Research Philosophy of Modern Cryptography

Proposing novel cryptography schemes (e.g., encryption, signatures, and protocols) is one of the main research goals in modern cryptography. In this paper, based on more than 800 research papers since 1976 that we have surveyed, we introduce the research philosophy of cryptography behind these papers. We use ``benefits and ``novelty as the keywords to introduce the research philosophy of proposing new schemes, assuming that there is already one scheme proposed for a cryptography notion. Next, we introduce how benefits were explored in the literature and we have categorized the methodology into 3 ways for benefits, 6 types of benefits, and 17 benefit areas. As examples, we introduce 40 research strategies within these benefit areas that were invented in the literature. The introduced research strategies have covered most cryptography schemes published in top-tier cryptography conferences

Isogeny-based Quantum-resistant Undeniable Blind Signature Scheme

In this paper, we propose an Undeniable Blind Signature scheme (UBSS) based on isogenies between supersingular elliptic curves. The proposed UBSS is an extension of the Jao-Soukharev undeniable signature scheme. We formalize the notion of a UBSS by giving the formal definition. We then study its properties along with the pros and cons. Based on this, we provide a couple of its applcations. We then state the isogeny problems in a more general form and discuss their computational hardnesses. Finally, we prove that the proposed scheme is secure in the presence of a quantum adversary under certain assumptions

Design and Analysis of Opaque Signatures

Digital signatures were introduced to guarantee the authenticity and integrity of the underlying messages. A digital signature scheme comprises the key generation, the signature, and the verification algorithms. The key generation algorithm creates the signing and the verifying keys, called also the signer’s private and public keys respectively. The signature algorithm, which is run by the signer, produces a signature on the input message. Finally, the verification algorithm, run by anyone who knows the signer’s public key, checks whether a purported signature on some message is valid or not. The last property, namely the universal verification of digital signatures is undesirable in situations where the signed data is commercially or personally sensitive. Therefore, mechanisms which share most properties with digital signatures except for the universal verification were invented to respond to the aforementioned need; we call such mechanisms “opaque signatures”. In this thesis, we study the signatures where the verification cannot be achieved without the cooperation of a specific entity, namely the signer in case of undeniable signatures, or the confirmer in case of confirmer signatures; we make three main contributions. We first study the relationship between two security properties important for public key encryption, namely data privacy and key privacy. Our study is motivated by the fact that opaque signatures involve always an encryption layer that ensures their opacity. The properties required for this encryption vary according to whether we want to protect the identity (i.e. the key) of the signer or hide the validity of the signature. Therefore, it would be convenient to use existing work about the encryption scheme in order to derive one notion from the other. Next, we delve into the generic constructions of confirmer signatures from basic cryptographic primitives, e.g. digital signatures, encryption, or commitment schemes. In fact, generic constructions give easy-to-understand and easy-to-prove schemes, however, this convenience is often achieved at the expense of efficiency. In this contribution, which constitutes the core of this thesis, we first analyze the already existing constructions; our study concludes that the popular generic constructions of confirmer signatures necessitate strong security assumptions on the building blocks, which impacts negatively the efficiency of the resulting signatures. Next, we show that a small change in these constructionsmakes these assumptions drop drastically, allowing as a result constructions with instantiations that compete with the dedicated realizations of these signatures. Finally, we revisit two early undeniable signatures which were proposed with a conjectural security. We disprove the claimed security of the first scheme, and we provide a fix to it in order to achieve strong security properties. Next, we upgrade the second scheme so that it supports a iii desirable feature, and we provide a formal security treatment of the new scheme: we prove that it is secure assuming new reasonable assumptions on the underlying constituents

