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：US08666070B2

公开(公告)日：2014-03-04

申请号：US11483553

申请日：2006-07-11

申请人： Farhad Pezeshki ,  Robert J. Lambert

发明人： Farhad Pezeshki ,  Robert J. Lambert

IPC分类号： H04L9/00

CPC分类号： H04L9/3247 ,  G06F7/725 ,  G06F9/30058 ,  G06F12/1408 ,  G06F21/52 ,  G06F21/75 ,  G06F21/755 ,  G06F2207/7223 ,  G06F2207/7242 ,  G06K19/073 ,  G06K19/07363 ,  H04L9/003 ,  H04L2209/04 ,  Y02D10/13

摘要： A method of masking a cryptographic operation using a secret value, comprising the steps of dividing the secret value into a plurality of parts; combining with each part a random value to derive a new part such that the new parts when combined are equivalent to the original secret value; and utilizing each of the individual parts in the operation.

公开(公告)号：US08666062B2

公开(公告)日：2014-03-04

申请号：US12101590

申请日：2008-04-11

申请人： Robert J. Lambert

发明人： Robert J. Lambert

IPC分类号： H04L9/00

CPC分类号： G06F7/72 ,  G06F7/724 ,  G06F7/725 ,  G06F7/726

摘要： In general terms, the invention provides a finite field engine and methods for operating on elements in a finite field. The finite field engine provides finite field sub-engines suitable for any finite field size requiring a fixed number of machine words. The engine reuses these engines, along with some general purpose component or specific component providing modular reduction associated with the exact reduction (polynomial or prime) of a specific finite field. The engine has wordsized suitable code capable of adding, subtracting, multiplying, squaring, or inverting finite field elements, as long as the elements are representable in no more than the given number of words. The wordsized code produces unreduced values. Specific reduction is then applied to the unreduced value, as is suitable for the specific finite field. In this way, fast engines can be produced for many specific finite fields, without duplicating the bulk of the engine instructions (program).

摘要翻译： 一般来说，本发明提供了一种有限域引擎和用于在有限域中对元素进行操作的方法。 有限域引擎提供适合于需要固定数量的机器字的任何有限域大小的有限域子引擎。 引擎重新使用这些引擎，以及一些通用组件或特定组件，提供与特定有限域的精确减少（多项式或素数）相关联的模块化减少。 只要元素可以表示为不超过给定数量的单词，发动机就已经对适合的代码进行了加密，减法，乘法，平方或反转的适当代码。 字节码产生未减少的值。 然后将特定的减少应用于未减少的值，如适用于特定有限域。 以这种方式，可以为许多特定的有限域生产快速发动机，而不会重复大量的发动机指令（程序）。

公开(公告)号：US20130101112A1

公开(公告)日：2013-04-25

申请号：US13621021

申请日：2012-09-15

申请人： Farhad Pezeshki ,  Robert J. Lambert

发明人： Farhad Pezeshki ,  Robert J. Lambert

IPC分类号： H04L9/32

CPC分类号： H04L9/3247 ,  G06F7/725 ,  G06F9/30058 ,  G06F12/1408 ,  G06F21/52 ,  G06F21/75 ,  G06F21/755 ,  G06F2207/7223 ,  G06F2207/7242 ,  G06K19/073 ,  G06K19/07363 ,  H04L9/003 ,  H04L2209/04 ,  Y02D10/13

摘要： A method of masking a cryptographic operation using a secret value, comprising the steps of dividing the secret value into a plurality of parts; combining with each part a random value to derive a new part such that the new parts when combined are equivalent to the original secret value; and utilizing each of the individual parts in the operation.

摘要翻译： 一种使用秘密值掩蔽密码操作的方法，包括以下步骤：将秘密值分割成多个部分; 与每个部分组合一个随机值以导出新的部分，使得当组合的新部分等同于原始秘密值时; 并且在操作中使用每个单独的部件。

公开(公告)号：US20130073867A1

公开(公告)日：2013-03-21

申请号：US13619557

申请日：2012-09-14

申请人： Robert J. LAMBERT

发明人： Robert J. LAMBERT

IPC分类号： G06F21/00

CPC分类号： G06F7/725 ,  G06F7/723 ,  G06F2207/7233 ,  H04L9/003 ,  H04L9/0891 ,  H04L9/3066 ,  H04L9/3252

摘要： A method of inhibiting the disclosure of confidential information through power analysis attacks on processors in cryptographic systems. The method masks a cryptographic operation using a generator G. A secret value, which may be combined with the generator G to form a secret generator is generated. The secret value is divided into a plurality of parts. A random value is generated for association with the plurality of parts. Each of the plurality of parts is combined with the random value to derive a plurality of new values such that the new values when combined are equivalent to the secret value. Each of the new values is used in the cryptographic operation, thereby using the secret generator in place of the generator G in the cryptographic operation. The introduction of randomness facilitates the introduction of noise into algorithms used by cryptographic systems so as to mask the secret value and provide protection against power analysis attacks.

