New Trapdoor Projection Maps for Composite-Order Bilinear Groups

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Provided by: UC Regents
Topic: Security
Format: PDF
An asymmetric pairing over groups of composite order is a bilinear map e: G1 G2 - GT for groups G1 and G2 of composite order N = pq. The authors observe that a recent construction of pairing-friendly elliptic curves in this setting by the researcher exhibits surprising and unprecedented structure: projecting an element of the order-N2 group G1 - G2 onto the bilinear groups G1 and G2 requires knowledge of a trapdoor. This trapdoor, the square root of a certain number modulo N, seems strictly weaker than the trapdoors previously used in composite-order bilinear cryptography.
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