公开(公告)号：US20070064932A1

公开(公告)日：2007-03-22

申请号：US11333296

申请日：2006-01-18

申请人： Marinus Struik ,  Daniel Brown ,  Scott Vanstone ,  Robert Gallant ,  Adrian Antipa ,  Robert Lambert

发明人： Marinus Struik ,  Daniel Brown ,  Scott Vanstone ,  Robert Gallant ,  Adrian Antipa ,  Robert Lambert

IPC分类号： H04L9/30

CPC分类号： H04L9/3066 ,  G06F7/725 ,  H04L9/30 ,  H04L9/3252

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。

公开(公告)号：US20060140400A1

公开(公告)日：2006-06-29

申请号：US11272152

申请日：2005-11-14

申请人： Daniel Brown ,  Robert Gallant ,  Scott Vanstone ,  Marinus Struik

发明人： Daniel Brown ,  Robert Gallant ,  Scott 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。

公开(公告)号：US08788827B2

公开(公告)日：2014-07-22

申请号：US13620206

申请日：2012-09-14

申请人： Marinus Struik ,  Daniel R. Brown ,  Scott A. Vanstone ,  Robert P. Gallant ,  Adrian Antipa ,  Robert J. Lambert

发明人： Marinus Struik ,  Daniel R. Brown ,  Scott A. Vanstone ,  Robert P. Gallant ,  Adrian Antipa ,  Robert J. Lambert

IPC分类号： H04L29/06 ,  H04L9/30

CPC分类号： H04L9/3066 ,  G06F7/725 ,  H04L9/30 ,  H04L9/3252

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。

公开(公告)号：US20130064367A1

公开(公告)日：2013-03-14

申请号：US13620206

申请日：2012-09-14

申请人： Marinus Struik ,  Daniel R. Brown ,  Scott A. Vanstone ,  Robert P. Gallant ,  Adrian Antipa ,  Robert J. Lambert

发明人： Marinus Struik ,  Daniel R. Brown ,  Scott A. Vanstone ,  Robert P. Gallant ,  Adrian Antipa ,  Robert J. Lambert

IPC分类号： H04L9/00 ,  H04L9/28

CPC分类号： H04L9/3066 ,  G06F7/725 ,  H04L9/30 ,  H04L9/3252

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。

公开(公告)号：US08806197B2

公开(公告)日：2014-08-12

申请号：US13478288

申请日：2012-05-23

申请人： Marinus Struik ,  Daniel R. Brown ,  Scott A. Vanstone ,  Robert P. Gallant ,  Adrian Antipa ,  Robert J. Lambert

发明人： Marinus Struik ,  Daniel R. Brown ,  Scott A. Vanstone ,  Robert P. Gallant ,  Adrian Antipa ,  Robert J. Lambert

IPC分类号： H04L29/06

CPC分类号： H04L9/3066 ,  G06F7/725 ,  H04L9/30 ,  H04L9/3252

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.

公开(公告)号：US20120230494A1

公开(公告)日：2012-09-13

申请号：US13478288

申请日：2012-05-23

申请人： Marinus Struik ,  Daniel R. Brown ,  Scott A. Vanstone ,  Robert P. Gallant ,  Adrian Antipa ,  Robert J. Lambert

发明人： Marinus Struik ,  Daniel R. Brown ,  Scott A. Vanstone ,  Robert P. Gallant ,  Adrian Antipa ,  Robert J. Lambert

IPC分类号： H04L9/08

CPC分类号： H04L9/3066 ,  G06F7/725 ,  H04L9/30 ,  H04L9/3252

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。

公开(公告)号：US08204232B2

公开(公告)日：2012-06-19

申请号：US11333296

申请日：2006-01-18

申请人： Marinus Struik ,  Daniel R. Brown ,  Scott A. Vanstone ,  Robert P. Gallant ,  Adrian Antipa ,  Robert J. Lambert

发明人： Marinus Struik ,  Daniel R. Brown ,  Scott A. Vanstone ,  Robert P. Gallant ,  Adrian Antipa ,  Robert J. Lambert

