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Categoria: Ciências Exactas → Matemática
Data: 2011-02-09
Elliptic curves have deep and beautiful properties. They are plane curves of the type y2 = x3 + a x + b that have been studied since the XIX century. That equation in the affine plane corresponds to the homogeneous equation y2 z= x3 + a xz2 + b z3, which describes in space a family of algebraic surfaces with two parameters a and b. The computational variation of these equations generates beautiful animations that stimulate our imagination and evoke our mathematical creativity. Cryptography refers to secure methods to transmit and safeguard secret and valuable information. Since 1977 the RSA public key system has been widely used. It is based on prime number theory and on the difficulty of factoring very large integers. With the impact of the elliptic curve method for integer factorization, Elliptic Curve Cryptography (ECC) was invented by mathematicians in 1985, and since then the mathematical sophistication of cryptography has been raised to a whole new level. The security of the ECC algorithms is based on the discrete logarithm problem of elliptic curves, which seems to be a much harder problem in finite field arithmetic. Recent mathematical advances imply that a certain desired security level can be attained with significantly smaller keys, for instance, a 160-bit ECC key provides the same level of security as a 1024-bit RSA key. The theory of elliptic curves illustrates the beauty of the links between number theory, algebra and geometry and provides a powerful mathematical tool to strengthen security of e-commerce and secure communications.
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ZappStream disponível em código-aberto

O ZappStream é um servidor de vídeos que permite uma gestão eficiente da largura de banda e acesso directo a qualquer parte de um vídeo durante a sua transmissão.

O código do ZappStream é agora disponibilizado para que possa ser utilizado e melhorado no âmbito de outras iniciativas.