Secret Key Cryptosystem based on Non-Systematic Polar Codes

Polar codes are a new class of error correcting linear block codes, whose generator matrix is specified by the knowledge of transmission channel parameters, code length and code dimension. Moreover, regarding computational security, it is assumed that an attacker with a restricted processing power has unlimited access to the transmission media. Therefore, the attacker can construct the generator matrix of polar codes, especially in the case of Binary Erasure Channels, on which this matrix can be easily constructed. In this paper, we introduce a novel method to keep the generator matrix of polar codes in secret in a way that the attacker cannot access the required information to decode the intended polar code. With the help of this method, a secret key cryptosystem is proposed based on non-systematic polar codes. In fact, the main objective of this study is to achieve an acceptable level of security and reliability through taking advantage of the special properties of polar codes. The analyses revealed that our scheme resists the typical attacks on the secret key cryptosystems based on linear block codes. In addition, by employing some efficient methods, the key length of the proposed scheme is decreased compared to that of the previous cryptosystems. Moreover, this scheme enjoys other advantages including high code rate, and proper error performance as well

Matris kodlar ile McEliece şifreleme sistemi

06.03.2018 tarihli ve 30352 sayılı Resmi Gazetede yayımlanan “Yükseköğretim Kanunu İle Bazı Kanun Ve Kanun Hükmünde Kararnamelerde Değişiklik Yapılması Hakkında Kanun” ile 18.06.2018 tarihli “Lisansüstü Tezlerin Elektronik Ortamda Toplanması, Düzenlenmesi ve Erişime Açılmasına İlişkin Yönerge” gereğince tam metin erişime açılmıştır.Bilgi çağında yaşadığımız bu günlerde bilginin transferi (internet, cep telefonları, bankacılık vs. ) ya da depolanması (CD vs.) aşamasında meydana gelebilecek bilgi zedelenmelerini koruma ve düzeltme amacıyla kodlama kullanılmaktadır. Bu anlamda kullanılan kodlar içinde lineer kodlar önemli bir yer tutmaktadır. Lineer kodlar ailesinin içinden olan matris kodlar zengin bir yapıya sahiptir. Ayrıca, matris kodlar ile hata düzeltme kabiliyetleri artmakta ve bunun sonucunda bilgi daha güvenilir iletilmektedir.Bu tez altı bölümden oluşmaktadır. Birinci bölümde, tanımlar ve teoremler verilmiştir.İkinci bölümde, şifreleme ve şifreleme sistemlerinin işleyişi ele alınmıştır.Üçüncü bölümde, kodlama ile ilgili temel tanım ve teoremler verilmiştir. Ayrıca lineer kodların cebirsel yapıları ve dekodlaması ile ilgili tanım ve teoremler verilmiştir.Dördüncü bölümde, sonlu cisim üzerinde tanımlanan matris kodlar ile ilgili tanımlar işlenmiştir. Ayrıca matris kodların işleyişi ele alınmıştır.Beşinci bölümde, McEliece şifreleme sistemi incelenmiş ve matris kodlar, McEliece şifreleme sistemine uygulanmıştır.Anahtar kelimeler: Lineer kodlar, matris kodlar, McEliece şifreleme sistemiAltıncı ve son bölüm, sonuç ve öneriler kısmından oluşmuştur.As we live in the information age, coding is used in order to protect or correct the messages in the transferring (via internet, mobile phones, banking, etc.) or the storing (CD,etc.) processes. So, linear codes are important in the transferring or the storing. Due to richness of their structure array codes which are linear are also an important codes. However, the information is then transferred into the source more securely by increasing the error correction capability with array codes.This thesis consists of six chapters. In the first chapter, some basic definitions of abstract algebra are given.In the second chapter, cryptology and the process of some classical cryptosystems are discussed.In the third chapter, some basic definitions and theorems associated with coding theory is given. However, some basic definitions and theorems associated with the algebraic structure and decoding of linear codes are given.In fourth chapter, the definitions of array codes over finite field are discussed. Moreover, the process of array codes is given.In the fifth chapter, the McEliece cryptosystem with array codes is given and their applications to the array codes are investigated.Key Words: Linear codes, array codes, McEliece cryptosystemIn the sixth and the last chapter, the conclusion and the future works are given

On Private-Key Cryptosystems Based on Product Codes

. Recently J. and R.M. Campello de Souza proposed a private-key encryption scheme based on the product codes with the capability of correcting a special type of structured errors. In this paper, we show that J. and R.M. Campello de Souza's scheme is insecure against chosen-plaintext attacks, and consequently propose a secure modified scheme. 1 Introduction In 1978, McEliece [1] proposed a public-key cryptosystem based on algebraic coding theory. The idea of the cryptosystem is based on the fact that the decoding problem of a general linear code is an NP-complete problem. Compared with other public-key cryptosystems [2,3], McEliece's scheme has the advantage of high-speed encryption and decryption. However, the scheme is subjected to some weaknesses [4,5]. Rao and Nam [6,7] modified McEliece's scheme to construct a private-key algebraic-code cryptosystem which allows the use of simpler codes. The Rao-Nam system is still subjected to some chosen-plaintext attacks [7-10], and therefore is..