Kriptografi Anabilim Dalı (disiplinlerarası)

CAN (controller area network) için güvenli haberleşme protokolü

The widespread communication of vehicles with each other and road infrastructure has raised concerns about how to ensure network security of the electronic control units (ECUs) in the vehicle. The fact that networks such as the Controller Area Network (CAN), which is commonly used in in-vehicle communications, will also be connected to external networks (e.g. 3G / 4G mobile networks) will allow malicious adversaries to benefit from the vulnerability of the CAN. The authentication of messages of ECUs in the vehicle is required to ensure that in-vehicle communications are secured. However, the cryptographic algorithms and protocols that can be used for this message verification process should be selected considering the real-time communication requirement in the vehicle.

Kriptografide yüksek performanslı sayı kuramsal dönüşümler

Theoretical advances in physics opened up a new window into quantum computation. This window rendered a number of mathematically hard problems unusable for cryptographic applications. For instance, Shor showed that it is possible factor integers by a quantum algorithm efficiently thus rendering the standard public-key encryption scheme RSA insecure. In February 2016, NIST launched a standardization process for post-quantum cryptography algorithms to study the effect of quantum computing on the current generation of cryptographic algorithms and to build the next generation cryptosystems that are resistant to quantum attacks. One type of quantum safe cryptographic systems is based on lattices. In order to improve the performance in lattice based systems, Number Theoretic Transforms (NTT) are used. In this thesis, the performance of NTT in cryptography is studied. First, Peikert's Scheme and its realization BCNS Algorithm and NewHope key encapsulation method is discussed. Next, SWIFFTX hash function that uses NTT as a building block is presented. Finally, an efficient GPU implementation of SWIFFTX hash function is provided. Experimental results indicate almost 10x improvement in speed and 5 Watts decrease in power consumption per 2 16 hashes.

Gerçekleme ataklarına karsı matematıksel tedbırler

Parola tabanlı kimliği doğrulanmış anahtar değişim protokolleri üzerine

Authentication and key agreement protocols play an important role in today's digital world. Key agreement methods mostly mimic Diffie-Hellman key exchange protocol, but unfortunately they are susceptible to man-in-the-middle attacks. Password based authenticated key exchange (PAKE) protocols promise to handle these key agreement and authentication without requiring existence of certificate authorities or trusted third parties. More importantly, PAKE protocols enable agreement on low-entropy passwords rather than high-entropy cryptographic keys shared by only involved parties. Even if PAKE protocols are not widely used in practice, they are already included in IEFT (RFC), ISO security standards and TLS cryptographic suite. In this thesis, by following these recent developments, we first present these PAKE protocols in three forms, namely balanced PAKE protocols, augmented PAKE protocols and password authenticated key retrieval (PAKR) protocols and within both single and multi server settings. Particularly, we revisit EKE, SPEKE, PAK, PPK, J-PAKE, SPAKE, SESPAKE balanced, and SRP, AugPAKE, OPAQUE, B-SPEKE augmented protocols. Then, we summarize security attacks to these protocols. Afterwards, detailed explanations of the attacks against these protocols are given. We further present current state of the art for PAKE protocols. Finally, we draw attention to possible extensions for PAKE protocols and state currently open questions about the subject.

Hafif siklet kriptografi üzerine bir çalışma

Technology is evolving rapidly and with technology, the internet is also changing. People used to use internet to connect to each other. But with the changes in recent years, the internet is starting to be used more to connect devices to each other. These devices can range from powerful computing devices, such as desktop computers and tablets, to resource contrained devices, such as RFID tags and sensor networks. When it comes to these constrained devices, conventional cryptographic algorithms fail to provide necessary security and performance. Therefore, specific algorithms, designed with the limitations of constrained devices in mind, called lightweight algorithms are needed. For this reason, NIST has started a Lightweight Cryptography Project to standardize lightweight algorithms. In this thesis, we first explain what lightweight cryptography is, along with its target devices and performance metrics and give two examples of lightweight algorithms, block cipher PRESENT and stream cipher TRIVIUM . After that, we summarize the Lightweight Cryptography Project and give its timeline. Lastly, we talk about ASCON , one of the second round algorithms of the Lightweight Cryptography Project.

