Author
Charles Rackoff
Bio: Charles Rackoff is an academic researcher from University of Toronto. The author has contributed to research in topics: Mathematical proof & Password. The author has an hindex of 25, co-authored 52 publications receiving 10501 citations.
Papers published on a yearly basis
Papers
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TL;DR: A computational complexity theory of the “knowledge” contained in a proof is developed and examples of zero-knowledge proof systems are given for the languages of quadratic residuosity and 'quadratic nonresiduosity.
Abstract: Usually, a proof of a theorem contains more knowledge than the mere fact that the theorem is true. For instance, to prove that a graph is Hamiltonian it suffices to exhibit a Hamiltonian tour in it; however, this seems to contain more knowledge than the single bit Hamiltonian/non-Hamiltonian.In this paper a computational complexity theory of the “knowledge” contained in a proof is developed. Zero-knowledge proofs are defined as those proofs that convey no additional knowledge other than the correctness of the proposition in question. Examples of zero-knowledge proof systems are given for the languages of quadratic residuosity and 'quadratic nonresiduosity. These are the first examples of zero-knowledge proofs for languages not known to be efficiently recognizable.
3,117 citations
04 Oct 2019
TL;DR: Permission to copy without fee all or part of this material is granted provided that the copies arc not made or distributed for direct commercial advantage.
Abstract: Usually, a proof of a theorem contains more knowledge than the mere fact that the theorem is true. For instance, to prove that a graph is Hamiltonian it suffices to exhibit a Hamiltonian tour in it; however, this seems to contain more knowledge than the single bit Hamiltonian/non-Hamiltonian.In this paper a computational complexity theory of the “knowledge” contained in a proof is developed. Zero-knowledge proofs are defined as those proofs that convey no additional knowledge other than the correctness of the proposition in question. Examples of zero-knowledge proof systems are given for the languages of quadratic residuosity and 'quadratic nonresiduosity. These are the first examples of zero-knowledge proofs for languages not known to be efficiently recognizable.
1,962 citations
11 Aug 1991
TL;DR: A formalization of chosen ciphertext attack is given in the model which is stronger than the "lunchtime attack" considered by Naor and Yung, and it is proved a non-interactive public-key cryptosystem based on non-Interactive zero-knowledge proof of knowledge to be secure against it.
Abstract: The zero-knowledge proof of knowledge, first denned by Fiat, Fiege and Shamir, was used by Galil, Haber and Yung as a means of constructing (out of a trapdoor function) an interactive public-key cryptosystem provably secure against chosen ciphertext attack. We introduce a revised setting which permits the definition of a non-interactive analogue, the non-interactive zero-knowledge proof of knowledge, and show how it may be constructed in that setting from a non-interactive zero-knowledge proof system for NP (of the type introduced by Blum, Feldman and Micali). We give a formalization of chosen ciphertext attack in our model which is stronger than the "lunchtime attack" considered by Naor and Yung, and prove a non-interactive public-key cryptosystem based on non-interactive zero-knowledge proof of knowledge to be secure against it.
1,198 citations
TL;DR: Any pseudorandom bit generator can be used to construct a block private key cryptos system which is secure against chosen plaintext attack, which is one of the strongest known attacks against a cryptosystem.
Abstract: We show how to efficiently construct a pseudorandom invertible permutation generator from a pseudorandom function generator. Goldreich, Goldwasser and Micali [“How to construct random functions,” P...
1,075 citations
01 Dec 1985
TL;DR: Zero-knowledge proofs as discussed by the authors are proofs that convey no additional knowledge other than the correctness of the proposition in question, i.e., the proof of a theorem contains more knowledge than the mere fact that the theorem is true.
Abstract: Usually, a proof of a theorem contains more knowledge than the mere fact that the theorem is true. For instance, to prove that a graph is Hamiltonian it suffices to exhibit a Hamiltonian tour in it; however, this seems to contain more knowledge than the single bit Hamiltonian/non-Hamiltonian.In this paper a computational complexity theory of the “knowledge” contained in a proof is developed. Zero-knowledge proofs are defined as those proofs that convey no additional knowledge other than the correctness of the proposition in question. Examples of zero-knowledge proof systems are given for the languages of quadratic residuosity and 'quadratic nonresiduosity. These are the first examples of zero-knowledge proofs for languages not known to be efficiently recognizable.
769 citations
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Book•
01 Jan 1996TL;DR: A valuable reference for the novice as well as for the expert who needs a wider scope of coverage within the area of cryptography, this book provides easy and rapid access of information and includes more than 200 algorithms and protocols.
Abstract: From the Publisher:
A valuable reference for the novice as well as for the expert who needs a wider scope of coverage within the area of cryptography, this book provides easy and rapid access of information and includes more than 200 algorithms and protocols; more than 200 tables and figures; more than 1,000 numbered definitions, facts, examples, notes, and remarks; and over 1,250 significant references, including brief comments on each paper.
13,597 citations
19 Aug 2001
TL;DR: This work proposes a fully functional identity-based encryption scheme (IBE) based on the Weil pairing that has chosen ciphertext security in the random oracle model assuming an elliptic curve variant of the computational Diffie-Hellman problem.
Abstract: We propose a fully functional identity-based encryption scheme (IBE). The scheme has chosen ciphertext security in the random oracle model assuming an elliptic curve variant of the computational Diffie-Hellman problem. Our system is based on the Weil pairing. We give precise definitions for secure identity based encryption schemes and give several applications for such systems.
7,083 citations
IBM1
TL;DR: It is argued that the random oracles model—where all parties have access to a public random oracle—provides a bridge between cryptographic theory and cryptographic practice, and yields protocols much more efficient than standard ones while retaining many of the advantages of provable security.
Abstract: We argue that the random oracle model—where all parties have access to a public random oracle—provides a bridge between cryptographic theory and cryptographic practice. In the paradigm we suggest, a practical protocol P is produced by first devising and proving correct a protocol PR for the random oracle model, and then replacing oracle accesses by the computation of an “appropriately chosen” function h. This paradigm yields protocols much more efficient than standard ones while retaining many of the advantages of provable security. We illustrate these gains for problems including encryption, signatures, and zero-knowledge proofs.
5,313 citations
TL;DR: This work proposes a fully functional identity-based encryption (IBE) scheme based on bilinear maps between groups and gives precise definitions for secure IBE schemes and gives several applications for such systems.
Abstract: We propose a fully functional identity-based encryption (IBE) scheme. The scheme has chosen ciphertext security in the random oracle model assuming a variant of the computational Diffie--Hellman 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 IBE schemes and give several applications for such systems.
5,110 citations
01 Jan 1987
TL;DR: Simple identification and signature schemes which enable any user to prove his identity and the authenticity of his messages to any other user without shared or public keys are described.
Abstract: In this paper we describe simple identification and signature schemes which enable any user to prove his identity and the authenticity of his messages to any other user without shared or public keys. The schemes are provably secure against any known or chosen message attack if factoring is difficult, and typical implementations require only 1% to 4% of the number of modular multiplications required by the RSA scheme. Due to their simplicity, security and speed, these schemes are ideally suited for microprocessor-based devices such as smart cards, personal computers, and remote control systems.
4,193 citations