Secret Sharing Schemes Based on Resilient Boolean Maps

We introduce a linear code based on resilient maps on vector spaces over finite fields, we give a basis of this code and upper and lower bounds for its minimal distance. Then the use of the introduced code for building vector space secret sharing schemes is explained and an estimation of the robustness of the schemes against cheaters is provided

Disjoint difference families and their applications

Difference sets and their generalisations to difference families arise from the study of designs and many other applications. Here we give a brief survey of some of these applications, noting in particular the diverse definitions of difference families and the variations in priorities in constructions. We propose a definition of disjoint difference families that encompasses these variations and allows a comparison of the similarities and disparities. We then focus on two constructions of disjoint difference families arising from frequency hopping sequences and showed that they are in fact the same. We conclude with a discussion of the notion of equivalence for frequency hopping sequences and for disjoint difference families

A Study on Cheating Prevention in Secret Sharing Schemes

研究成果の概要 (和文) : 通常の秘密分散における不正防止に関する研究においては、正当なシェアを観測した後に改ざんするシェアの値を決定する不正者に対して安全な4つの方式を提案した。方式は全て、同じ不正者特定を有する従来の方式と比較して最小のシェアサイズを実現している。また、従来存在しなかった、任意の有限体で安全性を保証する不正検知可能な秘密分散法の提案も行った。シェア同士の演算により、秘密を復元することなく秘密に関する演算を行うd-multiplicative秘密分散法に関しては、不正成功確率が0となる方式が存在する条件を明らかにするとともに、閾値型、および一般のアクセス構造に対し、高確率で不正を検知する方式を提案した。研究成果の概要 (英文) : With respect to secret sharing schemes secure against rushing adversaries who determine their forged shares after observing shares of honest users, we construct four type of schemes secure against rushing adversaries. The sizes of shares of each proposed scheme achieves smallest bit length compared to those of existing schemes with the same security level. Further, we construct a scheme which can detect the fact of cheating and which ensure security whatever an finite field the secret belongs to. We should note that no existing schemes guarantee such a security feature. With respect to d-multiplicative secret sharing schemes which enable each user to compute a share of a polynomial with degree less than d (where d is a predetermined constant), we clarify conditions with which a secure d-multiplicative scheme (in which no user can cheat the other users) exists. Furthermore, we construct secure and efficient schemes secure against threshold adversary and general adversary, respectively

Key-collisions in (EC)DSA: Attacking Non-repudiation

A new kind of attack on the non-repudiation property of digital signature schemes is presented. We introduce a notion of key-collisions, which may allow an attacker to claim that the message (presented to a judge) has been signed by someone else. We show how to compute key-collisions for the DSA and ECDSA signature schemes effectively. The main idea of these attacks has been inspired by the well-known notion of message-collisions, where an attacker claims that the signature presented at the court belongs to a different message. Both of these collision-based attacks significantly weaken the non-repudiation property of signature schemes. Moreover, they weaken the non-repudiation of protocols based on these schemes. It is shown that key-collision resistance of the (EC)DSA schemes requires the incorporation of a mechanism ensuring honest generation of (EC)DSA instances. The usage of such a mechanism shall be verifiable by an independent third party without revealing any secret information. We propose and discuss basic general countermeasures against key-collision attacks on the (EC)DSA schemes