Kimlik ve özellik tabanlı eşleme tabanlı kimlik doğrulama protokolleri

Authentication is one of the most important goals in cryptography. It provides sharing information with only authorized people and protecting data from being modified. Authentication can be achieved in various ways such as password-based, symmetric-key and public-key. The public-key authentication is the most preferred one among these options. It provides construction of key pairs and verification with based on hard mathematical problems. Public-key authentication is used as a basis for two important idea: Identity-Based Authentication (IBA) and Attribute-Based Authentication (ABA). The IBA systems are actually specialized publickey encryption systems where the public key is generated using an identity information of the user. ABA systems, which are the other important idea, are the generalizations of the IBA systems. While IBA systems cover only one attribute about users, ABA systems cover more than one attribute. In this thesis, identity-based and attribute-based authentication protocols are analyzed and a new attribute based authentication protocol is proposed. First, it is given the details and comparison of ID-based authentication protocols Shim,Yuan and Li, Tseng 2017 and Tseng 2015 which are based on elliptic curve. Shim,Yuan and Li and Tseng 2017 use pairings for authentication, while Tseng 2015 uses hash functions. Their securities and performances are analyzed. They provide the security properties such as known-key security, forward secrecy, key-compromise impersonation and unknown-key share. They also resist the passive, man-in-the-middle and reveal attacks. The protocols are more efficient than the protocols which are based on public-key by virtue of elliptic curve. Tseng 2015 is the most efficient one among them since it uses only hash functions. Also, the Zhang, Mu and Zhang attribute-based authentication protocol is studied. Then a new protocol, which is inspired from it, is designed. While Zhang et al. is based on public-key, the new protocol is constructed on elliptic curve basis. Moreover, controlling of attributes is simplified. It decreases the number of operations to determine necessary attributes. In this way, computational cost is reduced. The security analysis of the new protocol is presented and showed that the protocol is resistant to the following attack scenarios; adaptive chosen ciphertext, keycompromise impersonation, probing resistance, indistinguishable to eavesdroppers, forward secrecy and unknown key-share.

Kafes tabanlı algoritmaların verimli gerçeklenmesi

Quantum computing and quantum computers have been discussed for almost three decades. However, they remain mainly in theory. Almost all big companies like Google, IBM, and Microsoft have put their effort to build the most scalable quantum computers in recent years. These computers can change the game in cryptography since the known hard problems such as integer factorization and discrete logarithms can be broken with a large-scale quantum computer. These computers would seriously jeopardize the confidentiality and integrity of all digital communications. The question of when large-scale quantum computers will be built is still an open question. There are some educated predictions that sufficiently large quantum computers will be built to break all public-key schemes currently in use within the next ten or so years. That is why the National Institute of Standards and Technology (NIST) has announced a standardization process in 2016 to prepare our information security systems to be able to resist in quantum computing. The first two rounds of this process have been completed, and there are seven on-going candidates and eight alternate candidates. Among these 15 schemes, seven of them are based on lattices. In this thesis, we study the efficient implementation of lattice-based schemes. We first propose an efficient and compact variant of NewHope, one of the most efficient second-round candidates of the NIST post-quantum standardization project. The proposed algorithm NewHope-Compact heavily uses recent advances on Number Theoretic Transform (NTT), so that transformation from one polynomial to another is easy. To make it possible, we changed the definition of a component in component-wise multiplication during polynomial multiplication and show that changing the security level only requires to change the size of the polynomial and the definition of a component. Then, we present various optimizations for lattice-based KEMs using the NTT on the popular ARM Cortex-M4 microcontroller. Improvements come in the form of a faster code using more efficient modular reductions, optimized small-degree polynomial multiplications, and more aggressive layer merging in the NTT, but also in the form of reduced stack usage. We test our optimizations in software implementations of Kyber, one of the round three candidates in the NIST post-quantum project, NewHope, and NewHope-Compact.