公开(公告)号：US08145697B2

公开(公告)日：2012-03-27

申请号：US11931236

申请日：2007-10-31

申请人： Robert J. Lambert

发明人： Robert J. Lambert

IPC分类号： G06F15/00 ,  H04K1/00

CPC分类号： G06F7/724 ,  G06F17/10 ,  G06F2207/7209 ,  H04L9/302

摘要： This invention describes a method for evaluating a polynomial in an extension field Fqm, wherein the method comprises the steps of partitioning the polynomial into a plurality of parts, each part is comprised of smaller polynomials using a q-th power operation in a field of characteristic q; and computing for each part components of qth powers from components of smaller powers. A further embodiment of the invention provides for a method of converting a field element represented in terms of a first basis to its representation in a second basis, comprising the steps of partitioning a polynomial, being a polynomial in the second basis, into a plurality of parts, wherein each part is comprised of smaller polynomials using a qth power operation in a field of characteristic q; evaluating the polynomial at a root thereof by computing for each part components of qth powers from components of smaller powers; and evaluating the field element at the root of the polynomial.

摘要翻译： 本发明描述了一种用于评估扩展字段Fqm中的多项式的方法，其中该方法包括以下步骤：将多项式划分成多个部分，每个部分由在特征域中使用第q次幂操作的较小多项式组成 q; 并且从小功率的组件计算每个零件的第q个功率的分量。 本发明的另一个实施例提供了一种在第二基础上将以第一基础表示的场元素转换为其表示的方法，包括以下步骤：将作为第二基础的多项式的多项式划分成多个 部分，其中每个部分由在特征q的场中使用第q次幂操作的较小多项式组成; 通过对来自较小功率的分量的q次幂的每个部分分量进行计算来评估其根的多项式; 并评估多项式根的场元素。

公开(公告)号：US08086656B2

公开(公告)日：2011-12-27

申请号：US11867594

申请日：2007-10-04

申请人： Robert J. Lambert

发明人： Robert J. Lambert

IPC分类号： G06F7/72

CPC分类号： G06F7/724 ,  G06F17/10 ,  G06F2207/7209 ,  H04L9/302

摘要： This invention describes a method for evaluating a polynomial in an extension field FqM, wherein the method comprises the steps of partitioning the polynomial into a plurality of parts, each part is comprised of smaller polynomials using a q−th power operation in a field of characteristic q; and computing for each part components of q−th powers from components of smaller powers. A further embodiment of the invention provides for a method of converting a field element represented in terms of a first basis to its representation in a second basis, comprising the steps of partitioning a polynomial, being a polynomial in the second basis, into a plurality of parts, wherein each part is comprised of smaller polynomials using a q−th power operation in a field of characteristic q; evaluating the polynomial at a root thereof by computing for each part components of q−th powers from components of smaller powers; and evaluating the field element at the root of the polynomial.

摘要翻译： 本发明描述了一种用于评估扩展字段FqM中的多项式的方法，其中所述方法包括以下步骤：将所述多项式划分为多个部分，每个部分由在特征q的场中使用aq次幂操作的较小多项式组成 ; 并且从较小功率的分量计算q个功率的每个部分分量。 本发明的另一个实施例提供了一种在第二基础上将以第一基础表示的场元素转换为其表示的方法，包括以下步骤：将作为第二基础的多项式的多项式划分成多个 部分，其中每个部分由在特征q的场中使用aq次幂运算的较小多项式组成; 通过从较小功率的分量计算q次幂的每个部分分量来评估其根的多项式; 并评估多项式根的场元素。

