Since there is no key transmiited with the data, the chances of data being decrypted are null. Ferreira, the practical application of state of the art security in real environments, 334355. Recently, a variety of chaosbased cryptosystems have been proposed. The study of certain continued fractions in this last setting b egins in the 1970s with the works of baum and sweet 5, 6, later developed by mills and robbins 7. Continued fractions have numerous applications in cryptography. On the use of continued fractions for stream ciphers cryptology. Generalizing cryptosystems based on the subset sum problem. A number theory based pseudorandom sequence called partial quotient pq sequence is generated from the continued fraction expansion of some irrational numbers and is used to create sub vectors to. Legendres theorem on diophantine approximations of the form. In this paper, we propose a new scheme for image encryption based on the use of a chaotic map with large key space and engle continued. The attack combines the continued fraction algorithm and coppersmith s technique and can be seen as a generalization of the attacks of wiener and bl omermay on rsa. Introduction in this paper, we consider three cryptosystems that are based on the use of polynomials with restricted coe. Pdf on the use of continued fractions for stream ciphers.
The modulus n of a rsa cryptosystem is the product of two large primes p and q. Most of the chaotic systems used in cryptography have good chaotic properties like ergodicity, sensitivity to initial values and sensitivity to control parameters. Adleman abstract an encryption method is presented with the novel property that publicly revealing an encryption key does not thereby reveal the corresponding decryption key. As an additional contribution, we construct a very natural lwebased cryptosystem that is secure under. Cryptosystems based on continued fractions kanso 2011. Request pdf new attack on the rsa cryptosystem based on continued fractions this paper presents a new improved attack on rsa based on wieners technique using continued fractions.
Cryptosystems play an important role in many cryptographic applications. In this paper, we apply the continued fraction method to launch an attack on the three rsatype cryptosystems when the private exponent d is sufficiently small. We present and analyze a sequence of rational numbers, whose randomness. Once we leave the comfort of \\mathbbz\, we have several options. Zeng, continued fractions and berlekampmassey algorithm, 2431.
Simulation results show that the suggested cryptosystems seem to be good candidates for use in cryptographic applications. Towards faster cryptosystems, ii university of missouri. Some of these systems are used in designing a pseudo random bit generator prbg for stream cipher applications. Finally, we show how to find the fraction jr using the method of continued fractions. An efficient prbg based on chaotic map and engel continued. Also it is very simple to initialize the system and to generate new keys. Cryptography, continued fraction, statistical tests, prbg, chaotic map 1. Chaos systems have many important features like ergodicity. The ntru public key cryptosystem is also based on a hard. Couriers or other secure means are not needed to transmit. The applicability of known attacks on sspbased cryptosystems is determined by a metric called the subset sum density16. Advantages and disadvantages of symmetric cryptosystems advantages a symmetric cryptosystem is faster.
Sciences and technologies of image and telecommunications higher institute of biotechnology, sfax tunisia 2laboratory lirmm, umr 5506 cnrs university of montpellier ii 161, rue ada, 34392 montpellier cedex 05, france. Pdf a cryptanalytic attack on the luc cryptosystem using. In 7 the same authors have used the random sequence generated to encrypt. Publickey cryptosystems from the worstcase shortest. Cryptanalysis of rsatype cryptosystems based on lucas. Some of these novel chaotic encryption schemes are not very suitable for image encryption due to their density function which is not uniformly distributed or due to their small key space. New attack on the rsa cryptosystem based on continued. In 1997, verheul and van tilborg proposed an extension of wieners attack that allows the rsa cryptosystem to be broken by an exhaustive search when d is a few bits longer than. In this paper, we propose a prbg based on the use of the standard chaotic map with large key space and the engle continued fractions ecf map. A new attack on the rsa cryptosystem based on continued fractions. A method for obtaining digital signatures and publickey. It is the responsibility of child classes to implement specific cryptosystems. We discuss three cryptosystems, ntru, spifi, and enroot, that are based on the use of polynomials with restricted coe. Pdf a new image cryptosystem based on chaotic map and.
Theres a set of publickey cryptosystems based on lattices, which are becoming increasingly. Boneh and franklins identitybased encryption scheme is perhaps the most famous. A cryptanalytic attack on the luc cryptosystem using continued. Birthday attacks against certain structured cryptosystems.
Its security is based on the difficulty of finding the prime factors of large integers. A complete and explicit security reduction algorithm for. Introduction recently, a variety of cryptosystems have been proposed. Continued fractions computing with continued fractions. In symmetric cryptosystems, encrypted data can be transferred on the link even if there is a possibility that the data will be intercepted. Publickey cryptosystems based on composite degree residuosity classes 3 will denote that the problem p1 is polynomially reducible resp. Many of them are based on chaotic systems 15 which possess good cryptographic characteristics. Cryptosystems based on continued fractions, security and. The classes defined in this module should not be called directly. Theres a set of publickey cryptosystems based on lattices, which are becoming increasingly important. Rather than avoiding pairings, one can seek them out to construct new schemes. Ultimately, regardless of the nature of the numbers involved, we must represent them with a finite number of bits. A crypt analytic att ack on the luc cryptosystem using continued fractions 1 min rs, st is equal to rs in 491974 49. Over the 2adic numbers, however, continued fractions fail to converge in general.
Attacking codelatticebased cryptosystems using partial knowledge. In recent years, a variety of chaosbased cryptosystems have been proposed. The chaotic nature of the standard map and the good statistical proper. By adapting prior cryptosystems to different sizes of q, we obtain semantically secure cryptosystems based on the worstcase hardness of gapsvp and its tovariant. Although the encryption scheme proposed in this paper is based on a hard mathematical problem, its use is fast. Lets look at the continued fraction expansion of an. A generalized attack on rsa type cryptosystems sciencedirect. On the use of continued fractions for stream ciphers. The outputs of the standard map are used as the inputs of ecfmap. This paper discusses an asymmetric cryptosystem based on fractions, the r ksystem, which can be implemented fast using only additions and multiplications. Continued fractions and rsa with small secret exponent. The ecfmap is employed to generate a pseudo random sequence which satisfies uniform distribution, zero cocorrelation and ideal nonlinearity to achieve higher level of security. An efficient prbg based on chaotic map and engel continued fractions article pdf available in journal of software engineering and applications 312. In this paper, we propose a new scheme for image encryption based on the use of a chaotic map with large key space and engle continued fractions ecf map.
Preface 1 1 overview of cryptography and its applications. This paper presents a new improved attack on rsa based on wieners technique using continued fractions. Cryptosystems based on gfq can be translated to systems using the group e, where e is an elliptic curve defined over gf secret. In recent years, a growing number of cryptosystems based on chaos have been proposed, many of them fundamentally flawed by a lack of robustness and. In section 4, we present some lemmas that will be used in the paper. Cryptanalysis based on 2adic rational approximat ion. A complete and explicit security reduction algorithm for rsabased cryptosystems. Ding, lower bounds on the weight complexities of cascaded binary sequences, 3943. Continued fractions, diophantine approximations, rsa cryp. Cryptosystems based on continued fractions cryptosystems based on continued fractions kanso, ali 20111001 00.
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