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Method for scalar multiplication in elliptic curve groups over prime fields for side-channel attack resistant cryptosystems
Method for scalar multiplication in elliptic curve groups over prime fields for side-channel attack resistant cryptosystems
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机译:侧信道抗攻击密码系统素数域上椭圆曲线群上标量乘法的方法
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摘要
A method and device for transforming data with a secret parameter in an elliptic curve cryptosystem based on an elliptic curve defined over an underlying prime field, includes multiplying a point of the elliptic curve; representing the data to be transformed, by a scalar representing the secret parameter, wherein the multiplying includes performing at least one point addition operation and at least one point doubling operation on points of the elliptic curve; providing a representation in affine coordinates of the elliptic curve point to be multiplied and a representation in projective coordinates of intermediate elliptic curve points obtained during the multiplying; performing both the point addition operation and the point doubling operation by means of a sequence of elementary prime field operation types, the elementary prime field operation types including: a first type of prime field operations including field multiplication and field squaring of coordinates of the elliptic curve points and a second type of prime field operations including field addition, field doubling, and field subtraction of coordinates of the elliptic curve points.
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