This paper describes a parallel Jacobi method for lattice basis reduction and a GPU implementation using CUDA. Our experiments have shown that the parallel implementation is more than fifty times as fast as the serial counterpart, which is about twice as fast as the well-known LLL lattice reduction algorithm.

Very recent attacks like ladder leak demonstrated feasibility to recover private key with side channel using just one bit of secret nonce. ECDSA nonce bias can be exploited in many ways. Some on involve complicated Fourier analysis and lattice mathematics. In this paper will enable cryptographers identify efficient ways which cracked curves NIST256p, SECP256k1, NIST521p weak nonce, kind that cr...

In this paper, we introduce a new parallel variant of the LLL lattice basis reduction algorithm. Our new, multi-threaded algorithm is the first to provide an efficient, parallel implementation of the Schorr-Euchner algorithm for today’s multi-processor, multi-core computer architectures. Experiments with sparse and dense lattice bases show a speed-up factor of about 1.8 for the 2-thread and abo...

In this paper, using the LLL reduction method and an algorithm for the computation of the integral points of a class of conics, we find small solutions of a class of bivariate modular equations of second degree. We use our result for attacking DSA and ECDSA.

The Korkine-Zolotareff (KZ) reduction is one of the often used reduction strategies for decoding lattices. A KZ reduction algorithm involves solving shortest vector problems (SVPs) and basis expansion. In this paper, first we improve the commonly used Schnorr-Euchner search strategy for solving SVPs. Then, we derive upper bounds on the magnitudes of the entries of any solution of a SVP when its...

Das Lovasz Local Lemma (LLL) ist eine der wichtigsten probabilistischen Methoden. Es wird angewendet um zu beweisen, dass bestimmte Ereignisse mit einer positiven Wahrscheinlichkeit eintreten können.[7] Da diese Wahrscheinlichkeit oft sehr klein ist, liefert das LLL keine effizienten Algorithmen. J.Beck hat als erster eine Methode entwickelt, um aus dem Existenzbeweis der LLL einen Polynomialze...

At the 1990 EuroCrypt Conference, Niemi proposed a new public-key cryptosystem based on modular knapsacks. Y.M. Chee in Singapore, A. Joux and J. Stern in Paris independently found that this cryptosystem is insecure. Our two cryptanalytic methods are slightly different, but they are both based on the LLL algorithm. This is one more example of a cryptosystem that can be broken using this powerfu...

BACKGROUND Considering promising results in animal models and patients, therapeutic use of MSCs for immune disease is likely to undergo continued evaluation. Low-lever laser (LLL) has been widely applied to retard the inflammatory reaction. LLL treatment can potentially be applied in anti-inflammatory therapy followed by stem cell therapy. AIM OF THE STUDY The purpose of this study was to inv...

OBJECTIVE To quantitatively assess and compare the quality of life (QoL) of women with a self-reported diagnosis of lower limb lymphedema (LLL), to women with lower limb swelling (LLS), and to women without LLL or LLS following treatment for endometrial cancer. METHODS 1399 participants in the Australian National Endometrial Cancer Study were sent a follow-up questionnaire 3-5 years after dia...