Elliptic Curve Point Multiplication
A method for elliptic curve point multiplication is proposed with complex multiplication by \(\sqrt-2\) or by \((1\pm \sqrt-7)/2\) instead of point doubling, speeding up multiplication about 1.34 times. Complex multiplication is given by isogeny of degree 2. Higher radix makes it possible to use one instead of two point doublings and to speed up computation about 1.61 times. Algorithm, representing exponent in \(\sqrt-2\)-adic notation for digital signature protocols, is proposed. Key agreement and public key encryption protocols can be implemented directly in \(\sqrt-2\)-adic notation.
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