Tõhus peit- ja aktiivse ründaja vastu kaitstud turvaline ühisarvutus

Turvaline ühisarvutus on tänapäevase krüptograafia üks tähtsamaid kasutusviise, mis koondab elegantsed matemaatilised lahendused praktiliste rakenduste ehitamiseks, võimaldades mitmel erineval andmeomanikul sooritada oma andmetega suvalisi ühiseid arvutusi, ilma neid andmeid üksteisele avaldamata. Passiivse ründaja vastu turvalised protokollid eeldavad, et kõik osapooled käituvad ausalt. Aktiivse ründaja vastu turvalised protokollid ei lekita privaatseid andmeid sõltumata ründaja käitumisest. Käesolevas töös esitatakse üldine meetod, mis teisendab passiivse ründaja vastu turvalised ühisarvutusprotokollid turvaliseks aktiivse ründaja vastu. Meetod on optimeeritud kolme osapoolega arvutusteks üle algebraliste ringide; praktikas on see väga efektiivne mudel, mis teeb reaalse maailma rakendused teostatavateks. Meetod lisab esialgsele arvutusprotokollile täitmisjärgse verifitseerimisfaasi, mis muudab valesti käitunud osapooltel vahelejäämise vältimise tõenäosuse kaduvväikseks, säilitades esialgse protokolli turvagarantiid. Lisaks uurib käesolev töö rünnete uut eesmärki, mis seisneb mingi ausa osapoole vaate manipuleerimises sellisel viisil, et ta saaks midagi teada teise ausa osapoole privaatsete andmete kohta. Ründaja ise ei tarvitse seda infot üldse teada saada. Sellised ründed on olulised, sest need kohustavad ausat osapoolt tühjendama oma süsteemi teiste osapoolte andmetest, kuid see ülesanne võib olla päris mittetriviaalne. Eelnevalt pakutud verifitseerimismehhanisme täiendatakse nii, et privaatsed andmed oleksid kaitstud ka ausate osapoolte eest. Paljud ühisarvutusplatvormid on varustatud programmeerimiskeelega, mis võimaldab kirjutada privaatsust säilitavaid rakendusi ilma allolevale krüptograafiale mõtlemata. Juhul, kui programm sisaldab tingimuslauseid, kus arvutusharu valik sõltub privaatsetest andmetest, ei tohi ükski osapool haru valikust midagi teada, nii et üldjuhul peavad osapooled täitma kõik harud. Harude suure arvu kor-ral võib arvutuslik lisakulu olla ülisuur, sest enamik vahetulemustest visatakse ära. Käesolevas töös pakutakse selliseid lisakulusid vähendavat optimeerimist.Secure multiparty computation is one of the most important employments of modern cryptography, bringing together elegant mathematical solutions to build up useful practical applications. It allows several distinct data owners to perform arbitrary collaborative computation on their private data without leaking any information to each other. Passively secure protocols assume that all parties follow the protocol rules. Actively secure protocols do not leak private data regardless of the attacker’s behaviour. This thesis presents a generic method for turning passively secure multiparty protocols to actively secure ones. The method is optimized for three party computation over algebraic rings, which has proven to be quite an efficient model, making large real-world applications feasible. Our method adds to the protocol a post-execution verification phase that allows a misbehaving party to escape detection only with negligible probability. It preserves the privacy guarantees of the original protocol. In this thesis, we also study a new adversarial goal in multiparty protocols. The goal is to manipulate the view of some honest party in such a way, that this honest party learns the private data of some other honest party. The adversary itself might not learn this data at all. Such attacks are significant because they create a liability to the first honest party to clean its systems from the second honest party’s data, which may be a highly non-trivial task in practice. We check the security of our verification mechanism in this new model, and we propose some minor modifications that ensure data protection also from the honest parties. Many secure multiparty computation platforms come with a programming language that allows the developer to write privacy-preserving applications without thinking of the underlying cryptography. If a program contains conditional statements where the choice of the computational branch depends on private data, then no party should know which branch has been executed, so in general the parties need to execute all of them. If the number of branches is large, the computational overhead may be enormous, as most of the intermediate results are just discarded. In this thesis, we propose an automatic optimization that reduces this overhead

