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Method of elliptic curve cryptographic digital signature generation and verification using reduced base tau expansion in non-adjacent form
Method of elliptic curve cryptographic digital signature generation and verification using reduced base tau expansion in non-adjacent form
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机译:椭圆曲线密码数字签名生成和验证的方法,方法是使用非相邻形式的减少的基tau展开
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摘要
A method of generating and verifying a digital signature by selecting an elliptic curve; selecting a point G; generating x and M; reducing x; generating a base tau expansion, in non-adjacent form, of the reduced x; multiplying G by the expansion; computing h=Hash(M); generating k; reducing k; generating a base tau expansion, in non-adjacent form, of the reduced k; multiplying G by the expansion of k to form K=(Kx,Ky); computing R=(Kx mod q); returning to the step of generating k if R=0, otherwise computing S=(k{circumflex over ( )}−1)(h+xR); returning to the step of generating k if S=0, otherwise transmitting y, q, M, R, and S; receiving y, q, M, R, and S; proceeding with the next step if 0Rq and 0Sq, otherwise not verifying the digital signature and stopping; forming h=Hash(M); computing f=((S{circumflex over ( )}−1) mod q), b=(hf mod q), and t=(Rf mod q); reducing b and t; generating a base tau expansion, in non-adjacent form, of the reduced b; multiplies G by the result of the last step to form a point B; reduces t; generates a base tau expansion, in non-adjacent form, of the reduced b and t; multiplying G by the expansion of t; computing V=B+T, where V=(Vx,Vy); computing v=(Vx mod q); and verifying the digital signature if v=R, otherwise not verifying the digital signature.
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机译:一种通过选择椭圆曲线生成和验证数字签名的方法;选择点G;产生x和M;减少x;以非相邻形式生成缩减后的x的基本tau展开; G乘以扩展;计算h= Hash(M);产生k;减少k;以减少的k的非相邻形式生成基本tau展开;用G乘以k的扩展来形成K=(K x Sub>,K y Sub>);计算R=(K x Sub> mod q);返回到如果R等于0则生成k的步骤,否则计算S等于(k(k)≤1)(h + xR);如果S等于0,则返回生成k的步骤,否则发送y,q,M,R和S;接收y,q,M,R和S;如果0 x Sub>,V y Sub>);计算v=(V x Sub> mod q);如果v等于R,则验证数字签名;否则,不验证数字签名。
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