In this thesis, we study hash functions. We focus mainly on the famous Merkle-Damg˚ard construction and its generalisation. We show that even this generalised construction is not resistant to multicollision attacks. Combinatorics on words plays a fundamental role in the construction of our attack. We prove that regularities unavoidably appear in long words with bounded number of symbol occurences. We present our original results concerning regularities in long words. We lower some earlier published estimates, thus reducing the comlexity of the attack. Our results show that generalised iterated hash functions are interesting rather from the theoretical than practical point of view. 1

Cryptography is the art of protecting information by encrypting the original message into an unreadable format. A cryptographic hash function is a hash function which takes an arbitrary length of the text message as input and converts that text into a fixed length of encrypted characters which is infeasible to invert. The values returned by the hash function are called as the message digest or simply hash values. Because of its versatility, hash functions are used in many applications such as message authentication, digital signatures, and password hashing [Thomsen and Knudsen, 2005]. The purpose of this study is to apply Huffman data compression algorithm to the SHA-1 hash function in cryptography. Huffman data compression algorithm is an optimal compression or prefix algorithm where the frequencies of the letters are used to compress the data [Huffman, 1952]. An integrated approach is applied to achieve new compressed hash function by integrating Huffman compressed codes in the core functionality of hashing computation of the original hash function.

Recent years have witnessed several real threats to the most widely used hash functions which are generally inspired from MD4, such as MD5, RIPEMD, SHA0 and SHA1. These extraordinary developments in cryptanalysis of hash functions brought the attention of the cryptology researchers to the alternative designs. Tiger is an important type of alternative hash functions and is proved to be secure so far as there is no known collision attack on the full (24 rounds) Tiger. It is designed by Biham and Anderson in 1995 to be very fast on modern computers. In two years some weaknesses have been found for Tiger-hash function. First, in FSE 006 Kelsey and Lucks found a collision for 16-17 rounds of Tiger and a pseudo-near-collision for 20 rounds. Then, Mendel et al extended this attack to find 19-round collision and 22-round pseudo-near-collision. Finally in 2007, Mendel and Rijmen found a pseudo-near-collision for the full Tiger. In this work, we modify the attack of Kelsey and Lucks slightly and present the exact values of the differences used in the attack. Moreover, there have been several cryptanalysis papers investigating the randomness properties of the designed hash functions under the encryption modes. In these papers, related-key boomerang and related-key rectangle attacks are performed on MD4,MD5, HAVAL and SHA. In this thesis, we introduce our 17,19 and 21-round related-key boomerang and rectangle distinguishers to the encryption mode of Tiger.

One of the most basic properties expected from block ciphers and hash functions is passing statistical randomness testing, as they are supposed to behave like random mappings. Previously, testing of AES candidate block ciphers was done by using the statistical tests defined in the NIST Test Suite. As some of the tests in this suite require long sequences, data sets are formed by concatenating the outputs of the algorithms obtained from various input types. However, the nature of block cipher and hash function algorithms necessitates devising tests and test parameters focused particularly on short sequences, therefore we propose a package of statistical randomness tests which produce reliable results for short sequences and test the outputs of the algorithms directly rather than concatenations. Moreover, we propose an alternative method to evaluate the test results and state the required computations of related probabilities for the new evaluation method. We also propose another package of statistical tests which are designed basing on certain cryptographic properties of block ciphers and hash functions to evaluate their randomness, namely the cryptographic randomness testing. The packages are applied to the AES finalists, and produced more precise results than those obtained in similar applications. Moreover, the packages are also applied to SHA-3 second round candidate algorithms.

