In this paper, we propose a generic construction of chosen-ciphertext secure cryptosystems against adversaries with a bounded number of decrytion queries from arbitrary semantically secure encryption in a black box manner. Our construction is not only an alternative to the previously known technique, i.e. the Naor-Yung paradigm [37, 19, 42], but also has some interesting properties. Especially, (1) it does not require non-interactive zero-knowledge proof, and (2) its component ciphertexts can be compressed into only one if the underlying encryption has a certain homomorphic property. Consequently, when applying our construction to the ElGamal encryption, ciphertext overhead of the resulting scheme will be only one group element which is considered optimal since it is the same as the original ElGamal. Disadvantages to previous schemes are that the upper bound of the number of decryption queries (e.g. 2 30) has to be known before set-up phase, and the size of public key is large. 1
In this paper, we give the definition of the bit commitment channel, implement its formulization, prove the implementation of the zero-knowledge proof with with it and introduce four schemes of implementing the bit commitment channel. It is suggested that zero-knowledge proof algorithm can bebased on bit commitment channel and an instance for this is given.
Theoretical computer science has found fertile ground in many areas of mathematics. The approach has been to consider classical problems through the prism of computational complexity, where the number of basic computational steps taken to solve a problem is the crucial qualitative parameter. This new approach has led to a sequence of advances, in setting and solving new mathematical challenges as well as in harnessing discrete mathematics to the task of solving real-world problems. In this talk, I will survey the development of modern cryptography -- the mathematics behind secret communications and protocols -- in this light. I will describe the complexity theoretic foundations underlying the cryptographic tasks of encryption, pseudo-randomness number generators and functions, zero knowledge interactive proofs, and multi-party secure protocols. I will attempt to highlight the paradigms and proof techniques which unify these foundations, and which have made their way into the mainstream of complexity theory.
In this tutorial, selected topics of cryptology and of computational complexity theory are presented. We give a brief overview of the history and the foundations of classical cryptography, and then move on to modern public-key cryptography. Particular attention is paid to cryptographic protocols and the problem of constructing key components of protocols such as one-way functions. A function is one-way if it is easy to compute, but hard to invert. We discuss the notion of one-way functions both in a cryptographic and in a complexity-theoretic setting. We also consider interactive proof systems and present some interesting zero-knowledge protocols. In a zero-knowledge protocol, one party can convince the other party of knowing some secret information without disclosing any bit of this information. Motivated by these protocols, we survey some complexity-theoretic results on interactive proof systems and related complexity classes.
We describe efficient constructions for various cryptographic primitives in private-key as well as public-key cryptography. Our main results are two new constructions of pseudo-random functions. We prove the pseudo-randomness of one construction under the assumption that factoring (Blum integers) is hard while the other construction is pseudo-random if the decisional version of the Diffie--Hellman assumption holds. Computing the value of our functions at any given point involves two subset products. This is much more efficient than previous proposals. Furthermore, these functions have the advantage of being in TC 0 (the class of functions computable by constant depth circuits consisting of a polynomial number of threshold gates). This fact has several interesting applications. The simple algebraic structure of the functions implies additional features such as a zero-knowledge proof for statements of the form " y = f s ( x )" and " y ≠ f s ( x )" given a commitment to a key s of a pseudo-random function f s .
An identification scheme based on a generator matrix of error-correcting codes over GF(q) is proposed, it is proved that the given protocol is a zero-knowledge interactive proof in the random oracle model, and it is shown that the scheme is secure when parameters are selected properly.
Magdi El-Soudani, Heba S. El-Refaey, Hebat-Allah M. Mourad
Zero knowledge proofs form an important category in the public key identification protocols, they are depending on number theory. In 1989, Stern announced his protocol which is based on syndrome-decoding problem, he also studied the attacks against this type of problems. In this paper, we propose a broadcasting variant based on the Stern’ s Identification scheme. Broadcasting is applied when there are one prover and many verifiers. In the proposed broadcasting scheme, the prover is communicating with verifiers through a broadcasting channel so he is running the identification session once, which minimizes the time and the communication complexity. We have developed Stern basic scheme to be adequate for broadcasting applications, but the underlying hard problem that the security of Stern identification scheme depends on, is used as it is.
