992 research outputs found
An efficient and secure RSA--like cryptosystem exploiting R\'edei rational functions over conics
We define an isomorphism between the group of points of a conic and the set
of integers modulo a prime equipped with a non-standard product. This product
can be efficiently evaluated through the use of R\'edei rational functions. We
then exploit the isomorphism to construct a novel RSA-like scheme. We compare
our scheme with classic RSA and with RSA-like schemes based on the cubic or
conic equation. The decryption operation of the proposed scheme turns to be two
times faster than RSA, and involves the lowest number of modular inversions
with respect to other RSA-like schemes based on curves. Our solution offers the
same security as RSA in a one-to-one communication and more security in
broadcast applications.Comment: 18 pages, 1 figur
Fault attacks on RSA and elliptic curve cryptosystems
This thesis answered how a fault attack targeting software used to program EEPROM can threaten hardware devices, for instance IoT devices. The successful fault attacks proposed in this thesis will certainly warn designers of hardware devices of the security risks their devices may face on the programming leve
Algorithms and cryptographic protocols using elliptic curves
En els darrers anys, la criptografia amb corbes el.lĂptiques ha
adquirit una importĂ ncia creixent, fins a arribar a formar part en
la actualitat de diferents estĂ ndards industrials. Tot i que s'han
dissenyat variants amb corbes el.lĂptiques de criptosistemes
clà ssics, com el RSA, el seu mà xim interès rau en la seva
aplicaciĂł en criptosistemes basats en el Problema del Logaritme
Discret, com els de tipus ElGamal. En aquest cas, els
criptosistemes el.lĂptics 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,
aixĂ com els requeriments bĂ sics per a que una corba
sigui criptogrĂ ficament Ăştil, estretament relacionat amb la seva
cardinalitat. Revisarem alguns mètodes que permetin descartar
corbes no criptogrĂ ficament Ăştils, aixĂ com altres que permetin
obtenir corbes bones a partir d'una de donada. Finalment,
descriurem algunes aplicacions, com sĂłn el seu Ăşs 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
The zheng-seberry public key cryptosystem and signcryption
In 1993 Zheng-Seberry presented a public key cryptosystem that was considered efficient and secure in the sense of indistinguishability of encryptions (IND) against an adaptively chosen ciphertext adversary (CCA2). This thesis shows the Zheng-Seberry scheme is not secure as a CCA2 adversary can break the scheme in the sense of IND. In 1998 Cramer-Shoup presented a scheme that was secure against an IND-CCA2 adversary and whose proof relied only on standard assumptions. This thesis modifies this proof and applies it to a modified version of the El-Gamal scheme. This resulted in a provably secure scheme relying on the Random Oracle (RO) model, which is more efficient than the original Cramer-Shoup scheme. Although the RO model assumption is needed for security of this new El-Gamal variant, it only relies on it in a minimal way
Oblivious transfer for secure communication
Over the past four decades, computational power and algorithmic strategies have advanced tremendously resulting in an enormous increase in the key sizes required for secure cryptosystems such as RSA. At the same time, the electronic devices have grown smaller and portable requiring algorithms running on them to be optimized in size and efficiency while providing security, at least, equivalent to that provided on a typical desktop computer. As a result, the industry is moving towards newer cryptosystems such as ECC and NTRU that are well suited for resource constrained environments. While, ECC claims to provide security equivalent to that of RSA for a fraction of key size, NTRU is inherently suited for embedded systems technology. However, implementation of new cryptosystems requires the development of protocols analogous to those developed using older cryptosystems. In this thesis, we fulfill a part of this requirement by providing protocols for Oblivious Transfer using ECC and NTRU. Oblivious Transfer, in turn, has applications in simultaneous contract signing, digital certified mail, simultaneous exchange of secrets, secure multiparty computations, private information retrieval, etc. Furthermore, we introduce the idea of basing Oblivious Transfer on public-key exchange protocols. The presentation in the thesis uses Diffie-Hellman Key Exchange, but the scheme is generalizable to any cryptosystem that has a public-key exchange strategy. In fact, our proposal may especially be suited for Quantum Cryptography where the security of key exchange protocols has been proven
The Security of Elliptic Curve Cryptosystems - A Survey
Elliptic curve cryptography or ECC is a public-key cryptosystem. This paper introduces ECC and describes its present applications. A mathematical background is given initially. Then its2019; major cryptographic uses are given. These include its2019; use in encryption, key sharing and digital signatures. The security of these ECC-based cryptosystems are discussed. It was found that ECC was well suited for low-power and resource constrained devices because of its2019; small key size
Group ring based public key cryptosystems
In this paper, we propose two cryptosystems based on group rings and existing
cryptosystem. First one is Elliptic ElGamal type group ring public key
cryptosystem whose security is greater than security of cryptosystems based on
elliptic curves discrete logarithmic problem (ECDLP). Second is ElGamal type
group ring public key cryptosystem, which is analogous to ElGamal public key
cryptosystem but has comparatively greater security. Examples are also given
for both the proposed cryptosystems
Hard isogeny problems over RSA moduli and groups with infeasible inversion
We initiate the study of computational problems on elliptic curve isogeny
graphs defined over RSA moduli. We conjecture that several variants of the
neighbor-search problem over these graphs are hard, and provide a comprehensive
list of cryptanalytic attempts on these problems. Moreover, based on the
hardness of these problems, we provide a construction of groups with infeasible
inversion, where the underlying groups are the ideal class groups of imaginary
quadratic orders.
Recall that in a group with infeasible inversion, computing the inverse of a
group element is required to be hard, while performing the group operation is
easy. Motivated by the potential cryptographic application of building a
directed transitive signature scheme, the search for a group with infeasible
inversion was initiated in the theses of Hohenberger and Molnar (2003). Later
it was also shown to provide a broadcast encryption scheme by Irrer et al.
(2004). However, to date the only case of a group with infeasible inversion is
implied by the much stronger primitive of self-bilinear map constructed by
Yamakawa et al. (2014) based on the hardness of factoring and
indistinguishability obfuscation (iO). Our construction gives a candidate
without using iO.Comment: Significant revision of the article previously titled "A Candidate
Group with Infeasible Inversion" (arXiv:1810.00022v1). Cleared up the
constructions by giving toy examples, added "The Parallelogram Attack" (Sec
5.3.2). 54 pages, 8 figure
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
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