A Note on the Ate Pairing

The Ate pairing has been suggested since it can be computed efficiently on ordinary elliptic curves with small values of the traces of Frobenius $t$. However, not all pairing-friendly elliptic curves have this property. In this paper, we generalize the Ate pairing and find a series of variations of the Ate pairing. We show that the shortest Miller loop of the variations of the Ate pairing can possibly be as small as $r^{1/\varphi(k)}$ on more pairing-friendly curves generated by the method of complex multiplications, and hence speed up the pairing computation significantly

Identification of Apo-A1 as a biomarker for early diagnosis of bladder transitional cell carcinoma

<p>Abstract</p> <p>Background</p> <p>Bladder transitional cell carcinoma (BTCC) is the fourth most frequent neoplasia in men, clinically characterized by high recurrent rates and poor prognosis. Availability of urinary tumor biomarkers represents a convenient alternative for early detection and disease surveillance because of its direct contact with the tumor and sample accessibility.</p> <p>Results</p> <p>We tested urine samples from healthy volunteers and patients with low malignant or aggressive BTCC to identify potential biomarkers for early detection of BTCC by two-dimensional electrophoresis (2-DE) coupled with mass spectrometry (MS) and bioinformatics analysis. We observed increased expression of five proteins, including fibrinogen (Fb), lactate dehydrogenase B (LDHB), apolipoprotein-A1 (Apo-A1), clusterin (CLU) and haptoglobin (Hp), which were increased in urine samples of patients with low malignant or aggressive bladder cancer. Further analysis of urine samples of aggressive BTCC showed significant increase in Apo-A1 expression compared to low malignant BTCC. Apo-A1 level was measured quantitatively using enzyme-linked immunosorbent assay (ELISA) and was suggested to provide diagnostic utility to distinguish patients with bladder cancer from controls at 18.22 ng/ml, and distinguish patients with low malignant BTCC from patients with aggressive BTCC in two-tie grading system at 29.86 ng/ml respectively. Further validation assay showed that Apo-A1 could be used as a biomarker to diagnosis BTCC with a sensitivity and specificity of 91.6% and 85.7% respectively, and classify BTCC in two-tie grading system with a sensitivity and specificity of 83.7% and 89.7% respectively.</p> <p>Conclusion</p> <p>Taken together, our findings suggest Apo-A1 could be a potential biomarker related with early diagnosis and classification in two-tie grading system for bladder cancer.</p

A Note on the Ate Pairing

Abstract. The Ate pairing has been suggested since it can be computed efficiently on ordinary elliptic curves with small values of the traces of Frobenius t. However, not all pairing-friendly elliptic curves have this property. In this paper, we generalize the Ate pairing and find a series of variations of the Ate pairing. We show that the shortest Miller loop of the variations of the Ate pairing can possibly be as small as r 1/ϕ(k) on more pairing-friendly curves generated by the method of complex multi-plications, and hence speed up the pairing computation significantly

Speeding up the Bilinear Pairings Computation on Curves with Automorphisms

Abstract. In this paper we present a new algorithm for computing the bilinear pairings on a family of non-supersingular elliptic curves with non-trivial automorphisms. We obtain a short iteration loop in Miller’s algorithm using non-trivial efficient automorphisms. The proposed algo-rithm is as efficient as the algorithm in [12]