Maiorana-McFarland Functions with High Second-Order Nonlinearity

The second-order nonlinearity, and the best quadratic approximations, of Boolean functions are studied in this paper. We prove that cubic functions within the Maiorana-McFarland class achieve very high second order nonlinearity, which is close to an upper bound that was recently proved by Carlet et al., and much higher than the second order nonlinearity obtained by other known constructions. The structure of the cubic Boolean functions considered allows the efficient computation of (a subset of) their best quadratic approximations

Modifying Boolean Functions to Ensure Maximum Algebraic Immunity

The algebraic immunity of cryptographic Boolean functions is studied in this paper. Proper modifications of functions achieving maximum algebraic immunity are proved, in order to yield new functions of also maximum algebraic immunity. It is shown that the derived results apply to known classes of functions. Moreover, two new efficient algorithms to produce functions of guaranteed maximum algebraic immunity are developed, which further extend and generalize known constructions of functions with maximum algebraic immunity

Cryptography as the Means to Protect Fundamental Human Rights

Cryptography is traditionally considered as a main information security mechanism, providing several security services such as confidentiality, as well as data and entity authentication. This aspect is clearly relevant to the fundamental human right of privacy, in terms of securing data from eavesdropping and tampering, as well as from masquerading their origin. However, cryptography may also support several other (legal) requirements related to privacy. For example, in order to fulfil the data minimisation principle—i.e., to ensure that the personal data that are being processed are adequate and limited only to what is necessary in relation to the purposes for which they are processed—the use of advanced cryptographic techniques such as secure computations, zero-knowledge proofs or homomorphic encryption may be prerequisite. In practice though, it seems that the organisations performing personal data processing are not fully aware of such solutions, thus adopting techniques that pose risks for the rights of individuals. This paper aims to provide a generic overview of the possible cryptographic applications that suffice to address privacy challenges. In the process, we shall also state our view on the public “debate” on finding ways so as to allow law enforcement agencies to bypass the encryption of communication

