Trapdoor one-way functions on elliptic curves and their application to shorter signatures and asymmetric encryption
    15.
    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

    IPC分类号: H04L9/30

    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。

    Method and apparatus for performing elliptic curve arithmetic
    16.
    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

    IPC分类号: H04L9/00 H04L9/14

    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。

    System and method for accessing private networks
    18.
    发明授权
    System and method for accessing private networks 有权
    用于访问专用网络的系统和方法

    公开(公告)号:US09118667B2

    公开(公告)日:2015-08-25

    申请号:US13487055

    申请日:2012-06-01

    IPC分类号: H04L29/06 H04L9/32 H04W12/06

    摘要: A system and method are provided for using a mobile device to authenticate access to a private network. The mobile device may operate to receive a challenge from an authentication server, the challenge having being generated according to a request to access a private network; obtain a private value; use the private value, the challenge, and a private key to generate a response to the challenge; and send the response to the authentication server. An authentication server may operate to generate a challenge; send the challenge to a mobile device; receive a response from the mobile device, the response having been generated by the mobile device using a private value, the challenge, and a private key; verify the response; and confirm verification of the response with a VPN gateway to permit a computing device to access a private network.

    摘要翻译: 提供了一种用于使用移动设备认证对专用网络的访问的系统和方法。 移动设备可以操作以从认证服务器接收挑战,所述挑战是根据访问专用网络的请求而生成的; 获得私人价值; 使用私有价值,挑战和私钥来产生对挑战的回应; 并将响应发送给认证服务器。 验证服务器可以操作以产生挑战; 将挑战发送到移动设备; 从所述移动设备接收响应,所述响应已由所述移动设备使用私有值,所述挑战和私钥生成; 验证回应; 并使用VPN网关确认响应的验证,以允许计算设备访问专用网络。

    Key agreement and transport protocol with implicit signatures
    20.
    发明授权
    Key agreement and transport protocol with implicit signatures 失效
    具有隐式签名的密钥协商和传输协议

    公开(公告)号:US08090947B2

    公开(公告)日:2012-01-03

    申请号:US12837104

    申请日:2010-07-15

    IPC分类号: H04L9/30

    摘要: A key establishment protocol between a pair of correspondents includes the generation by each correspondent of respective signatures. The signatures are derived from information that is private to the correspondent and information that is public. After exchange of signatures, the integrity of exchange messages can be verified by extracting the public information contained in the signature and comparing it with information used to generate the signature. A common session key may then be generated from the public and private information of respective ones of the correspondents.

    摘要翻译: 一对记者之间的密钥建立协议包括每个记者生成各个签名。 签名来自对记者的私人信息和公开的信息。 在签名交换之后,可以通过提取签名中包含的公开信息并将其与用于生成签名的信息进行比较来验证交换消息的完整性。 然后可以从相应记者的公共和私人信息生成公共会话密钥。