公开(公告)号：US07299253B2

公开(公告)日：2007-11-20

申请号：US09948793

申请日：2001-09-10

申请人： Robert J. Lambert

发明人： Robert J. Lambert

IPC分类号： G06F15/00

CPC分类号： G06F7/724 ,  G06F17/10 ,  G06F2207/7209 ,  H04L9/302

摘要： This invention describes a method for evaluating a polynomial in an extension field FqM, wherein the method comprises the steps of partitioning the polynomial into a plurality of parts, each part is comprised of smaller polynomials using a q-th power operation in a field of characteristic q; and computing for each part components of q-th powers from components of smaller powers. A further embodiment of the invention provides for a method of converting a field element represented in terms of a first basis to its representation in a second basis, comprising the steps of partitioning a polynomial, being a polynomial in the second basis, into a plurality of parts, wherein each part is comprised of smaller polynomials using a q-th power operation in a field of characteristic q; evaluating the polynomial at a root thereof by computing for each part components of q-th powers from components of smaller powers; and evaluating the field element at the root of the polynomial.

摘要翻译： 本发明描述了一种用于评估扩展字段F≠M的多项式的方法，其中该方法包括以下步骤：将多项式划分为多个部分，每个部分是 由在特征q的场中使用aq ^{功率运算的较小多项式组成; 并且从较小功率的分量计算每个零部件的功率的功率。 本发明的另一个实施例提供了一种在第二基础上将以第一基础表示的场元素转换为其表示的方法，包括以下步骤：将作为第二基础的多项式的多项式划分成多个 部分，其中每个部分由在特征q的场中使用aq 功率运算的较小多项式组成; 通过对来自较小功率的分量的功率的各部分分量进行计算来评估其根的多项式; 并评估多项式根的场元素。}

公开(公告)号：US06337909B1

公开(公告)日：2002-01-08

申请号：US08948796

申请日：1997-10-10

申请人： Scott A. Vanstone ,  Donald B. Johnson ,  Robert J. Lambert ,  Ronald C. Mullin

发明人： Scott A. Vanstone ,  Donald B. Johnson ,  Robert J. Lambert ,  Ronald C. Mullin

IPC分类号： H04L928

CPC分类号： H04L9/3013 ,  G06F7/725 ,  H04L9/3066

摘要： The public key, either short term “session” key or long term key, is generated by combining a pair of components. A first component is obtained by utilizing an integer with a relatively low Hamming weight as an exponent to facilitate exponentiation. The second component is a precomputed secret value that is of the form resulting from the exponentiation of the generator of the group element by an integer that has the requisite Hamming weight. The two components are combined to provide the public key and the two exponents combined to provide the corresponding private key.

摘要翻译： 通过组合一对组件来生成公钥，短期“会话”密钥或长期密钥。 通过利用具有相对较低的汉明重量的整数作为指数来获得第一分量以促成取幂。 第二个组件是预先计算的秘密值，其形式是由组元素的生成器乘以具有所需汉明权重的整数而产生的。 组合两个组件以提供公钥和两个指数组合以提供相应的私钥。

公开(公告)号：US5530037A

公开(公告)日：1996-06-25

申请号：US360511

申请日：1994-12-21

申请人： Patrick F. McDonnell ,  Robert J. Lambert

发明人： Patrick F. McDonnell ,  Robert J. Lambert

IPC分类号： A61L20060101 ,  A61L2/08 ,  A61L24/02 ,  A61L24/06 ,  C09J20060101 ,  C09J4/00 ,  C09J4/04 ,  C08J3/28 ,  C08K5/13

CPC分类号： A61L2/081 ,  A61L24/06 ,  C09J4/00

摘要： A curable cyanoacrylate adhesive composition intended for medical and/or veterinary uses is sterilized in liquid form by gamma irradiation. The composition comprisesa) a cyanoacrylate monomerb) a combination of an anionic stabilizer and a free-radical stabilizer in amounts effective to stabilize the composition during irradiation and to stabilize the sterilized composition during storage prior to cure, wherein the free radical stabilizer is a selected phenolic antioxidant (but not including hydroquinone).The preferred free radical stabilizer is butylated hydroxyanisole. After irradiation the cyanoacrylate monomer is substantially ungelled.

摘要翻译： 用于医疗和/或兽医用途的可固化的氰基丙烯酸酯粘合剂组合物通过γ辐射以液体形式灭菌。 组合物包含a）氰基丙烯酸酯单体b）阴离子稳定剂和自由基稳定剂的组合，其量有效地在照射期间稳定组合物，并且在固化之前储存期间稳定灭菌组合物，其中自由基稳定剂是 选择酚类抗氧化剂（但不包括氢醌）。 优选的自由基稳定剂是丁基化羟基苯甲醚。 在辐射后，氰基丙烯酸酯单体基本上未凝胶化。