摘要:
Accelerated computation of combinations of group operations in a finite field is provided by arranging for at least one of the operands to have a relatively small bit length. In a elliptic curve group, verification that a value representative of a point R corresponds the sum of two other points uG and vG is obtained by deriving integers w,z of reduced bit length and so that v=w/z. The verification equality R=uG+vQ may then be computed as −zR+(uz mod n) G+wQ=O with z and w of reduced bit length. This is beneficial in digital signature verification where increased verification can be attained.
摘要:
Accelerated computation of combinations of group operations in a finite field is provided by arranging for at least one of the operands to have a relatively small bit length. In a elliptic curve group, verification that a value representative of a point R corresponds the sum of two other points uG and vG is obtained by deriving integers w,z of reduced bit length and so that v=w/z. The verification equality R=uG+vQ may then be computed as −zR+(uz mod n) G+wQ=O with z and w of reduced bit length. This is beneficial in digital signature verification where increased verification can be attained.
摘要翻译:通过将至少一个操作数布置成具有相对较小的比特长度来提供有限域中的组操作的组合的加速计算。 在椭圆曲线组中,代表点R的值对应于其他两个点uG和vG的和的验证是通过导出比特长度减小的整数w,z获得的,并且使得v = w / z。 然后,验证等式R = uG + vQ可以被计算为-zR +(uz mod n)G + wQ = 0,其中z和w为减少的比特长度。 这在数字签名验证中是有益的,其中可以实现增加的验证。
摘要:
Accelerated computation of combinations of group operations in a finite field is provided by arranging for at least one of the operands to have a relatively small bit length. In a elliptic curve group, verification that a value representative of a point R corresponds the sum of two other points uG and vG is obtained by deriving integers w,z of reduced bit length and so that v=w/z. The verification equality R=uG+vQ may then be computed as −zR+(uz mod n) G+wQ=O with z and w of reduced bit length. This is beneficial in digital signature verification where increased verification can be attained.
摘要翻译:通过将至少一个操作数布置成具有相对较小的比特长度来提供有限域中的组操作的组合的加速计算。 在椭圆曲线组中,代表点R的值对应于其他两个点uG和vG的和的验证是通过导出比特长度减小的整数w,z获得的,并且使得v = w / z。 然后,验证等式R = uG + vQ可以被计算为-zR +(uz mod n)G + wQ = 0,其中z和w的比特长度减小。 这在数字签名验证中是有益的,其中可以实现增加的验证。
摘要:
Accelerated computation of combinations of group operations in a finite field is provided by arranging for at least one of the operands to have a relatively small bit length. In a elliptic curve group, verification that a value representative of a point R corresponds the sum of two other points uG and vG is obtained by deriving integers w,z of reduced bit length and so that v=w/z. The verification equality R=uG+vQ may then be computed as −zR+(uz mod n) G+wQ=O with z and w of reduced bit length. This is beneficial in digital signature verification where increased verification can be attained.
摘要翻译:通过将至少一个操作数布置成具有相对较小的比特长度来提供有限域中的组操作的组合的加速计算。 在椭圆曲线组中,代表点R的值对应于其他两个点uG和vG的和的验证是通过导出比特长度减小的整数w,z获得的,并且使得v = w / z。 然后,验证等式R = uG + vQ可以被计算为-zR +(uz mod n)G + wQ = 0,其中z和w为减少的比特长度。 这在数字签名验证中是有益的,其中可以实现增加的验证。
摘要:
Accelerated computation of combinations of group operations in a finite field is provided by arranging for at least one of the operands to have a relatively small bit length. In a elliptic curve group, verification that a value representative of a point R corresponds the sum of two other points uG and vG is obtained by deriving integers w,z of reduced bit length and so that v=w/z. The verification equality R=uG+vQ may then be computed as −zR+(uz mod n) G+wQ=O with z and w of reduced bit length. This is beneficial in digital signature verification where increased verification can be attained.
摘要翻译:通过将至少一个操作数布置成具有相对较小的比特长度来提供有限域中的组操作的组合的加速计算。 在椭圆曲线组中,代表点R的值对应于其他两个点uG和vG的和的验证是通过导出比特长度减小的整数w,z获得的,并且使得v = w / z。 然后,验证等式R = uG + vQ可以被计算为-zR +(uz mod n)G + wQ = 0,其中z和w为减少的比特长度。 这在数字签名验证中是有益的,其中可以实现增加的验证。
摘要:
A potential bias in the generation of a private key is avoided by selecting the key and comparing it against the system parameters. If a predetermined condition is attained it is accepted. If not it is rejected and a new key is generated.
摘要:
A potential bias in the generation or a private key is avoided by selecting the key and comparing it against the system parameters. If a predetermined condition is attained it is accepted. If not it is rejected and a new key is generated.
摘要:
The present invention provides a new trapdoor one-way function. In a general sense, some quadratic algebraic integer z is used. One then finds a curve E and a rational map defining [z] on E. The rational map [z] is the trapdoor one-way function. A judicious selection of z will ensure that [z] can be efficiently computed, that it is difficult to invert, that determination of [z] from the rational functions defined by [z] is difficult, and knowledge of z allows one to invert [z] on a certain set of elliptic curve points. Every rational map is a composition of a translation and an endomorphism. The most secure part of the rational map is the endomorphism as the translation is easy to invert. If the problem of inverting the endomorphism and thus [z] is as hard as the discrete logarithm problem in E, then the size of the cryptographic group can be smaller than the group used for RSA trapdoor one-way functions.
摘要:
A new trapdoor one-way function is provided. In a general sense, some quadratic algebraic integer z is used. One then finds a curve E and a rational map defining [z] on E. The rational map [z] is the trapdoor one-way function. A judicious selection of z will ensure that [z] can be efficiently computed, that it is difficult to invert, that determination of [z] from the rational functions defined by [z] is difficult, and knowledge of z allows one to invert [z] on a certain set of elliptic curve points.
摘要:
A new trapdoor one-way function is provided. In a general sense, some quadratic algebraic integer z is used. One then finds a curve E and a rational map defining [z] on E. The rational map [z] is the trapdoor one-way function. A judicious selection of z will ensure that [z] can be efficiently computed, that it is difficult to invert, that determination of [z] from the rational functions defined by [z] is difficult, and knowledge of z allows one to invert [z] on a certain set of elliptic curve points.