In large-scale distributed systems, where adversarial attacks can have widespread impact, authentication provides protection from threats involving impersonation of entities and tampering of data. Practical solutions to authentication problems in distributed systems must meet specific constraints of the target system, and provide a reasonable balance between security and cost. The goal of this dissertation is to address the problem of building practical and efficient authentication mechanisms to secure distributed applications. This dissertation presents techniques to construct efficient digital signature schemes using trapdoor hash functions for various distributed applications. Trapdoor hash functions are collision-resistant hash functions associated with a secret trapdoor key that allows the key-holder to find collisions between hashes of different messages. The main contributions of this dissertation are as follows: 1. A common problem with conventional trapdoor hash functions is that revealing a collision producing message pair allows an entity to compute additional collisions without knowledge of the trapdoor key. To overcome this problem, we design an efficient trapdoor hash function that prevents all entities except the trapdoor key-holder from computing collisions regardless of whether collision producing message pairs are revealed by the key-holder. 2. We design a technique to construct efficient proxy signatures using trapdoor hash functions to authenticate and authorize agents acting on behalf of users in agent-based computing systems. Our technique provides agent authentication, assurance of agreement between delegator and agent, security without relying on secure communication channels and control over an agent’s capabilities. 3. We develop a trapdoor hash-based signature amortization technique for authenticating real-time, delay-sensitive streams. Our technique provides independent verifiability of blocks comprising a stream, minimizes sender-side and receiver-side delays, minimizes communication overhead, and avoids transmission of redundant information. 4. We demonstrate the practical efficacy of our trapdoor hash-based techniques for signature amortization and proxy signature construction by presenting discrete log-based instantiations of the generic techniques that are efficient to compute, and produce short signatures. Our detailed performance analyses demonstrate that the proposed schemes outperform existing schemes in computation cost and signature size. We also present proofs for security of the proposed discrete-log based instantiations against forgery attacks under the discrete-log assumption.

Σκοπός της διπλωματικής εργασίας είναι ο σχεδιασμός και η υλοποίηση σε υλικό κρυπτογραφικών μηχανισμών με τέτοιο τρόπο έτσι ώστε να αποκτήσουν ιδιότητες αυτό-ελέγχου χρησιμοποιώντας μηχανισμούς ανίχνευσης σφαλμάτων. Για το σκοπό αυτό θα προσπαθήσουμε να επιλέξουμε μέσα από γνωστούς μηχανισμούς ανίχνευσης λαθών που είναι διαθέσιμοι στη βιβλιογραφία, αυτούς που θα μας βοηθήσουν να εισάγουμε στο σύστημά μας τις επιθυμητές ιδιότητες αυτό-ελέγχου λαμβάνοντας παράλληλα φροντίδα για την διατήρηση των ιδιαίτερων χαρακτηριστικών του. Λόγω της κρισιμότητας που έχει η διαδικασία κρυπτογράφησης είναι πολύ σημαντικό να πραγματοποιείται χωρίς σφάλματα. Πιθανά σφάλματα θα μπορούσε να τα εκμεταλλευτεί κάποιος εισβολέας ώστε να διαβάσει το περιεχόμενο του μηνύματος κατά τη διάρκεια μιας μετάδοσης ή θα μπορούσαν να προκαλέσουν λάθη στο ίδιο το μήνυμα και την hash value που του αντιστοιχεί. Για αυτούς τους λόγους θα προσπαθήσουμε να εισάγουμε στην υλοποίηση του αλγόριθμου κρυπτογράφησης μηχανισμούς ανίχνευσης σφαλμάτων ώστε να διασφαλιστεί η απροβλημάτιστη λειτουργία του. Παράλληλα λόγω των ιδιαίτερων απαιτήσεων που υπάρχουν για ένα σύστημα κρυπτογράφησης που έχουν να κάνουν με ταχύτητα επεξεργασίας και την όσο το δυνατόν μικρότερη επιφάνεια ολοκλήρωσης θα λάβουμε ιδιαίτερη φροντίδα ώστε το σύστημα μας να διατηρήσει αυτά τα επιθυμητά χαρακτηριστικά. / The purpose of this thesis is the design and implementation in hardware of cryptographic mechanisms in order to gain self-checking properties using error detection techniques. In order to do so we will try to pick through known error detection mechanisms, those who will help us apply the desired self-checking characteristics to our system while taking care to maintain its characteristics. It is critical for the encryption process to be error-free. Possible errors could be exploited by an attacker to read the contents of the message during a broadcast or could cause errors in the message itself and the hash value that corresponds. For these reasons, we try to apply error detection mechanisms to the hardware implementation of the hash algorithms in order to ensure trouble free operation. At the same time, due to the special requirements of an encryption system about high processing speed and the smallest integration area possible we will take care so as our system to maintain these desired characteristics.

