On the Design of Cryptographic Primitives

The main objective of this work is twofold. On the one hand, it gives a brief overview of the area of two-party cryptographic protocols. On the other hand, it proposes new schemes and guidelines for improving the practice of robust protocol design. In order to achieve such a double goal, a tour through the descriptions of the two main cryptographic primitives is carried out. Within this survey, some of the most representative algorithms based on the Theory of Finite Fields are provided and new general schemes and specific algorithms based on Graph Theory are proposed

Identification Protocols in Cryptography

In this paper we examine the role of Identification Protocols in the field of Cryptography. Firstly, the rationale behind the need for Identification Protocols is discussed. Secondly, we examine, in detail, challenge-response protocols, based upon zero-knowledge proofs, that form a subset of Identification Protocols in general. Thirdly, the mathematical tools necessary for the understanding of how these protocols work is given. Finally, we discuss four main Identification Protocols: Fiat-Shamir, Feige-Fiat-Shamir, Schnorr and Guillou- Quisquater. This discussion includes the theory, practical examples and the security aspects of each protocol

An identity-based key infrastructure suitable for messaging applications

Abstract—Identity-based encryption (IBE) systems are relatively recently proposed; yet they are highly popular for messaging applications since they offer new features such as certificateless infrastructure and anonymous communication. In this paper, we intended to propose an IBE infrastructure for messaging applications. The proposed infrastructure requires one registration authority and at least one public key generator and they secret share the master secret key. In addition, the PKG also shares the same master secret with each user in the system in a different way. Therefore, the PKG will never be able to learn the private keys of users under non-collusion assumption. We discuss different aspects of the proposed infrastructure such as security, key revocation, uniqueness of the identities that constitute the main drawbacks of other IBE schemes. We demonstrate that our infrastructure solves many of these drawbacks under certain assumptions

Practical IBC Using Hybrid-Mode Problems: Factoring and Discrete Logarithm

Shamir proposed the concept of the ID-based cryptosystem (IBC) in 1984. Instead of generating and publishing a public key for each user, the ID-based scheme permits each user to choose his name or network address as his public key. This is advantageous to public-key cryptosystems because the public-key verification is so easy and direct. In such a way, a large public key file is not required. Since new cryptographic schemes always face security challenges and many integer factorization problem and discrete logarithm based cryptographic systems have been deployed, therefore, the purpose of this paper is to design practical IBC using hybrid mode problems factoring and discrete logarithm. We consider the security against a conspiracy of some entities in the proposed system and show the possibility of establishing a more secure system

Practical IBC using Hybrid-Mode Problems: Factoring and Discrete Logarithm

Shamir proposed the concept of the ID-based cryptosystem (IBC) in 1984. Instead of generating and publishing a public key for each user, the ID-based scheme permits each user to choose his name or network address as his public key. This is advantageous to public-key cryptosystems because the public-key verification is so easy and direct. In such a way, a large public key file is not required. Since new cryptographic schemes always face security challenges and many integer factorization problem and discrete logarithm based cryptographic systems have been deployed, therefore, the purpose of this paper is to design practical IBC using hybrid mode problems factoring and discrete logarithm. We consider the security against a conspiracy of some entities in the proposed system and show the possibility of establishing a more secure system

A usability study of elliptic curves

In the recent years, the need of information security has rapidly increased due to an enormous growth of data transmission. In this thesis, we study the uses of elliptic curves in the cryptography. We discuss the elliptic curves over finite fields, attempts to attack; discrete logarithm, Pollard’s rho algorithm, baby-step giant-step algorithm, Pohlig-Hellman algorithm, function field sieve, and number field sieve. The main cryptographic reason to use elliptic curves over finite fields is to provide arbitrarily large finite cyclic groups having a computationally difficult discrete logarithm problem

Algorithms and cryptographic protocols using elliptic curves

En els darrers anys, la criptografia amb corbes el.líptiques ha adquirit una importància creixent, fins a arribar a formar part en la actualitat de diferents estàndards industrials. Tot i que s'han dissenyat variants amb corbes el.líptiques de criptosistemes clàssics, com el RSA, el seu màxim interès rau en la seva aplicació en criptosistemes basats en el Problema del Logaritme Discret, com els de tipus ElGamal. En aquest cas, els criptosistemes el.líptics garanteixen la mateixa seguretat que els construïts sobre el grup multiplicatiu d'un cos finit primer, però amb longituds de clau molt menor. Mostrarem, doncs, les bones propietats d'aquests criptosistemes, així com els requeriments bàsics per a que una corba sigui criptogràficament útil, estretament relacionat amb la seva cardinalitat. Revisarem alguns mètodes que permetin descartar corbes no criptogràficament útils, així com altres que permetin obtenir corbes bones a partir d'una de donada. Finalment, descriurem algunes aplicacions, com són el seu ús en Targes Intel.ligents i sistemes RFID, per concloure amb alguns avenços recents en aquest camp.The relevance of elliptic curve cryptography has grown in recent years, and today represents a cornerstone in many industrial standards. Although elliptic curve variants of classical cryptosystems such as RSA exist, the full potential of elliptic curve cryptography is displayed in cryptosystems based on the Discrete Logarithm Problem, such as ElGamal. For these, elliptic curve cryptosystems guarantee the same security levels as their finite field analogues, with the additional advantage of using significantly smaller key sizes. In this report we show the positive properties of elliptic curve cryptosystems, and the requirements a curve must meet to be useful in this context, closely related to the number of points. We survey methods to discard cryptographically uninteresting curves as well as methods to obtain other useful curves from a given one. We then describe some real world applications such as Smart Cards and RFID systems and conclude with a snapshot of recent developments in the field

A Group Signature Scheme Based on an RSA-Variant

The concept of group signatures allows a group member to sign messages anonymously on behalf of the group. However, in the case of a dispute, the identity of a signature’s originator can be revealed by a designated entity. In this paper we propose a new group signature scheme that is well suited for large groups, i.e., the length of the group’s public key and of signatures do notdepend on the size of the group. Our scheme is based on a variation of the RSA problem called strong RSA assumption. It is also more efficient than previous ones satisfying these requirements