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    Trapdoor one-way functions on elliptic curves and their application to shorter signatures and asymmetric encryption
    1.
    发明授权
    Trapdoor one-way functions on elliptic curves and their application to shorter signatures and asymmetric encryption 有权
    椭圆曲线上的Trapdoor单向函数及其对较短签名和非对称加密的应用

    公开(公告)号：US08213605B2

    公开(公告)日：2012-07-03

    申请号：US12945234

    申请日：2010-11-12

    申请人： Daniel Richard L. Brown ,  Robert Philip Gallant ,  Scott Alexander Vanstone ,  Marinus Struik

    发明人： Daniel Richard L. Brown ,  Robert Philip Gallant ,  Scott Alexander Vanstone ,  Marinus Struik

    IPC分类号： H04L9/30

    CPC分类号： H04L63/0823 ,  G06F21/64 ,  H04L9/3066 ,  H04L9/3252

    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.

    摘要翻译： 本发明提供了一种新的陷门单向功能。 在一般意义上，使用一些二次代数整数z。 然后找到曲线E和在E上定义[z]的有理图。有理图[z]是陷门单向函数。 z的明智选择将确保可以有效地计算[z]，难以反转，[z]定义的[z]的确定是困难的，而z的知识允许反转[ z]在一组椭圆曲线点上。 每一个合理的地图都是一个翻译和一个同化的组合。 理性地图中最安全的部分是翻译易翻译的同化。 如果反转内生的问题，因此[z]与E中的离散对数问题一样困难，则密码组的大小可以小于用于RSA陷门单向函数的组的大小。

    Incorporating data into cryptographic components of an ECQV certificate
    5.
    发明授权
    Incorporating data into cryptographic components of an ECQV certificate 有权
    将数据合并到ECQV证书的加密组件中

    公开(公告)号：US09003181B2

    公开(公告)日：2015-04-07

    申请号：US13070178

    申请日：2011-03-23

    申请人： Herbert Anthony Little ,  Matthew John Campagna ,  Scott Alexander Vanstone ,  Daniel Richard L. Brown

    发明人： Herbert Anthony Little ,  Matthew John Campagna ,  Scott Alexander Vanstone ,  Daniel Richard L. Brown

    IPC分类号： H04L29/00 ,  H04L9/08 ,  H04L9/30 ,  H04L9/32

    CPC分类号： H04L9/0844 ,  H04L9/3066 ,  H04L9/3263

    摘要： During generation of an implicit certificate for a requestor, a certificate authority incorporates information in the public-key reconstruction data, where the public-key reconstruction data is to be used to compute the public key of the requestor. The information may be related to one or more of the requestor, the certificate authority, and the implicit certificate. The certificate authority reversibly encodes the public-key reconstruction data in the implicit certificate and sends it to the requestor. After receiving the implicit certificate from the certificate authority, the requestor can extract the incorporated information from the public-key reconstruction data. The implicit certificate can be made available to a recipient, and the recipient can also extract the incorporated information.

    摘要翻译： 在为请求者生成隐式证书期间，证书颁发机构将公钥重构数据中的信息合并在一起，其中公钥重构数据将用于计算请求者的公开密钥。 信息可能与请求者，证书颁发机构和隐含证书中的一个或多个有关。 证书颁发机构对隐含证书中的公钥重构数据进行可逆编码，并将其发送给请求者。 从认证机构收到隐含证书后，请求者可以从公钥重构数据中提取合并信息。 隐式证书可以提供给收件人，收件人还可以提取合并的信息。

    INCORPORATING DATA INTO CRYPTOGRAPHIC COMPONENTS OF AN ECQV CERTIFICATE
    8.
    发明申请
    INCORPORATING DATA INTO CRYPTOGRAPHIC COMPONENTS OF AN ECQV CERTIFICATE 有权
    将数据纳入ECQV认证的CRYPTOGRAPHIC COMPONENTS

    公开(公告)号：US20120246465A1

    公开(公告)日：2012-09-27

    申请号：US13070178

    申请日：2011-03-23

    申请人： Herbert Anthony Little ,  Matthew John Campagna ,  Scott Alexander Vanstone ,  Daniel Richard L. Brown

    发明人： Herbert Anthony Little ,  Matthew John Campagna ,  Scott Alexander Vanstone ,  Daniel Richard L. Brown

    IPC分类号： H04L9/30

    CPC分类号： H04L9/0844 ,  H04L9/3066 ,  H04L9/3263

    摘要： During generation of an implicit certificate for a requestor, a certificate authority incorporates information in the public-key reconstruction data, where the public-key reconstruction data is to be used to compute the public key of the requestor. The information may be related to one or more of the requestor, the certificate authority, and the implicit certificate. The certificate authority reversibly encodes the public-key reconstruction data in the implicit certificate and sends it to the requestor. After receiving the implicit certificate from the certificate authority, the requestor can extract the incorporated information from the public-key reconstruction data. The implicit certificate can be made available to a recipient, and the recipient can also extract the incorporated information.

    摘要翻译： 在为请求者生成隐式证书期间，证书颁发机构将公钥重构数据中的信息合并在一起，其中公钥重构数据将用于计算请求者的公开密钥。 信息可能与请求者，证书颁发机构和隐含证书中的一个或多个有关。 证书颁发机构对隐含证书中的公钥重构数据进行可逆编码，并将其发送给请求者。 从认证机构收到隐含证书后，请求者可以从公钥重构数据中提取合并信息。 隐式证书可以提供给收件人，收件人还可以提取合并的信息。

    Method and apparatus for performing elliptic curve arithmetic
    10.
    发明授权
    Method and apparatus for performing elliptic curve arithmetic 有权
    执行椭圆曲线运算的方法和装置

    公开(公告)号：US08189772B2

    公开(公告)日：2012-05-29

    申请号：US12836101

    申请日：2010-07-14

    申请人： Scott Alexander Vanstone ,  Daniel Richard L. Brown

    发明人： Scott Alexander Vanstone ,  Daniel Richard L. Brown

    IPC分类号： H04L9/00 ,  H04L9/14

    CPC分类号： G06F7/725 ,  H04L9/002 ,  H04L9/0894 ,  H04L9/3066

    摘要： A method of performing a cryptographic operation on a point in an elliptic curve cryptosystem using an elliptic curve. The method comprises the steps of obtaining information that uniquely identifies the elliptic curve and performing computations on the point to obtain the result of the cryptographic operation. The computations use the information. The computations produce an incorrect result if the point is not on the elliptic curve.

    摘要翻译： 使用椭圆曲线对椭圆曲线密码系统中的点执行密码操作的方法。 该方法包括以下步骤：获得唯一地识别椭圆曲线的信息，并在点上执行计算以获得密码操作的结果。 计算使用信息。 如果点不在椭圆曲线上，计算将产生不正确的结果。