FIPS 140 ve ISO/IEC 15408'e göre şifreleme modülleridoğrulama süreci

With the advancement of technology, questions have arisen regarding the reliability of information technology products. Some standards have emerged to ensure the reliability of these products and to validate this reliability internationally. One of the standards issued to meet this need is ISO/IEC 15408 Common Criteria Standard. Thanks to this standard, the relevant institutions authorized to evaluate information technology products are evaluated and the reliability of this product is provided by the certificates issued by the competent authorities. In addition to this standard, the FIPS 140 standard has been created, which specifies the requirements of cryptographic modules specifically and is used for the approval and verification of these modules. This standard is used to determine the reliability of cryptographic modules. In this thesis, we first define these standards and how the evaluation process in accordance with them takes place in the world and how they should be implemented in Turkey. Then, we discuss the vulnerabilities of the AES-GCM algorithm in order to prevent the vulnerabilities of the cryptographic algorithms used in the cryptographic algorithm verification process, which is a part of the cryptographic module verification process, and talk about alternative AES modes. Finally, we complete the thesis by talking about test vectors that help us detect these vulnerabilities.

Permütasyon polinomları ve bükülmüş fonksiyonların inşası

This thesis consists of two main parts: In the first part, a study of several classes of permutation and complete permutation polynomials is given, while in the second part, a method of construction of several new classes of bent functions is described. The first part consists of the study of several classes of binomials and trinomials over finite fields. A complete list of permutation polynomials of the form f(x)=x^{(q^n-1)/(q-1)+ 1} + b x in F_{q^n}[x] is obtained for the case n=5, and a criterion on permutation polynomials of the same type is derived for the general case. Furthermore, it is shown that when q is odd, trinomials of the form f(x)= x^5 h(x^{q-1}) in F_{q^2}[x], where h(x)=x^5+x+1 never permutes F_{q^2}. A method of constructing several new classes of bent functions via linear translators and permutation polynomials forms the second part of the thesis. First, a way to lift a permutation over F_{2^t} to a permutation over F_{2^m} is described, where t | m. Then, via this method, 3-tuples of particular permutations that lead to new classes of bent functions are obtained. As a last step, the fact that none of the bent functions obtained here will be contained in Maiorana-McFarland class is proved.

Sıfır bilgi aralık ispatları ve dağıtık sistemlerdeki uygulamaları

Appropriate, effective, and efficient use of cryptographic protocols contributes to many novel advances in real-world privacy-preserving constructions. One of the most important cryptographic protocols is the zero-knowledge proofs. The zero-knowledge proofs have recently gained the utmost importance in terms of decentralized systems, especially in the context of privacy. In many decentralized systems, such as electronic voting, e-cash, e-auctions, or anonymous credentials, the zero-knowledge range proofs are used as the building blocks. In this thesis, we examine, summarise and compare range proofs based on zero-knowledge proofs, and examine their applications in decentralized systems such as distributed ledgers, confidential assets and smart contracts. We also, investigate different basis of OR-proofs and compare the efficiency of different basis approaches. To this end, we have modified the Mao's range proof to base-3 with a modified OR-proof. For each basis, we derive the number of computations in modulo exponentiations and the cost of numbers exchanged between parties. Then, we have generalized these costs for base-u construction. At the end of these comparisons, we observe that comparing the number of computations in modulo exponentiations with other base approaches, the base-3 approach is 5.5% more efficient. In addition, comparing the cost of numbers exchanged between prover and verifier, base-3 approach is 7% more efficient than other base approaches.