IPC分类号： H04L9/08

CPC分类号： H04L9/3066 ,  G06F7/725 ,  H04L9/30 ,  H04L9/3252

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。

公开(公告)号：US20050031122A1

公开(公告)日：2005-02-10

申请号：US10734231

申请日：2003-12-15

申请人： Scott Vanstone ,  John Proos ,  Marinus Struik

发明人： Scott Vanstone ,  John Proos ,  Marinus Struik

IPC分类号： H04L9/00 ,  H04L9/30

CPC分类号： H04L9/3093 ,  H04L9/005 ,  H04L2209/08 ,  H04L2209/12 ,  H04L2209/20 ,  H04L2209/26

摘要： A method of decrypting a message encrypted using a truncated ring cryptosystem. The method comprises selecting a window parameter T determining a plurality of windows of a predetermined size, each window being shifted by an amount less than or equal to the window parameter T. A decryption candidate is determined for each possible window. Each decryption candidate is tested to determine whether it is a valid message. The result of the decryption is chosen to be a valid message found in the previous step or if no valid message is found it is indicated that the message could not be decrypted. By this method, a constant number of decryption candidates are determined for each decryption.

摘要翻译： 一种解密使用截断的环密码系统加密的消息的方法。 该方法包括选择确定预定大小的多个窗口的窗口参数T，每个窗口移动小于或等于窗口参数T的量。为每个可能窗口确定解密候选。 对每个解密候选进行测试，以确定它是否是有效的消息。 解密的结果被选择为在前一步骤中找到的有效消息，或者如果没有找到有效的消息，则指示该消息不能被解密。 通过这种方法，为每个解密确定常数的解密候选。

公开(公告)号：US08855308B2

公开(公告)日：2014-10-07

申请号：US12549075

申请日：2009-08-27

申请人： Marinus Struik

发明人： Marinus Struik

IPC分类号： H04L9/00 ,  H04W12/02 ,  H04L1/18 ,  H04L29/06 ,  H04L29/08 ,  H04W4/12 ,  H04W24/00 ,  H04W28/04 ,  H04W28/06

CPC分类号： H04L63/0428 ,  H04L1/1803 ,  H04L1/1812 ,  H04L1/1867 ,  H04L29/06 ,  H04L47/34 ,  H04L63/0435 ,  H04L63/06 ,  H04L67/04 ,  H04L67/12 ,  H04L69/329 ,  H04L2209/80 ,  H04W4/12 ,  H04W12/02 ,  H04W12/04 ,  H04W24/00 ,  H04W28/04 ,  H04W28/06 ,  H04W56/0015

摘要： A method of transmitting messages from a sender to a recipient over a wireless channel, the messages including a sequence counter and a frame counter. The method comprises establishing initial values of the sequence counter and the frame counter at the sender. Initial values of the frame counter and the sequence counter are provided to the recipient. The sender sends compressed messages including the value of the sequence counter and not the frame counter and monitors for an acknowledgement of receipt by the recipient. When no acknowledgment is received, the sender sends uncompressed messages until an acknowledgement of receipt is received from the recipient. The sequence counter is incremented and the next value of the frame counter is established as the integer next larger than previous value of the frame counter which is congruent to the sequence counter modulo 256.

摘要翻译： 一种通过无线信道从发送方向接收者发送消息的方法，所述消息包括序列计数器和帧计数器。 该方法包括在发送方建立序列计数器和帧计数器的初始值。 帧计数器和序列计数器的初始值被提供给接收者。 发送方发送压缩消息，包括序列计数器的值，而不是帧计数器，并监视收件人的收到确认。 当没有接收到确认时，发送方发送未压缩的消息，直到从收件人收到收到确认。 序列计数器递增，并且帧计数器的下一个值被建立为接下来大于帧计数器的先前值的整数，其与序列计数器模256一致。

公开(公告)号：US20120284800A1

公开(公告)日：2012-11-08

申请号：US13551869

申请日：2012-07-18

申请人： Marinus Struik

发明人： Marinus Struik

IPC分类号： G06F21/00

CPC分类号： H04L63/123 ,  H04L63/04 ,  H04L63/0428 ,  H04L63/0876 ,  H04L63/105 ,  H04L63/162

摘要： A method of communicating in a secure communication system, comprises the steps of assembling as message at a sender, then determining a security level, and including an indication of the security level in a header of the message. The message is then sent to a recipient.

摘要翻译： 一种在安全通信系统中进行通信的方法包括以下步骤：在发送方处组装为消息，然后确定安全级别，并且包括消息头部中的安全级别的指示。 然后将该消息发送给收件人。