In this tutorial, selected topics of cryptology and of computational complexity theory are presented. We give a brief overview of the history and the foundations of classical cryptography, and then move on to modern public-key cryptography. Particular attention is paid to cryptographic protocols and the problem of constructing the key components of such protocols such as one-way functions. A function is one-way if it is easy to compute, but hard to invert. We discuss the notion of one-way functions both in a cryptographic and in a complexity-theoretic setting. We also consider interactive proof systems and present some interesting zero-knowledge protocols. In a zero-knowledge protocol one party can convince the other party of knowing some secret information without disclosing any bit of this information. Motivated by these protocols, we survey some complexity-theoretic results on interactive proof systems and related complexity classes.
Let n be a large composite number. Without factoring n, the computation of a 2 t (mod n)given a, t with gcd(a# n) = 1 and t!n can be done in t squarings modulo n.For t n (e.g., n?2 1024 and t!2 100 ), no lower complexity than t squarings is known to fulfill this task. Rivest et al suggested to use such constructions as good candidates for realising timed-release crypto problems. We argue the necessity for a zero-knowledge proof of the correctness of such constructions and propose the first practically efficient protocol for a realisation. Our protocol proves, in log 2 t standard crypto operations, the correctness of (a e ) 2 t (mod n) with respect to a e where e is an RSA encryption exponent. With such a proof, a Timed-release Encryption of a message M can be given as a 2 t M (mod n) with the assertion that the correct decryption of the RSA ciphertext M e (mod n) can be obtained by performing t squarings modulo n starting from a. Timed-release RSA signatures can be constructed analogously. Keywords Timed-release cryptography, Time-lock puzzles, Non-parallelisability, Efficient zero-knowledge protocols. 1
The present paper investigates the possibility of designing zero-knowledge identification schemes based on hard problems from coding theory. Zero-knowledge proofs were introduced by Goldwasser, Micali, and Rackoff (1985). Their practical significance was soon demonstrated in the work of Fiat and Shamir [1986], who turned zero-knowledge proofs of quadratic residuosity into efficient means of establishing user identities. In the present paper, we propose a new identification scheme, based on error-correcting codes, which is zero-knowledge and seems of practical value. Furthermore, we describe several variants, including one which has an identity-based character. The security of our schemes depends on the hardness of finding a word of given syndrome and prescribed (small) weight with respect to some randomly generated binary linear error-correcting code. This is, of course, not the first attempt to design a cryptographic scheme using tools from coding theory. The difference is that identification protocols do not follow the public key paradigm based on trap-door functions and described in the seminal Diffie-Hellman paper [1976]. Rather, they only require one-way functions, which opens the way to using, in a rather direct manner, simple combinatorial problems of the kind provided by coding theory. The resulting schemes compare favorably to their number-theoretic analogs.
Abstract In modern cryptologic theory, the design of cryptographic protocols is often based on the assumed difficulty of number theoretic problems. Especially, in order to prove the security of a cryptographic protocol based upon the assumed difficulty of a problem, a very important role is played by the legitimacy (as concerns the security of the cryptographic protocol) of that cryptographic assumption. Recently, Kurosawa, Ogata, and Tsujii proposed a new cryptographic assumption, the Chosen Discrete Logarithm Assumption (CDLA), and showed that any language in NP has a four‐move, zero‐knowledge interactive proof (ZKIP) under the CDLA. In this paper, we define the modified CDLA and consider its legitimacy. Our principal result (that the modified CDLA is not a legitimate cryptographic assumption) follows from a theoretical analysis of expected polynomial‐time algorithms and the concrete construction of an algorithm based on the Artin conjecture.