سيستم رمزنگاري مك آليس با كدهايLDPC

چكيده انگليسي :

McEliece Cryptosystem with LDPC Codes Mostafa Esmaeili mostafa esmaeili@ec iut ac ir 21 November 2011 Department of Electrical and Computer Engineering Isfahan University of Technology Isfahan 84156 83111 Iran Degree M Sc Language Farsi Supervisor Dr Mohammad Dakhilalian mdalian@ec iut ac irAbstractWith the wide spread of communications demands for reliable and secure data transmission is growing Areliable communication can be obtained via channel coding Designing channel codes started in 1948 withShannon s theorem In this theorem it is proven that codes with rates arbitrarily close to the channel capacityexist with error decoding probability arbitrarily close to zero In 1960 codes with sparse parity check matriceswere introduced but were mostly ignored in the next 30 years These codes were re discovered in the 1990 sand have been subject to many research projects Some classes of these codes e g QC LDPC codes have beenused in standards in Mobile Wireless WAN Secure transmission of data is achieved via cryptography Althoughthere exist many secure cryptosystems a system which could combine encoding encryption decoding decryption would be very useful in communication systems The first system of this kind wasintroduced by McEliece in 1978 known as the McEliece public key cryptosystem The security of this system isbased on the fact that generally decoding a linear code is a NP problem In this system the bits of a plain textare scrambled bits of the codeword associated with it are permuted and some of them are randomly changed Two main drawbacks of the McEliece cryptosystem is its large key size in order to hide the generator matrix ofthe applied code in the public key and low information rate During the last 33 years many variants of theMcEliece cryptosystem have been introduced some have changed the code used in it others have changed thestructure of the scrambler and permutation matrices and some have changed the method of changing the bits ofthe codeword But in all of these systems either one of the two problems remain unsolved or the cryptosystemhas a low level of security In this thesis a new symmetric key cryptosystem based on randomly puncturing aQC LDPC code is proposed A pseudo random number generator is applied to determine which bits of acodeword should be punctured One of the advantages of this cryptosystem is that with the absence of apermutation and scrambler matrices the key size has been reduced and codes with rates as high as 0 875 can beused which also increases the information rate Based on computer simulations of a parent code and itsassociated punctured code suggested amounts of how many bits can be punctured is provided It is shown thateven with small amounts of punctures the system is secure It is also shown that if an eavesdropper is providedwith the code that is used the system can remain secure This is a unique characteristic that previous algebraiccoded cryptosystems did not possess In similar cryptosystems if the applied code is revealed the system isbroken This is why the generator or parity check matrix of the applied code is part of the key or part of theprivate key in public key algebraic coded cryptosystems Key WordsCoding cryptography LDPC codes puncturing pseudo random number generator

اسماعيلي، مصطفي

سيستم رمزنگاري مك آليس با كدهايLDPC

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