Programmable hash functions and their applications

We introduce a new combinatorial primitive called *programmable hash functions* (PHFs). PHFs can be used to *program* the output of a hash function such that it contains solved or unsolved discrete logarithm instances with a certain probability. This is a technique originally used for security proofs in the random oracle model. We give a variety of *standard model* realizations of PHFs (with different parameters). The programmability makes PHFs a suitable tool to obtain black-box proofs of cryptographic protocols when considering adaptive attacks. We propose generic digital signature schemes from the strong RSA problem and from some hardness assumption on bilinear maps that can be instantiated with any PHF. Our schemes offer various improvements over known constructions. In particular, for a reasonable choice of parameters, we obtain short standard model digital signatures over bilinear maps

Advances in signatures, encryption, and E-Cash from bilinear groups

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2006.Includes bibliographical references (p. 147-161).We present new formal definitions, algorithms, and motivating applications for three natural cryptographic constructions. Our constructions are based on a special type of algebraic group called bilinear groups. 1. Re-Signatures: We present the first public key signature scheme where a semi-trusted proxy, given special information, can translate Alice's signature on a message into Bob's signature on the same message. The special information, however, allows nothing else, i.e., the proxy cannot translate from Bob to Alice, nor can it sign on behalf of either Alice or Bob. We show that a path through a graph can be cheaply authenticated using this scheme, with applications to electronic passports. 2. Re-Encryption: We present the first public key cryptosystem where a semi-trusted proxy, given special information, can translate an encryption of a message under Alice's key into an encryption of the same message under Bob's key. Again, the special information allows nothing else, i.e. the proxy cannot translate from Bob to Alice, decrypt on behalf of either Alice or Bob, or learn anything else about the message. We apply this scheme to create a new mechanism for secure distributed storage.(cont.) 3. Compact; E-Cash with Tracing and Bounded-Anonymity: We present an offline e-cash system where 2 coins can be stored in O(e + k) bits and withdrawn or spent in 0(f + k) time, where k is the security parameter. The best previously known schemes required at least one of these complexities to be 0(2t . k). In our system, a user's transactions are anonymous and unlinkable, unless she performs a forbidden action, such as double-spending a coin. Performing a forbidden action reveals the identity of the user, and optionally allows to trace all of her past transactions. We provide solutions without using a trusted party. We argue why features of our system are likely to be crucial to the adoption of any e-cash system.by Susan Hohenberger.Ph.D

