Kriptografi Anabilim Dalı (disiplinlerarası)

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.

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.

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.

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.