Critical Perspectives on Provable Security: Fifteen Years of Another Look Papers

We give an overview of our critiques of “proofs” of security and a guide to our papers on the subject that have appeared over the past decade and a half. We also provide numerous additional examples and a few updates and errata

Studies on the Security of Selected Advanced Asymmetric Cryptographic Primitives

The main goal of asymmetric cryptography is to provide confidential communication, which allows two parties to communicate securely even in the presence of adversaries. Ever since its invention in the seventies, asymmetric cryptography has been improved and developed further, and a formal security framework has been established around it. This framework includes different security goals, attack models, and security notions. As progress was made in the field, more advanced asymmetric cryptographic primitives were proposed, with other properties in addition to confidentiality. These new primitives also have their own definitions and notions of security. This thesis consists of two parts, where the first relates to the security of fully homomorphic encryption and related primitives. The second part presents a novel cryptographic primitive, and defines what security goals the primitive should achieve. The first part of the thesis consists of Article I, II, and III, which all pertain to the security of homomorphic encryption schemes in one respect or another. Article I demonstrates that a particular fully homomorphic encryption scheme is insecure in the sense that an adversary with access only to the public material can recover the secret key. It is also shown that this insecurity mainly stems from the operations necessary to make the scheme fully homomorphic. Article II presents an adaptive key recovery attack on a leveled homomorphic encryption scheme. The scheme in question claimed to withstand precisely such attacks, and was the only scheme of its kind to do so at the time. This part of the thesis culminates with Article III, which is an overview article on the IND-CCA1 security of all acknowledged homomorphic encryption schemes. The second part of the thesis consists of Article IV, which presents Vetted Encryption (VE), a novel asymmetric cryptographic primitive. The primitive is designed to allow a recipient to vet who may send them messages, by setting up a public filter with a public verification key, and providing each vetted sender with their own encryption key. There are three different variants of VE, based on whether the sender is identifiable to the filter and/or the recipient. Security definitions, general constructions and comparisons to already existing cryptographic primitives are provided for all three variants.Doktorgradsavhandlin

An Efficient and Provably Secure ID-Based Threshold Signcryption Scheme

Signcryption is a cryptographic primitive that performs digital signature and public key encryption simultaneously, at a lower computational costs and communication overheads than the signature-then-encryption approach. Recently, two identity-based threshold signcryption schemes[12],[26] have been proposed by combining the concepts of identity-based threshold signature and signcryption together. However, the formal models and security proofs for both schemes are not considered. In this paper, we formalize the concept of identity-based threshold signcryption and give a new scheme based on the bilinear pairings. We prove its confidentiality under the Decisional Bilinear Diffie-Hellman assumption and its unforgeability under the Computational Diffie-Hellman assumption in the random oracle model. Our scheme turns out to be more efficient than the two previously proposed schemes

A Provably Secure Short Signature Scheme from Coding Theory

Signatures with partially message recovery in which some parts of messages are not transmitted with signatures to make them shorter are useful where bandwidth is one of the crucial concern and especially in case of signing short messages in applications such as time stamping, certified email services and identitybased cryptosystems. In this paper, to have quantum-attackresistant short signatures, a signature scheme with partially message recovery from coding theory is proposed. The security of the proposed scheme is proved under Goppa Parametrized Bounded Decoding and the Goppa Code Distinguishing assumptions in the random oracle model. Relying on the partially message recovery property, the proposal is shorter than the Dallot signature scheme, the only provably secure and practical code-based signature scheme. We should highlight that our scheme can be used as a building block of code-based signature schemes with additional properties since it compared to Dallot signature scheme not only improves its communication overhead but also it preserves its signature efficiency

