adaptivelysound statistical NIZK arguments (unless NP ⊂ P/poly). Furthermore, we show that the assumption used in our construction holds with respect to generic adversaries that do not exploit the specific representation of the group elements. We also discuss how to avoid the nonstandard assumption in a preprocessing model.
Robust KeyEvolving Public Key Encryption Schemes. Available at http://eprint.iacr.org/2001/009
, 2001
"... We propose a keyevolving paradigm to deal with the key exposure problem of public key encryption schemes. The key evolving paradigm is like the one used for forwardsecure digital signature schemes. Let time be divided into time periods such that at time period j, the decryptor holds the secret key ..."
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Cited by 10 (0 self)
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We propose a keyevolving paradigm to deal with the key exposure problem of public key encryption schemes. The key evolving paradigm is like the one used for forwardsecure digital signature schemes. Let time be divided into time periods such that at time period j, the decryptor holds the secret key SKj, while the public key PK is fixed during its lifetime. At time period j, a sender encrypts a message m as 〈j, c〉, which can be decrypted only with the private key SKj. When the time makes a transit from period j to j + 1, the decryptor updates its private key from SKj to SKj+1 and deletes SKj immediately. The keyevolving paradigm assures that compromise of the private key SKj does not jeopardize the message encrypted at the other time periods. We propose two keyevolving public key encryption schemes with zresilience such that compromise of z private keys does not affect confidentiality of messages encrypted in other time periods. Assuming that the DDH problem is hard, we show one scheme semantically secure against passive adversaries and the other scheme semantically secure against the adaptive chosen ciphertext attack under the random oracle.
Statistically hiding sets
 In Proceedings of the The Cryptographers’ Track at the RSA Conference 2009, CTRSA 2009
, 2009
"... Zeroknowledge set is a primitive introduced by Micali, Rabin, and Kilian (FOCS 2003) which enables a prover to commit a set to a verifier, without revealing even the size of the set. Later the prover can give zeroknowledge proofs to convince the verifier of membership/nonmembership of elements in/ ..."
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Cited by 9 (0 self)
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Zeroknowledge set is a primitive introduced by Micali, Rabin, and Kilian (FOCS 2003) which enables a prover to commit a set to a verifier, without revealing even the size of the set. Later the prover can give zeroknowledge proofs to convince the verifier of membership/nonmembership of elements in/not in the committed set. We present a new primitive called Statistically Hiding Sets (SHS), similar to zeroknowledge sets, but providing an information theoretic hiding guarantee, rather than one based on efficient simulation. This is comparable to relaxing zeroknowledge proofs to witness independent proofs. More precisely, we continue to use the simulation paradigm for our definition, but do not require the simulator (nor the distinguisher) to be efficient. We present a new scheme for statistically hiding sets, which does not fit into the “Merkletree/mercurialcommitment” paradigm that has been used for all zeroknowledge set constructions so far. This not only provides efficiency gains compared to the best schemes in that paradigm, but also lets us provide statistical hiding; previous approaches required the prover to maintain growing amounts of state with each new proof for this.