Secure fingerprinting on sound foundations

The rapid development and the advancement of digital technologies open a variety of opportunities to consumers and content providers for using and trading digital goods. In this context, particularly the Internet has gained a major ground as a worldwiede platform for exchanging and distributing digital goods. Beside all its possibilities and advantages digital technology can be misuesd to breach copyright regulations: unauthorized use and illegal distribution of intellectual property cause authors and content providers considerable loss. Protections of intellectual property has therefore become one of the major challenges of our information society. Fingerprinting is a key technology in copyright protection of intellectual property. Its goal is to deter people from copyright violation by allowing to provably identify the source of illegally copied and redistributed content. As one of its focuses, this thesis considers the design and construction of various fingerprinting schemes and presents the first explicit, secure and reasonably efficient construction for a fingerprinting scheme which fulfills advanced security requirements such as collusion-tolerance, asymmetry, anonymity and direct non-repudiation. Crucial for the security of such s is a careful study of the underlying cryptographic assumptions. In case of the fingerprinting scheme presented here, these are mainly assumptions related to discrete logarithms. The study and analysis of these assumptions is a further focus of this thesis. Based on the first thorough classification of assumptions related to discrete logarithms, this thesis gives novel insights into the relations between these assumptions. In particular, depending on the underlying probability space we present new reuslts on the reducibility between some of these assumptions as well as on their reduction efficency.Die Fortschritte im Bereich der Digitaltechnologien bieten Konsumenten, Urhebern und Anbietern große Potentiale für innovative Geschäftsmodelle zum Handel mit digitalen Gütern und zu deren Nutzung. Das Internet stellt hierbei eine interessante Möglichkeit zum Austausch und zur Verbreitung digitaler Güter dar. Neben vielen Vorteilen kann die Digitaltechnik jedoch auch missbräuchlich eingesetzt werden, wie beispielsweise zur Verletzung von Urheberrechten durch illegale Nutzung und Verbreitung von Inhalten, wodurch involvierten Parteien erhebliche Schäden entstehen können. Der Schutz des geistigen Eigentums hat sich deshalb zu einer der besonderen Herausforderungen unseres Digitalzeitalters entwickelt. Fingerprinting ist eine Schlüsseltechnologie zum Urheberschutz. Sie hat das Ziel, vor illegaler Vervielfältigung und Verteilung digitaler Werke abzuschrecken, indem sie die Identifikation eines Betrügers und das Nachweisen seines Fehlverhaltens ermöglicht. Diese Dissertation liefert als eines ihrer Ergebnisse die erste explizite, sichere und effiziente Konstruktion, welche die Berücksichtigung besonders fortgeschrittener Sicherheitseigenschaften wie Kollusionstoleranz, Asymmetrie, Anonymität und direkte Unabstreitbarkeit erlaubt. Entscheidend für die Sicherheit kryptographischer Systeme ist die präzise Analyse der ihnen zugrunde liegenden kryptographischen Annahmen. Den im Rahmen dieser Dissertation konstruierten Fingerprintingsystemen liegen hauptsächlich kryptographische Annahmen zugrunde, welche auf diskreten Logarithmen basieren. Die Untersuchung dieser Annahmen stellt einen weiteren Schwerpunkt dieser Dissertation dar. Basierend auf einer hier erstmals in der Literatur vorgenommenen Klassifikation dieser Annahmen werden neue und weitreichende Kenntnisse über deren Zusammenhänge gewonnen. Insbesondere werden, in Abhängigkeit von dem zugrunde liegenden Wahrscheinlichkeitsraum, neue Resultate hinsichtlich der Reduzierbarkeit dieser Annahmen und ihrer Reduktionseffizienz erzielt

Quantum entanglement

All our former experience with application of quantum theory seems to say: {\it what is predicted by quantum formalism must occur in laboratory}. But the essence of quantum formalism - entanglement, recognized by Einstein, Podolsky, Rosen and Schr\"odinger - waited over 70 years to enter to laboratories as a new resource as real as energy. This holistic property of compound quantum systems, which involves nonclassical correlations between subsystems, is a potential for many quantum processes, including ``canonical'' ones: quantum cryptography, quantum teleportation and dense coding. However, it appeared that this new resource is very complex and difficult to detect. Being usually fragile to environment, it is robust against conceptual and mathematical tools, the task of which is to decipher its rich structure. This article reviews basic aspects of entanglement including its characterization, detection, distillation and quantifying. In particular, the authors discuss various manifestations of entanglement via Bell inequalities, entropic inequalities, entanglement witnesses, quantum cryptography and point out some interrelations. They also discuss a basic role of entanglement in quantum communication within distant labs paradigm and stress some peculiarities such as irreversibility of entanglement manipulations including its extremal form - bound entanglement phenomenon. A basic role of entanglement witnesses in detection of entanglement is emphasized.Comment: 110 pages, 3 figures, ReVTex4, Improved (slightly extended) presentation, updated references, minor changes, submitted to Rev. Mod. Phys