Contributions to secret sharing and other distributed cryptosystems

The present thesis deals with primitives related to the eld of distributed cryptography. First, we study signcryption schemes, which provide at the same time the functionalities of encryption and signature, where the unsigncryption operation is distributed. We consider this primitive from a theoretical point of view and set a security framework for it. Then, we present two signcryption schemes with threshold unsigncryption, with di erent properties. Furthermore, we use their authenticity property to apply them in the development of a di erent primitive: digital signatures with distributed veri cation. The second block of the thesis deals with the primitive of multi-secret sharing schemes. After stating some e ciency limitations of multi-secret sharing schemes in an information-theoretic scenario, we present several multi-secret sharing schemes with provable computational security. Finally, we use the results in multi-secret sharing schemes to generalize the traditional framework of distributed cryptography (with a single policy of authorized subsets) into a multipolicy setting, and we present both a multi-policy distributed decryption scheme and a multi-policy distributed signature scheme. Additionally, we give a short outlook on how to apply the presented multi-secret sharing schemes in the design of other multi-policy cryptosystems, like the signcryption schemes considered in this thesis. For all the schemes proposed throughout the thesis, we follow the same formal structure. After de ning the protocols of the primitive and the corresponding security model, we propose the new scheme and formally prove its security, by showing a reduction to some computationally hard mathematical problem.Avui en dia les persones estan implicades cada dia més en diferents activitats digitals tant en la seva vida professional com en el seu temps lliure. Molts articles de paper, com diners i tiquets, estan sent reemplaçats més i més per objectes digitals. La criptografia juga un paper crucial en aquesta transformació, perquè proporciona seguretat en la comunicació entre els diferents participants que utilitzen un canal digital. Depenent de la situació específica, alguns requisits de seguretat en la comunicació poden incloure privacitat (o confidencialitat), autenticitat, integritat o no-repudi. En algunes situacions, repartir l'operació secreta entre un grup de participants fa el procés més segur i fiable que quan la informació secreta està centralitzada en un únic participant; la criptografia distribuïda és l’àrea de la criptografia que estudia aquestes situacions. Aquesta tesi tracta de primitives relacionades amb el camp de la criptografia distribuïda. Primer, estudiem esquemes “signcryption”, que ofereixen a la vegada les funcionalitats de xifrat i signatura, on l'operació de “unsigncryption” està distribuïda. Considerem aquesta primitiva des d’un punt de vista teòric i establim un marc de seguretat per ella. Llavors, presentem dos esquemes “signcryption” amb operació de “unsigncryption” determinada per una estructura llindar, cada un amb diferents propietats. A més, utilitzem la seva propietat d’autenticitat per desenvolupar una nova primitiva: signatures digitals amb verificació distribuïda. El segon bloc de la tesi tracta la primitiva dels esquemes de compartició de multi-secrets. Després de demostrar algunes limitacions en l’eficiència dels esquemes de compartició de multi-secrets en un escenari de teoria de la informació, presentem diversos esquemes de compartició de multi-secrets amb seguretat computacional demostrable. Finalment, utilitzem els resultats obtinguts en els esquemes de compartició de multi-secrets per generalitzar el paradigma tradicional de la criptografia distribuïda (amb una única política de subconjunts autoritzats) a un marc multi-política, i presentem un esquema de desxifrat distribuït amb multi-política i un esquema de signatura distribuïda amb multi-política. A més, donem indicacions de com es poden aplicar els nostres esquemes de compartició de multi-secrets en el disseny d’altres criptosistemes amb multi-política, com per exemple els esquemes “signcryption” considerats en aquesta tesi. Per tots els esquemes proposats al llarg d’aquesta tesi, seguim la mateixa estructura formal. Després de definir els protocols de la primitiva primitius i el model de seguretat corresponent, proposem el nou esquema i demostrem formalment la seva seguretat, mitjançant una reducció a algun problema matemàtic computacionalment difícil

Provably Secure Group Signature Schemes from Code-Based Assumptions

We solve an open question in code-based cryptography by introducing two provably secure group signature schemes from code-based assumptions. Our basic scheme satisfies the CPA-anonymity and traceability requirements in the random oracle model, assuming the hardness of the McEliece problem, the Learning Parity with Noise problem, and a variant of the Syndrome Decoding problem. The construction produces smaller key and signature sizes than the previous group signature schemes from lattices, as long as the cardinality of the underlying group does not exceed $2^{24}$, which is roughly comparable to the current population of the Netherlands. We develop the basic scheme further to achieve the strongest anonymity notion, i.e., CCA-anonymity, with a small overhead in terms of efficiency. The feasibility of two proposed schemes is supported by implementation results. Our two schemes are the first in their respective classes of provably secure groups signature schemes. Additionally, the techniques introduced in this work might be of independent interest. These are a new verifiable encryption protocol for the randomized McEliece encryption and a novel approach to design formal security reductions from the Syndrome Decoding problem.Comment: Full extension of an earlier work published in the proceedings of ASIACRYPT 201

Pairing-Based Cryptographic Protocols : A Survey

The bilinear pairing such as Weil pairing or Tate pairing on elliptic and hyperelliptic curves have recently been found applications in design of cryptographic protocols. In this survey, we have tried to cover different cryptographic protocols based on bilinear pairings which possess, to the best of our knowledge, proper security proofs in the existing security models

Fast and Proven Secure Blind Identity-Based Signcryption from Pairings

We present the first blind identity-based signcryption (BIBSC). We formulate its security model and define the security notions of blindness and parallel one-more unforgeability (p1m-uf). We present an efficient construction from pairings, then prove a security theorem that reduces its p1m-uf to Schnorr¡¦s ROS Problem in the random oracle model plus the generic group and pairing model. The latter model is an extension of the generic group model to add support for pairings, which we introduce in this paper. In the process, we also introduce a new security model for (non-blind) identity-based signcryption (IBSC) which is a strengthening of Boyen¡¦s. We construct the first IBSC scheme proven secure in the strenghened model which is also the fastest (resp. shortest) IBSC in this model or Boyen¡¦s model. The shortcomings of several existing IBSC schemes in the strenghened model are shown