1.0Microsoft Researchhttps://www.microsoft.com/en-us/researchAndrea Fuenteshttps://www.microsoft.com/en-us/research/people/afuentes/Computing Modular Polynomials - Microsoft Researchrich600338<blockquote class="wp-embedded-content" data-secret="wOezIS0hIY"><a href="https://www.microsoft.com/en-us/research/publication/computing-modular-polynomials-2/">Computing Modular Polynomials</a></blockquote><iframe sandbox="allow-scripts" security="restricted" src="https://www.microsoft.com/en-us/research/publication/computing-modular-polynomials-2/embed/#?secret=wOezIS0hIY" width="600" height="338" title="“Computing Modular Polynomials” — Microsoft Research" data-secret="wOezIS0hIY" frameborder="0" marginwidth="0" marginheight="0" scrolling="no" class="wp-embedded-content"></iframe><script type="text/javascript">
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We present a new probabilistic algorithm to compute modular polynomials modulo a prime. Modular polynomials parameterize pairs of isogenous elliptic curves and are useful in many aspects of computational number theory and cryptography. Our algorithm has the distinguishing feature that it does not involve the computation of Fourier coefficients of modular forms. We avoid computing […]