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rFzeitoundoerthurFom Abstract. In a seminal work at EUROCRYPT '96, Coppersmith showed how to nd all small roots of a univariate polynomial congruence in polynomial time: this has found many applications in public-key cryptanalysis and in a few security proofs. However, the running time of the algorithm is a high-degree polynomial, which limits… (More)

Boneh et al. showed at Crypto 99 that moduli of the form N = p r q can be factored in polynomial time when r log p. Their algorithm is based on Coppersmith's technique for finding small roots of polynomial equations. In this paper we show that N = p r q s can also be factored in polynomial time when r or s is at least (log p) 3 ; therefore we identify a new… (More)

Boneh et al. showed at Crypto 99 that moduli of the form N = p r q can be factored in polynomial time when r ≥ log p. Their algorithm is based on Coppersmith's technique for finding small roots of polynomial equations. Recently, Coron et al. showed that N = p r q s can also be factored in polynomial time, but under the stronger condition r ≥ log 3 p. In… (More)

We describe a new technique for improving the efficiency of the masking countermeasure against side-channel attacks. Our technique is based on using common shares between secret variables, in order to reduce the number of finite field multiplications. Our algorithms are proven secure in the ISW probing model with n t + 1 shares against t probes. For AES, we… (More)

A common countermeasure against side-channel attacks consists in using the masking scheme originally introduced by Ishai, Sahai and Wagner (ISW) at Crypto 2003, and further generalized by Rivain and Prouff at CHES 2010. The countermeasure is provably secure in the probing model, and it was showed by Duc, Dziembowski and Faust at Eurocrypt 2014 that the… (More)

Boneh et al. showed at Crypto 99 that moduli of the form N = p r q can be factored in polynomial time when r log p. Their algorithm is based on Coppersmith's technique for finding small roots of polynomial equations. In this paper we show that N = p r q s can also be factored in polynomial time when r or s is at least (log p) 3 ; therefore we identify a new… (More)

- Rina Zeitoun
- 2015

Coppersmith described at Eurocrypt 96 a polynomial-time algorithm for finding small roots of univariate modular equations, based on lattice reduction. In this paper we describe the first improvement of the asymptotic complexity of Coppersmith's algorithm. Our method consists in taking advantage of Coppersmith's matrix structure, in order to apply LLL… (More)

This article introduces a new Combined Attack on a CRT-RSA implementation resistant against Side-Channel Analysis and Fault Injection attacks. Such implementations prevent the attacker from obtaining the signature when a fault has been induced during the computation. Indeed, such a value would allow the attacker to recover the RSA private key by computing… (More)

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