Converse results to the Wiener attack on RSA

A well-known attack on RSA with low secret-exponent d was given by Wiener about 15 years ago. Wiener showed that using continued fractions, one can efficiently recover the secret-exponent d from the public key (N,e) as long as d < N 1/4. Interestingly, Wiener stated that his attack may sometimes also work when d is slightly larger than N 1/4. This raises the question of how much larger d can be: could the attack work with non-negligible probability for d=N 1/4 + ρ for some constant ρ > 0? We answer this question in the negative by proving a converse to Wiener’s result. Our result shows that, for any fixed ε > 0 and all sufficiently large modulus lengths, Wiener’s attack succeeds with negligible probability over a random choice of d < N δ (in an interval of size Ω(N δ )) as soon as δ > 1/4 + ε. Thus Wiener’s success bound d 1/4. The known attacks in this class (by Verheul and Van Tilborg and Dujella) run in exponential time, so it is natural to ask whether there exists an attack in this class with subexponential run-time. Our second converse result answers this question also in the negative.

Efficient extension of standard Schnorr/RSA signatures into Universal Designated-Verifier Signatures

Universal Designated-Verifier Signature (UDVS) schemes are digital signature schemes with additional functionality which allows any holder of a signature to designate the signature to any desired designated-verifier such that the designated-verifier can verify that the message was signed by the signer, but is unable to convince anyone else of this fact. Since UDVS schemes reduce to standard signatures when no verifier designation is performed, it is natural to ask how to extend the classical Schnorr or RSA signature schemes into UDVS schemes, so that the existing key generation and signing implementation infrastructure for these schemes can be used without modification. We show how this can be efficiently achieved, and provide proofs of security for our schemes in the random oracle model.

An ideal and robust threshold RSA

We present a novel implementation of the threshold RSA. Our solution is conceptually simple, and leads to an easy design of the system. The signing key is shared in additive form, which is desirable for collaboratively performing cryptographic transformations, and its size, at all times, is logn, where n is the RSA modulus. That is, the system is ideal.

On the provable security of an efficient RSA-based pseudorandom generator

Pseudorandom Generators (PRGs) based on the RSA inversion (one-wayness) problem have been extensively studied in the literature over the last 25 years. These generators have the attractive feature of provable pseudorandomness security assuming the hardness of the RSA inversion problem. However, despite extensive study, the most efficient provably secure RSA-based generators output asymptotically only at most O(logn) bits per multiply modulo an RSA modulus of bitlength n, and hence are too slow to be used in many practical applications. To bring theory closer to practice, we present a simple modification to the proof of security by Fischlin and Schnorr of an RSA-based PRG, which shows that one can obtain an RSA-based PRG which outputs Ω(n) bits per multiply and has provable pseudorandomness security assuming the hardness of a well-studied variant of the RSA inversion problem, where a constant fraction of the plaintext bits are given. Our result gives a positive answer to an open question posed by Gennaro (J. of Cryptology, 2005) regarding finding a PRG beating the rate O(logn) bits per multiply at the cost of a reasonable assumption on RSA inversion.

Revisión sobre la capacidad de repetir sprint o RSA en jugadores de fútbol

En los últimos años, la capacidad para repetir esprines (RSA), se ha considerado como un factor limitante del rendimiento en el contexto deportivo del fútbol. En este sentido, esta revisión analiza los aspectos importantes que condicionan el rendimiento de la RSA, tales como los aspectos fisiológicos, los diferentes métodos de entrenamiento que se utilizan así como los test más utilizados para su evaluación. Por ello, el objetivo principal de esta revisión es dar a conocer los métodos y recomendaciones más importantes que se encuentran en la bibliografía para mejorar el rendimiento de los jugadores de fútbol en estas acciones de alta intensidad, así como conocer los test RSA más adecuados para realizar un seguimiento del rendimiento de los futbolistas a lo largo de la temporada.

RSA-Based Password-Authenticated Key Exchange, Revisited

The RSA-based Password-Authenticated Key Exchange (PAKE) protocols have been proposed to realize both mutual authentication and generation of secure session keys where a client is sharing his/her password only with a server and the latter should generate its RSA public/private key pair (e, n), (d, n) every time due to the lack of PKI (Public-Key Infrastructures). One of the ways to avoid a special kind of off-line (so called e-residue) attacks in the RSA-based PAKE protocols is to deploy a challenge/response method by which a client verifies the relative primality of e and φ(n) interactively with a server. However, this kind of RSA-based PAKE protocols did not give any proof of the underlying challenge/response method and therefore could not specify the exact complexity of their protocols since there exists another security parameter, needed in the challenge/response method. In this paper, we first present an RSA-based PAKE (RSA-PAKE) protocol that can deploy two different challenge/response methods (denoted by Challenge/Response Method1 and Challenge/Response Method2). The main contributions of this work include: (1) Based on the number theory, we prove that the Challenge/Response Method1 and the Challenge/Response Method2 are secure against e-residue attacks for any odd prime e; (2) With the security parameter for the on-line attacks, we show that the RSA-PAKE protocol is provably secure in the random oracle model where all of the off-line attacks are not more efficient than on-line dictionary attacks; and (3) By considering the Hamming weight of e and its complexity in the RSA-PAKE protocol, we search for primes to be recommended for a practical use. We also compare the RSA-PAKE protocol with the previous ones mainly in terms of computation and communication complexities.

基于RSA签名的优化公平交换协议

公平性是电子商务协议的基本安全要求.RSA是应用最为广泛的公钥密码体制之一.公平交换协议可以使得参与交换的双方以公平的方式交换信息,这样,要么任何一方都可以得到对方的信息,要么双方都得不到对方的信息.分析了现有的公平交换协议构造方法、体系结构及其在实用性和效率方面存在的问题.在此基础上,利用精心构造的扩环中可公开验证的、加密的RSA签名,提出了一种完全基于RSA签名方案的优化公平交换协议,并对其安全性和效率进行了证明和分析.分析表明,提出的方案是简洁、高效、安全的。

基于RSA密码体制构造一类新型的CEMBS

公平性是电子商务协议的基本安全要求之一. CEMBS是一种重要的用于构造公平交换协议的密码部件.分析了现有的CEMBS构造方法中存在的问题,首次提出了一种基于RSA密码体制的简洁、高效、安全的CEMBS构造方法.在此基础上,利用这一新型的CEMBS构建了一类重要的公平交换协议.