Stark dostu simetrik anahtar ilkellerine karşı Gröbner baz saldırısı: JARVIS, MiMC ve GMiMCerf

A number of arithmetization-oriented ciphers emerge for use in advanced cryptographic protocols such as secure multi-party computation (MPC), fully homomorphic encryption (FHE) and zero-knowledge proofs (ZK) in recent years. The standard block ciphers like AES and the hash functions SHA2/SHA3 are proved to be efficient in software and hardware but not optimal to use in this field, for this reason, new kind of cryptographic primitives proposed. However, unlike traditional ones, there is no standard approach to design and analyze such block ciphers and the hash functions, therefore their security analysis needs to be done carefully. In 2018, StarkWare launched a public STARK-Friendly Hash (SFH) Challenge to select an efficient and secure hash function to be used within ZK-STARKs, transparent and post-quantum secure proof systems. The block cipher JARVIS is one of the first ciphers designed for STARK applications but, shortly after its publication, the cipher has been shown vulnerable to Gröbner basis attack. This master thesis aims to describe a Gröbner basis attack on new block ciphers, MiMC, GMiMCerf (SFH candidates) and the variants of JARVIS. We present the complexity of Gröbner basis attack on JARVIS-like ciphers, results from our experiments for the attack on reduced-round MiMC and a structure we found in the Gröbner basis for GMiMCerf.

Uzun diziler için yeni bir hafif sıklet istatistiksel rastgelelik test paketi ve diğer test paketleriyle değerlendirmeli olarak karşılaştırılması

Playing rolling dice or toss a coin is fair or not depends on whether the materialplayed is fair or not. Generating a random number is equivalent to both dice and coingame. Random numbers have a wide usage area. Hence generating a random numberis very important, and it should be fair. In other words, the generator should not haveany bias. Using statistical randomness tests, we can determine whether a generatorgenerates random numbers or not, that is, whether the generated numbers follow apattern or not. In the literature, there are many statistical randomness tests. Some ofthese tests were selected, and they form a test suite. While defining a randomness testsuit, the suites in the literature, the features of the sequences are not considered. Inthis thesis, a test suite is proposed to test a long sequence. Some tests in the literatureare already in a suitable format to be applied to long sequences. In addition, someapproximations have been used to apply those tests designed for relatively shortersequences to long sequences, or the sequences have been manipulated using to makethem suitable for those tests while ignoring whether manipulations damage the struc-ture of sequence or not. It has been evaluated that the test suites in the literature usingsuch manipulations to long sequences may give incomplete results. In this thesis, theappropriate tests in the literature are modified into long sequence tests using threedifferent methods, and new long sequence tests are proposed. Sequences generatedfrom true and pseudo-random number generators are tested with the proposed test suite. By collecting proposed tests together according to their time performance, su-per lightweight and lightweight test suites are proposed. The mutual correlation ofthe tests with each other is evaluated. Sensitivities to bias sequences are tested andcompared with tests in the literature.

Kriptografik yanlış kullanım tespit eden araçlar

Today digital devices are an inevitable part of our lives. We use these devices for things like sharing photos, communicating with friends, and exchanging money. All these actions need privacy. In fact, properly used cryptographic systems can fulfill this need for privacy. However, in some cases developers can make mistakes, because of the reason such as lack of knowledge about cryptography and hard usage of cryptographic APIs. Thus, cryptographic misuse detection has become a new field of study and tools have begun to be designed to detect these misuses. In this study, we discuss 11 detection tools. They are CryptoLint [61], CMA [87], CDRep [77], sPECTRA [68], BinSight [79], CHIRON [85], CryptoGuard [84] and CRYLOGGER [83] in Android platform; iCryptoTracer [76] and Automated Binary Analysis [65] on iOS platform and CRYPTOREX [94] on IoT platform. Moreover, we give a comprehensive rule set and discuss shortcomings of each tool to contribute to future studies.

Maksimum rank uzaklıklı bazı kodların uygulanması üzerine çalışmalar

With the development of quantum computers that can process much faster than classical computers, the classical cryptosystems used today began to be strengthened or replaced with other cryptosystems. Parallel to this aim, studies for faster and more effective use of cryptosystems using coding theory have also increased. In this thesis, coding and decoding of maximum rank distance codes was implemented using programming.