Signal processing techniques in cryptography

Cryptography is the study of mathematical techniques concerning telecommunication security stream ciphers comprise an important class of cryptographic algorithms. Shift registers with linear (LFSR) or nonlinear (FSR) feedback are the basic building blocks in stream ciphers. The security of these systems is mainly attributed to pseudorandom characteristics of the keystreams. Amongst the cryptographic measures of a sequence is its complexity defined as the length of the shortest FSR that generates the sequence. Especially the linear complexity is important for assessing resistance to cryptanalytic attacks like the Berlekamp-Massey algorithm (BMA). Hence high linear complexity is prerequisite for keystreams. Such sequences are generated by applying nonlinear Boolean functions either as filters or combiners. However resistance of cryptosystems to various attacks is also associated with properties of the functions used. Determining the connections between several cryptographic criteria of sequences remains an open problem. In this thesis, pseudorandom properties of sequences are studied, by using system theoretic concepts. A new unified approach for analyzing the linear complexity is developed via controllability and observability conditions applied to sequence generators. A new generalized Fourier transform is introduced allowing the generation of sequences with prescribed linear complexity. Moreover new classes of nonlinear filters are constructed which guarantee high values of the linear complexity. Furthermore the nonlinear complexity of binary sequences and its connections to other cryptographic criteria is studied. A new efficient recursive algorithm is presented, which produces the minimal FSR of a given sequence, thus generalizing the BMA to the nonlinear case. Connections between nonlinear complexity and Lempel-Ziv complexity are also established. Moreover a lower bound for the Lempel-Ziv compression ratio of a sequence is proved which depends on its nonlinear complexity. Finally the problem of computing best quadratic approximations of Boolean functions is studied. Efficient formulas for computing such approximations for a class of functions with degree 3 and 4 are proved. The methodology is independent from the number of variables and reveals new design principles for cryptographic functions. An analysis of recently proposed cryptographic functions indicates potential weaknesses if construction parameters are not properly chosen.Η κρυπτογραφία αποτελεί τον κύριο επιστημονικό κλάδο για τη μελέτη της ασφάλειας των τηλεπικοινωνίων οι αλγόριθμοι ροής αποτελούν σημαντική κατηγορία κρυπτογραφικών αλγορίθμων. Βασικό δομικό τους στοιχείο αποτελούν οι καταχωρητές ολίσθησης με γραμμική (LFSR) ή μη γραμμική (FSR) συνάρτηση ανάδρασης. Η ασφάλεια των αλγορίθμων ροής έγκειται στα χαρακτηριστικά τυχαιότητας που εμφανίζει η ακολουθία του κλειδιού. Η πολυπλοκότητα είναι ένα εκ των διαφόρων κρυπτογραφικών κριτηρίων των ακολουθιών η οποία ορίζεται ως το μήκος του μικρότερου FSR που παράγει την ακολουθία. Ιδιαίτερα η γραμμική πολυπλοκότητα είναι πολύ σημαντική η οποία πρέπει να είναι υψηλή προκειμένου το σύστημα να είναι ασφαλές σε διάφορες επιθέσεις όπως ο αλγόριθμος Berlekamp-Massey (BMA). Για την παραγωγή ακολουθιών υψηλής γραμμικής πολυπλοκότητας χρησιμοποιούνται μη γραμμικές λογικές συναρτήσεις είτε ως φίλτρα η συνδυαστές. Ωστόσο η ασφάλεια του συστήματος εξαρτάται επίσης και από επιμέρους ιδιότητες αυτών των λογικών συναρτήσεων. Επίσης υπάρχουν ανοιχτά ερωτήματα όσον αφορά τις σχέσεις μεταξύ των διαφόρων κρυπτογραφικών κριτηρίων των ακολουθιών. Στην παρούσα διατριβή μελετώνται χαρακτηριστικά τυχαιότητας των ακολουθιών, χρησιμοποιώντας εργαλεία της θεωρίας συστημάτων. Έμφαση δίνεται στη γραμμική πολυπλοκότητα η οποία μελετάται με χρήση των εννοιών της ελεγξιμότητας και παρατηρησιμότητας των συστημάτων παραγωγής ακολουθιών. Αναπτύσσεται ένας νέος γενικευμένος μετασχηματισμός Fourier που περιγράφει όλες τις περιοδικές ακολουθίες και επιτρέπει την κατασκευή ακολουθιών με οποιαδήποτε τιμή για τη γραμμική πολυπλοκότητα. Eπίσης κατασκευάζεται μια νέα οικογένεια μη γραμμικών φίλτρων η οποία παράγει ακολουθίες υψηλής γραμμικής πολυπλοκότητας. Μελετάται επίσης η μη γραμμική πολυπλοκότητα, καθώς και σχέσεις της με άλλα κρυπτογραφικά κριτήρια. Αναπτύσσεται ένας νέος αναδρομικός αλγόριθμος για την εύρεση του ελάχιστου FSR που παράγει μια ακολουθία, γενικεύοντας τον BMA στη μη γραμμική περίπτωση. Επιπλέον αναδεικνύεται η σχέση της μη γραμμικής πολυπλοκότητας με την πολυπλοκότητα Lempel-Ziv καθώς και με τον βαθμό συμπίεσης. Τέλος αναπτύσσονται τεχνικές για την εύρεση βέλτιστων τετραγωνικών προσεγγίσεων για κατηγορία συναρτήσεων βαθμού 3 και 4 ανεξαρτήτως του πλήθους των μεταβλητών. Οι τεχνικές αυτές καθορίζουν νέες σχεδιαστικές αρχές που πρέπει να τηρούνται στην κατασκευή κρυπτογραφικών συναρτήσεων. Μελέτη γνωστών συναρτήσεων καταδεικνύει κρυπτογραφικές τους αδυναμίες

Privacy Issues in Stylometric Methods

Stylometry is a well-known field, aiming to identify the author of a text, based only on the way she/he writes. Despite its obvious advantages in several areas, such as in historical research or for copyright purposes, it may also yield privacy and personal data protection issues if it is used in specific contexts, without the users being aware of it. It is, therefore, of importance to assess the potential use of stylometry methods, as well as the implications of their use for online privacy protection. This paper aims to present, through relevant experiments, the possibility of the automated identification of a person using stylometry. The ultimate goal is to analyse the risks regarding privacy and personal data protection stemming from the use of stylometric techniques to evaluate the effectiveness of a specific stylometric identification system, as well as to examine whether proper anonymisation techniques can be applied so as to ensure that the identity of an author of a text (e.g., a user in an anonymous social network) remains hidden, even if stylometric methods are to be applied for possible re-identification

Evaluating the Performance of Lightweight Ciphers in Constrained Environments—The Case of Saturnin

The use of lightweight cryptographic algorithms is essential for addressing security in highly constrained environments such as the Internet of Things. In this paper, the performance of lightweight block ciphers in such highly constrained environments is studied. More precisely, focusing—as a case study—on an important family of lightweight ciphers called “Saturnin”, which has been evaluated as a candidate for standardization in the relative ongoing NIST’s competition, we analyze its efficiency in case that it is implemented in a specific resource-constrained environment. To evaluate the results, a comparative study with the Advanced Encryption Standard (AES) is performed, through an appropriate experimental environment. Our results illustrate that significant gain in performance can be achieved, since Saturnin—whose design is inspired by the design of AES—can be almost two times faster than AES in such restricted environments