A New Attack on Three Variants of the RSA Cryptosystem

International audienceIn 1995, Kuwakado, Koyama and Tsuruoka presented a new RSA-type scheme based on singular cubic curves y^2 ≡ x^3 + bx^2 (mod N) where N = pq is an RSA modulus. Then, in 2002, Elkamchouchi, Elshenawy and Shaban introduced an extension of the RSA scheme to the field of Gaussian integers using a modulus N = P Q where P and Q are Gaussian primes such that p = |P | and q = |Q| are ordinary primes. Later, in 2007, Castagnos's proposed a scheme over quadratic fields quotients with an RSA modulus N = pq. In the three schemes, the public exponent e is an integer satisfying the key equation ed − k^(p^2 − 1) (q^2 − 1) = 1. In this paper, we apply the continued fraction method to launch an attack on the three schemes when the private exponent d is sufficiently small. Our attack can be considered as an extension of the famous Wiener attack on RSA

Candida albicans-produced farnesol stimulates Pseudomonas quinolone signal production in LasR-defective Pseudomonas aeruginosa strains

Candida albicans has been previously shown to stimulate the production of Pseudomonas aeruginosa phenazine toxins in dual-species colony biofilms. Here, we report that P. aeruginosa lasR mutants, which lack the master quorum sensing system regulator, regain the ability to produce quorum-sensing-regulated phenazines when cultured with C. albicans. Farnesol, a signalling molecule produced by C. albicans, was sufficient to stimulate phenazine production in LasR− laboratory strains and clinical isolates. P. aeruginosa ΔlasR mutants are defective in production of the Pseudomonas quinolone signal (PQS) due to their inability to properly induce pqsH, which encodes the enzyme necessary for the last step in PQS biosynthesis. We show that expression of pqsH in a ΔlasR strain was sufficient to restore PQS production, and that farnesol restored pqsH expression in ΔlasR mutants. The farnesol-mediated increase in pqsH required RhlR, a transcriptional regulator downstream of LasR, and farnesol led to higher levels of N-butyryl-homoserine lactone, the small molecule activator of RhlR. Farnesol promotes the production of reactive oxygen species (ROS) in a variety of species. Because the antioxidant N-acetylcysteine suppressed farnesol-induced RhlR activity in LasR− strains, and hydrogen peroxide was sufficient to restore PQS production in las mutants, we propose that ROS are responsible for the activation of downstream portions of this quorum sensing pathway. LasR mutants frequently arise in the lungs of patients chronically infected with P. aeruginosa. The finding that C. albicans, farnesol or ROS stimulate virulence factor production in lasR strains provides new insight into the virulence potential of these strains