Cryptography on a simplified elliptical curve
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United States of America Patent
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Jan 9, 2018
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N/A
app pub date -
Jun 9, 2016
filing date -
Jun 16, 2009
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Abstract
A cryptographic calculation includes obtaining a point P(X,Y) from a parameter t on an elliptical curve Y2=f(X) and from polynomials satisfying: −f(X1(t))·f(X2(t))=U(t)2 in the finite body Fq, irrespective of the parameter t, q=3 mod 4. A value of the parameter t is obtained and the point P is determined by: (i) calculating X1=X1 (t), X2=X2(t) and U=U(t); (ii) testing whether the term f(X−1) is a squared term in the finite body Fq and, if so, calculating the square root of the term f(X1), the point P having X1 as abscissa and Y1, the square root of the term f(X1), as ordinate; (iii) otherwise, calculating the square root of the term f(X2), the point P having X2, as abscissa and Y2, the square root of the term f(X2), as ordinate. The point P is useful in encryption, scrambling, signature, authentication or identification cryptographic applications.
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