Fair exchange in e-commerce and certified e-mail, new scenarios and protocols

We are witnessing a steady growth in the use of Internet in the electronic commerce field. This rise is promoting the migration from traditional processes and applications (paper based) to an electronic model. But the security of electronic transactions continues to pose an impediment to its implementation. Traditionally, most business transactions were conducted in person. Signing a contract required the meeting of all interested parties, the postman delivered certified mail in hand, and when paying for goods or services both customer and provider were present. When all parties are physically present, a transaction does not require a complex protocol. The participants acknowledge the presence of the other parties as assurance that they will receive their parts, whether a signature on a contract, or a receipt, etc. But with e-commerce growing in importance as sales and business channel, all these transactions have moved to its digital counterpart. Therefore we have digital signature of contracts, certified delivery of messages and electronic payment systems. With electronic transactions, the physical presence is not required,moreover, most of the times it is even impossible. The participants in a transaction can be thousands of kilometers away from each other, and they may not even be human participants, they can be machines. Thus, the security that the transaction will be executed without incident is not assured per se, we need additional security measures. To address this problem, fair exchange protocols were developed. In a fair exchange every party involved has an item that wants to exchange, but none of the participants is willing to give his item away unless he has an assurance he will receive the corresponding item from the other participants. Fair exchange has many applications, like digital signature of contracts, where the items to be exchanged are signatures on contracts, certified delivery of messages, where we exchange a message for evidence of receipt, or a payment process, where we exchange a payment (e-cash, e-check, visa, etc.) for digital goods or a receipt. The objective of this dissertation is the study of the fair exchange problem. In particular, it presents two new scenarios for digital contracting, the Atomic Multi- Two Party (AM2P) and the Agent Mediated Scenario (AMS), and proposes one optimistic contract signing protocol for each one. Moreover, it studies the efficiency of Multi-Party Contract Signing (MPCS) protocols from their architecture point of view, presenting a new lower bound for each architecture, in terms of minimum number of transactions needed. Regarding Certified Electronic Mail (CEM), this dissertation presents two optimistic CEMprotocols designed to be deployed on thecurrent e-mail infrastructure, therefore they assume the participation of multiple Mail Transfer Agents (MTAs). In one case, the protocol assumes untrusted MTAs whereas in the other one it assumes each User Agent (UA) trusts his own MTA. Regarding payment systems, this dissertation presents a secure and efficient electronic bearer bank check scheme allowing the electronic checks to be transferred fairly and anonymously.L’ús d’Internet en l’àmbit del comerç electrònic està experimentant un creixement estable. Aquest increment d’ús està promovent lamigració de processos tradicionals i aplicacions (basades en paper) cap a un model electrònic. Però la seguretat de les transaccions electròniques continua impedint la seva implantació. Tradicionalment, la majoria de les transaccions s’han dut a terme en persona. La firma d’un contracte requeria la presència de tots els firmants, el carter entrega les cartes certificades enmà, i quan es paga per un bé o servei ambdós venedor i comprador hi són presents. Quan totes les parts hi són presents, les transaccions no requereixen un protocol complex. Els participants assumeixen la presència de les altres parts com assegurança que rebran el que esperen d’elles, ja sigui la firma d’un contracte, un rebut d’entrega o un pagament. Però amb el creixement del comerç electrònic com a canal de venda i negoci, totes aquestes transaccions s’hanmogut al seu equivalent en el món electrònic. Així doncs tenim firma electrònica de contractes, enviament certificat de missatges, sistemes de pagament electrònic, etc. En les transaccions electròniques la presència física no és necessària, de fet, la majoria de vegades és fins it tot impossible. Els participants poden estar separats permilers de kilòmetres, i no és necessari que siguin humans, podrien sermàquines. Llavors, la seguretat de que la transacció s’executarà correctament no està assegurada per se, necessitem proporcionar mesures de seguretat addicionals. Per solucionar aquest problema, es van desenvolupar els protocols d’intercanvi equitatiu. En un intercanvi equitatiu totes les parts involucrades tenen un objecte que volen intercanviar, però cap de les parts implicades vol donar el seu objecte si no té la seguretat que rebrà els objectes de les altres parts. L’intercanvi equitatiu té multitud d’aplicacions, com la firma electrònica de contractes, on els elements a intercanviar son firmes de contractes, enviament certificat demissatges, on s’intercanvien unmissatge per una evidència de recepció, o un procés de pagament, on intercanviemun pagament (e-cash, visa, e-xec, etc.) per bens digitals o per un rebut. L’objectiu d’aquesta tesi és estudiar el problema de l’intercanvi equitatiu. En particular, la tesi presenta dos nous escenaris per a la firma electrònica de contractes, l’escenari multi-two party atòmic i l’escenari amb agents intermediaris, i proposa un protocol optimista per a cada un d’ells. A més, presenta un estudi de l’eficiència dels protocols de firma electrònica multi-part (Multi-Party Contract Signing (MPCS) protocols) des del punt de vista de la seva arquitectura, presentant una nova fita per a cada una, en termes de mínim nombre de transaccions necessàries. Pel que fa al correu electrònic certificat, aquesta tesi presenta dos protocols optimistes dissenyats per a ser desplegats damunt l’infraestructura actual de correu electrònic, per tant assumeix la participació demúltiples agents de transferència de correu. Un dels protocols assumeix que cap dels agents de transferència de correu participants és de confiança,mentre que l’altre assumeix que cada usuari confia en el seu propi agent. Pel que fa a sistemes de pagament, la tesi presenta un esquema de xec bancari al portador, eficient i segur, que garanteix que la transferència dels xecs es fa demanera anònima i equitativa