Σε αυτή τη μεταπτυχιακή διπλωματική εργασία μελετήθηκαν, αναπτύχτηκαν και συγκριθήκαν αρχιτεκτονικές για κρυπτογραφικές εφαρμογές που χρησιμοποιούνται στης τεχνικές πιστοποίησης μηνυμάτων. Σε αυτές χρησιμοποιήθηκαν και τεχνικές βελτιστοποίησης της απόδοσης. Στην ασφάλεια μετάδοσης των πληροφοριών, η πιστοποίηση μηνύματος είναι μία θεμελιώδης τεχνική, η οποία χρησιμοποιείται για να επιβεβαιώσει ότι τα ληφθέντα μηνύματα προέρχονται από τον σωστό αποστολέα και ότι δεν έχουν τροποποιηθεί κατά τη μετάδοση. Στην πιστοποίηση μηνύματος, απαιτείται η χρήση ενός κώδικα πιστοποίησης μηνύματος (Message Authentication Code-MAC). Οι τεχνικές για να δημιουργηθεί ένα MAC γίνεται με δύο τρόπους: α)Με χρήση μίας hash συνάρτησης σε συνδυασμό με ένα μυστικό κλειδί και αναφέρεται σαν HMAC (Hash-based MAC). β)Με χρήση ενός block cipher αλγορίθμου κρυπτογράφησης σε συνδυασμό με ένα μυστικό κλειδί και αναφέρεται σαν CMAC (Cipher block-based MAC). Θα υλοποιηθούν οι δύο παραπάνω τρόποι-μέθοδοι παραγωγής MAC, σε πλατφόρμες υλικού με γνώμονα την αύξηση της ρυθμαπόδοσης τους. Θα αποτιμηθεί ο ρόλος τους στα κρυπτογραφικά συστήματα ασφαλείας και σε ποιές περιπτώσεις συνίσταται η χρήση της κάθε μίας τεχνικής. Έτσι θα ξεκαθαριστούν οι διαφορές τους και θα καθοριστεί το προφίλ των εφαρμογών στης οποίες κάθε μια εκ των δύο αυτών τεχνικών ταιριάζει καλύτερα. Οι υλοποιήσεις συγκριθήκαν στην ίδια πλατφόρμα υλικού που χρησιμοποιήθηκε για την τελική υλοποίηση ώστε σε κάθε περίπτωση, ανάλογα με της απαιτήσεις της εκάστοτε εφαρμογής, να βρεθεί και η βέλτιστη λύση από πλευράς κόστους. / In the present M.Sc. thesis, several architectures for message authentication codes were studied, developed and compared to each other. Performance optimization techniques were exploited as well. Message Authentication Codes (MACs) are widely used in order to protect both a message's integrity -by ensuring that a different MAC will be produced if the message has changed - as well as its authenticity (only someone who knows the secret key could have generated a valid MAC). A message authentication code is an authentication tag (also called a checksum) derived by applying an authentication scheme, together with a secret key, to a message. Typically MACs are produced through: α) HMAC mechanism which is based on a FIPS approved collision-resistant hash function in combination with a secret key (Hash-based MAC). β)CMAC mechanism which is based on a block cipher algorithm in combination with a secret key (Cipher block-based MAC). The above two ways (mechanisms) for producing MACs were designed and implemented in hardware taking into consideration the increase of their throughput. The cryptographic systems in which the above two are exploited were described. Their key role in these systems was valued through an investigation concerning the way of their incorporation. Thus, the differences between them were clarified determining the applications where each one is better befitted. HMAC and CMAC designs are implemented in the same hardware FPGA platform and compared to each other in terms of operating frequency, area consumption and throughput. In this way, the best solution between them concerning their overall cost can be designated.

The goal of this thesis is to design and implement a framework allowing password recovery in a distributed environment. The research is therefore focused on analyzing the security of passwords, techniques used for attacks on them and also presents methods preventing attacks on passwords. Described is the Wrathion tool which is allowing password recovery using acceleration on graphic cards through the integration of OpenCL framework. Conducted is also an analysis of available environments providing means to run computing tasks on multiple devices, based on which the OpenMPI platform is chosen for extending Wrathion. Disclosed are various modifications and added components, and the entire system is also subjected to experiments aiming at the measuring of scalability and network traffic performance. The financial side of the use of Wrathion tool is also discussed in terms of its usability in cloud based distributed environment.

At the end of 70th of last century the concept began to emerge, now is referred as a cryptographic hash function. Currently, these functions are associated especially with a digital signature. In 2005, the worldwide most used function SHA-1 was broken. This fact led in 2007 NIST announced a public competition to create a new secure hash algorithm. This Thesis deals with issues of cryptographic hash functions from the beginning of their theoretical formulation to current events in this area. Key words: Cryptographic hash functions, SHA-1, MD5, NIST competition

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