Cryptographic Schemes based on Elliptic Curve Pairings

This thesis introduces the concept of certificateless public key cryptography (CLPKC). Elliptic curve pairings are then used to make concrete CL-PKC schemes and are also used to make other efficient key agreement protocols. CL-PKC can be viewed as a model for the use of public key cryptography that is intermediate between traditional certificated PKC and ID-PKC. This is because, in contrast to traditional public key cryptographic systems, CL-PKC does not require the use of certificates to guarantee the authenticity of public keys. It does rely on the use of a trusted authority (TA) who is in possession of a master key. In this respect, CL-PKC is similar to identity-based public key cryptography (ID-PKC). On the other hand, CL-PKC does not suffer from the key escrow property that is inherent in ID-PKC. Applications for the new infrastructure are discussed. We exemplify how CL-PKC schemes can be constructed by constructing several certificateless public key encryption schemes and modifying other existing ID based schemes. The lack of certificates and the desire to prove the schemes secure in the presence of an adversary who has access to the master key or has the ability to replace public keys, requires the careful development of new security models. We prove that some of our schemes are secure, provided that the Bilinear Diffie-Hellman Problem is hard. We then examine Joux’s protocol, which is a one round, tripartite key agreement protocol that is more bandwidth-efficient than any previous three-party key agreement protocol, however, Joux’s protocol is insecure, suffering from a simple man-in-the-middle attack. We show how to make Joux’s protocol secure, presenting several tripartite, authenticated key agreement protocols that still require only one round of communication. The security properties of the new protocols are studied. Applications for the protocols are also discussed

Efficient threshold cryptosystems

Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2001.Includes bibliographical references (p. 181-189).A threshold signature or decryption scheme is a distributed implementation of a cryptosystem, in which the secret key is secret-shared among a group of servers. These servers can then sign or decrypt messages by following a distributed protocol. The goal of a threshold scheme is to protect the secret key in a highly fault-tolerant way. Namely, the key remains secret, and correct signatures or decryptions are always computed, even if the adversary corrupts less than a fixed threshold of the participating servers. We show that threshold schemes can be constructed by putting together several simple distributed protocols that implement arithmetic operations, like multiplication or exponentiation, in a threshold setting. We exemplify this approach with two discrete-log based threshold schemes, a threshold DSS signature scheme and a threshold Cramer-Shoup cryptosystem. Our methodology leads to threshold schemes which are more efficient than those implied by general secure multi-party computation protocols. Our schemes take a constant number of communication rounds, and the computation cost per server grows by a factor linear in the number of the participating servers compared to the cost of the underlying secret-key operation. We consider three adversarial models of increasing strength. We first present distributed protocols for constructing threshold cryptosystems secure in the static adversarial model, where the players are corrupted before the protocol starts. Then, under the assumption that the servers can reliably erase their local data, we show how to modify these protocols to extend the security of threshold schemes to an adaptive adversarial model,(cont.) where the adversary is allowed to choose which servers to corrupt during the protocol execution. Finally we show how to remove the reliable erasure assumption. All our schemes withstand optimal thresholds of a minority of malicious faults in a realistic partially-synchronous insecure-channels communication model with broadcast. Our work introduces several techniques that can be of interest to other research on secure multi-party protocols, e.g. the inconsistent player simulation technique which we use to construct efficient schemes secure in the adaptive model, and the novel primitive of a simultaneously secure encryption which provides an efficient implementation of private channels in an adaptive and erasure-free model for a wide class of multi-party protocols. We include extensions of the above results to: (1) RSA-based threshold cryptosystems; and (2) stronger adversarial models than a threshold adversary, namely to proactive and creeping adversaries, who, under certain assumptions regarding the speed and detectability of corruptions, are allowed to compromise all or almost all of the participating servers.by StanisÅaw Jarecki.Ph.D