27 research outputs found

    Asymmetric Encryption for Wiretap Channels

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    Since the definition of the wiretap channel by Wyner in 1975, there has been much research to investigate the communication security of this channel. This thesis presents some further investigations into the wiretap channel which improve the reliability of the communication security. The main results include the construction of best known equivocation codes which leads to an increase in the ambiguity of the wiretap channel by using different techniques based on syndrome coding. Best known codes (BKC) have been investigated, and two new design models which includes an inner code and outer code have been implemented. It is shown that best results are obtained when the outer code employs a syndrome coding scheme based on the (23; 12; 7) binary Golay code and the inner code employs the McEliece cryptosystem technique based on BKC0s. Three techniques of construction of best known equivocation codes (BEqC) for syndrome coding scheme are presented. Firstly, a code design technique to produce new (BEqC) codes which have better secrecy than the best error correcting codes is presented. Code examples (some 50 codes) are given for the case where the number of parity bits of the code is equal to 15. Secondly, a new code design technique is presented, which is based on the production of a new (BEqC) by adding two best columns to the parity check matrix(H) of a good (BEqC), [n; k] code. The highest minimum Hamming distance of a linear code is an important parameter which indicates the capability of detecting and correcting errors by the code. In general, (BEqC) have a respectable minimum Hamming distance, but are sometimes not as good as the best known codes with the same code parameters. This interesting point led to the production of a new code design technique which produces a (BEqC) code with the highest minimum Hamming distance for syndrome coding which has better secrecy than the corresponding (BKC). As many as 207 new best known equivocation codes which have the highest minimum distance have been found so far using this design technique.Ministry of Higher Education and Scientific Research, Kurdistan Regional Government, Erbil-Ira

    Some Notes on Code-Based Cryptography

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    This thesis presents new cryptanalytic results in several areas of coding-based cryptography. In addition, we also investigate the possibility of using convolutional codes in code-based public-key cryptography. The first algorithm that we present is an information-set decoding algorithm, aiming towards the problem of decoding random linear codes. We apply the generalized birthday technique to information-set decoding, improving the computational complexity over previous approaches. Next, we present a new version of the McEliece public-key cryptosystem based on convolutional codes. The original construction uses Goppa codes, which is an algebraic code family admitting a well-defined code structure. In the two constructions proposed, large parts of randomly generated parity checks are used. By increasing the entropy of the generator matrix, this presumably makes structured attacks more difficult. Following this, we analyze a McEliece variant based on quasi-cylic MDPC codes. We show that when the underlying code construction has an even dimension, the system is susceptible to, what we call, a squaring attack. Our results show that the new squaring attack allows for great complexity improvements over previous attacks on this particular McEliece construction. Then, we introduce two new techniques for finding low-weight polynomial multiples. Firstly, we propose a general technique based on a reduction to the minimum-distance problem in coding, which increases the multiplicity of the low-weight codeword by extending the code. We use this algorithm to break some of the instances used by the TCHo cryptosystem. Secondly, we propose an algorithm for finding weight-4 polynomials. By using the generalized birthday technique in conjunction with increasing the multiplicity of the low-weight polynomial multiple, we obtain a much better complexity than previously known algorithms. Lastly, two new algorithms for the learning parities with noise (LPN) problem are proposed. The first one is a general algorithm, applicable to any instance of LPN. The algorithm performs favorably compared to previously known algorithms, breaking the 80-bit security of the widely used (512,1/8) instance. The second one focuses on LPN instances over a polynomial ring, when the generator polynomial is reducible. Using the algorithm, we break an 80-bit security instance of the Lapin cryptosystem

    Dihedral codes with prescribed minimum distance

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    Dihedral codes, particular cases of quasi-cyclic codes, have a nice algebraic structure which allows to store them efficiently. In this paper, we investigate it and prove some lower bounds on their dimension and minimum distance, in analogy with the theory of BCH codes. This allows us to construct dihedral codes with prescribed minimum distance. In the binary case, we present some examples of optimal dihedral codes obtained by this construction.Comment: 13 page

    Modern Cryptography Volume 1

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    This open access book systematically explores the statistical characteristics of cryptographic systems, the computational complexity theory of cryptographic algorithms and the mathematical principles behind various encryption and decryption algorithms. The theory stems from technology. Based on Shannon's information theory, this book systematically introduces the information theory, statistical characteristics and computational complexity theory of public key cryptography, focusing on the three main algorithms of public key cryptography, RSA, discrete logarithm and elliptic curve cryptosystem. It aims to indicate what it is and why it is. It systematically simplifies and combs the theory and technology of lattice cryptography, which is the greatest feature of this book. It requires a good knowledge in algebra, number theory and probability statistics for readers to read this book. The senior students majoring in mathematics, compulsory for cryptography and science and engineering postgraduates will find this book helpful. It can also be used as the main reference book for researchers in cryptography and cryptographic engineering areas

    Modern Cryptography Volume 1

    Get PDF
    This open access book systematically explores the statistical characteristics of cryptographic systems, the computational complexity theory of cryptographic algorithms and the mathematical principles behind various encryption and decryption algorithms. The theory stems from technology. Based on Shannon's information theory, this book systematically introduces the information theory, statistical characteristics and computational complexity theory of public key cryptography, focusing on the three main algorithms of public key cryptography, RSA, discrete logarithm and elliptic curve cryptosystem. It aims to indicate what it is and why it is. It systematically simplifies and combs the theory and technology of lattice cryptography, which is the greatest feature of this book. It requires a good knowledge in algebra, number theory and probability statistics for readers to read this book. The senior students majoring in mathematics, compulsory for cryptography and science and engineering postgraduates will find this book helpful. It can also be used as the main reference book for researchers in cryptography and cryptographic engineering areas

    Coding theory:a Gröbner basis approach

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    Good Gottesman-Kitaev-Preskill codes from the NTRU cryptosystem

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    We introduce a new class of random Gottesman-Kitaev-Preskill (GKP) codes derived from the cryptanalysis of the so-called NTRU cryptosystem. The derived codes are good in that they exhibit constant rate and average distance scaling Δn\Delta \propto \sqrt{n} with high probability, where nn is the number of bosonic modes, which is a distance scaling equivalent to that of a GKP code obtained by concatenating single mode GKP codes into a qubit-quantum error correcting code with linear distance. The derived class of NTRU-GKP codes has the additional property that decoding for a stochastic displacement noise model is equivalent to decrypting the NTRU cryptosystem, such that every random instance of the code naturally comes with an efficient decoder. This construction highlights how the GKP code bridges aspects of classical error correction, quantum error correction as well as post-quantum cryptography. We underscore this connection by discussing the computational hardness of decoding GKP codes and propose, as a new application, a simple public key quantum communication protocol with security inherited from the NTRU cryptosystem.Comment: 23 pages, 10 figures, comments welcome! Version 2 has minor correction
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