Değiştirilen ters fonksiyonun c-diferensiyel tekdüzeliği üzerine bazı çalışmalar

Lately, Ellingsen et al created a new concept by making minor changes on the old concept of (multiplicative) differential. This new definition which has potential to be capable of extending differential cryptanalysis in a completely new way is named as c-differential and brought with it the concept of c-differential uniformity. We examlify that how some known functions' behaviour, especially inverse function, would be under this extended differential. The main purpose of this thesis is to observe how the swapped inverse function, which is one of the variety of ways to modify the binary inverse function, impacts the function's c-differential uniformity. In this thesis, we proposed a new theorem including the new characterization of the $(0,\alpha)$-swapped inverse function in even characteristic under this new concept, $x^{2^n-2}+x^{2^n-1}/\alpha+(x-\alpha)^{2^n-1}/\alpha$ on $\matbb{F}_{2^n}$, and reached two conclusions for all $c\neq1$: we prove that its c-differential uniformity value can take 1,2,3 and 4 and attains its maximum value 4 under two special conditions satisfied by the trace mapping.

Ters fonksiyonun CCZ-denkliği üzerine bazı çalışmalar

Most cryptographic systems, like block ciphers, depend heavily on vectorial Boolean functions. A function with good cryptological properties should have low differential uniformity which is invariant under some equivalence classes. The more general one of these is CCZ-equivalence which is introduced by Carlet, Charpin and Zinoviev in 1998. In cryptography, CCZ-equivalence gained an interest since it preserves many significant properties like differential uniformity. Looking for permutations within the CCZ-class of a function for the construction of S-boxes used in block ciphers is also intriguing. In this thesis, we presented a detailed description on the results of Kölsch's paper about nonexistence of permutation polynomials in the form $L_m(x^{-1})+L_{m'}(x)$ over binary finite field. This proves that every permutation CCZ-equivalent to the inverse function is also affine equivalent to it. We also gave a criterian to be a permutation polynomial which is verified by using Kloosterman sums. }

Karışık tamsayılı doğrusal programlama yaklaşımı kullanılarak SP ağı tabanlı şifreleme algoritmalarının güvenlik limitlerinin hesaplanması üzerine

Block ciphers are one of the symmetric key encryption algorithms that are used in many devices. Its increasing popularity has led to the emergence of new cryptanalysis methods. Therefore, measuring block cipher's security bounds is one main indispensable need for its designers. Two of the most effective attacks on block ciphers are differential and linear cryptanalysis and these attacks' efficiencies are bonded with a number of active S-boxes of the cipher after a certain number of rounds. Consequently, measuring the number of active S-boxes is one of the techniques to measure the security bounds. There are various methods to calculate this number, both mathematically, and automatically. This thesis focuses on computing the minimum number of active S-boxes automatically, more specifically, using an optimization method called Mixed Integer Linear Programming, a method that achieved noticeable success across both the industrial and academic world. In this thesis, a summary of the studies in the literature on how to calculate the minimum number of active S-boxes with MILP will be given, the author's own ideas on this subject will also be shared, and the performance results of recent works and author's ideas will be compared.

İkilik tabanda polinomların çarpımının analizi ve uygulanması

N. Koblitz and V. Miller originally proposed the concept of elliptic curve cryptography in 1985. It is fast gaining popularity in public key cryptosystems as it boasts of an advantage over current public key cryptosystems, that is, the requirement of the key size be smaller and still maintain the same level of security. It takes advantage of elliptic curves' mathematical properties in finite fields. Elliptic curve cryptographic systems perform operations on points on elliptic curves. Elliptic curves can be represented over prime fields and can also be represented over binary fields. In the binary field representation, the elements of these finite fields are binary polynomials. Polynomial multiplication is a key operation in binary field elliptic curve cryptographic implementation and hence an area of interest in cryptography. In this thesis,we analyse some polynomial multiplication algorithms over binary fields. For 2-way algorithms we investigate schoolbook, Karatsuba and refined Karatsuba and for 3-way algorithms we investigate schoolbook, Karatsuba and CNH 3-way split algorithms. We define a 64-bit by 64-bit multiplication as the smallest unit of computation for a polynomial multiplication which can also be improved by the sliding window method. We have observed that an optimal size of eight for the window size is attained with a time memory trade off.