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1. 发明授权

US08913739B2 Method for scalar multiplication in elliptic curve groups over prime fields for side-channel attack resistant cryptosystems 有权
标题翻译：用于侧信道抗攻击密码系统的素数场上的椭圆曲线组中的标量乘法的方法
公开(公告)号：US08913739B2
公开(公告)日：2014-12-16
申请号：US12083861
申请日：2005-10-18
申请人： Jovan Golic
发明人： Jovan Golic
IPC分类号： H04L9/28 , G06F7/72
CPC分类号： G06F7/725 , G06F7/721 , G06F7/728 , G06F2207/7257 , G06F2207/7261
摘要： A method and device for transforming data with a secret parameter in an elliptic curve cryptosystem based on an elliptic curve defined over an underlying prime field, includes multiplying a point of the elliptic curve; representing the data to be transformed, by a scalar representing the secret parameter, wherein the multiplying includes performing at least one point addition operation and at least one point doubling operation on points of the elliptic curve; providing a representation in affine coordinates of the elliptic curve point to be multiplied and a representation in projective coordinates of intermediate elliptic curve points obtained during the multiplying; performing both the point addition operation and the point doubling operation by means of a sequence of elementary prime field operation types, the elementary prime field operation types including: a first type of prime field operations including field multiplication and field squaring of coordinates of the elliptic curve points and a second type of prime field operations including field addition, field doubling, and field subtraction of coordinates of the elliptic curve points.
摘要翻译：一种用于基于椭圆曲线在椭圆曲线密码系统中的秘密参数来转换数据的方法和装置，包括：将椭圆曲线的点相乘; 表示要变换的数据，代表表示秘密参数的标量，其中所述乘法包括对所述椭圆曲线的点执行至少一个点加法运算和至少一个加倍运算; 提供要乘以的椭圆曲线点的仿射坐标中的表示和在乘法期间获得的中间椭圆曲线点的投影坐标中的表示; 通过基本素场操作类型的序列来执行点加法运算和点加倍运算，所述基本素数运算类型包括：包括场乘法和椭圆曲线坐标的场平方的第一类素数场运算点和第二种类型的主场操作，包括场加法，场倍增和椭圆曲线点的坐标的场减法。

2. 发明授权

US08712038B2 Cryptography on a simplified elliptical curve 有权
标题翻译：简化椭圆曲线上的密码学
公开(公告)号：US08712038B2
公开(公告)日：2014-04-29
申请号：US13377381
申请日：2010-06-15
申请人： Thomas Icart
发明人： Thomas Icart
IPC分类号： H04K1/00 , H04L9/00 , H04L9/28 , H04L9/30
CPC分类号： H04L9/3066 , G06F7/725 , G06F2207/7261 , H04L9/005 , H04L2209/08 , H04L2209/26
摘要： A cryptographic calculation includes obtaining a point P(X,Y) from a parameter t on an elliptical curve Y2=f(X) and from polynomials satisfying: −f(X1(t))·f(X2(t))=U(t)2 in the finite body Fq, irrespective of the parameter t, q=3 mod 4. A value of the parameter t is obtained and the point P is determined by: (i) calculating X1=X1(t), X2=X2(t) and U=U(t); (ii) testing whether the term f(X−1) is a squared term in the finite body Fq and, if so, calculating the square root of the term f(X1), the point P having X1 as abscissa and Y1, the square root of the term f(X1), as ordinate; (iii) otherwise, calculating the square root of the term f(X2), the point P having X2, as abscissa and Y2, the square root of the term f(X2), as ordinate. The point P is useful in encryption, scrambling, signature, authentication or identification cryptographic applications.
摘要翻译：加密计算包括从椭圆曲线Y2 = f（X）上的参数t获得点P（X，Y）和满足以下条件的多项式：-f（X1（t））·f（X2（t））= U （t）2，与参数t，q = 3 mod 4无关。获得参数t的值，点P由下式确定：（i）计算X1 = X1（t），X2 = X2（t）和U = U（t）; （ii）测试f（X-1）是有限体Fq中的平方项，如果是，则计算项f（X1）的平方根，点P的X1为横坐标，Y1为术语f（X1）的平方根作为纵坐标; （iii）否则，计算术语f（X2）的平方根，具有X2的点P为横坐标，Y2为项f（X2）的平方根，为纵坐标。点P在加密，加密，签名，认证或识别加密应用中是有用的。

3. 发明授权

US08542820B2 Apparatus for calculating a result of a scalar multiplication 有权
标题翻译：用于计算标量乘法的结果的装置
公开(公告)号：US08542820B2
公开(公告)日：2013-09-24
申请号：US12366222
申请日：2009-02-05
申请人： Wieland Fischer
发明人： Wieland Fischer
IPC分类号： H04L29/06
CPC分类号： G06F7/57 , G06F7/725 , G06F2207/7223 , G06F2207/7261 , H04L9/003 , H04L9/004 , H04L9/3066 , H04L2209/046 , H04L2209/08
摘要： An apparatus for calculating a result of a scalar multiplication of a reference number with a reference point on an elliptic curve comprises a point selector and a processor. The point selector is configured to select randomly or pseudo-randomly an auxiliary point on the elliptic curve. The processor is configured to calculate the result of the scalar multiplication with a double-and-always-add process using the auxiliary point.
摘要翻译：用于计算参考号与椭圆曲线上的参考点的标量乘法的结果的装置包括点选择器和处理器。点选择器被配置为随机或伪随机选择椭圆曲线上的辅助点。处理器被配置为使用辅助点使用双重且始终添加的过程来计算标量乘法的结果。

4. 发明申请

US20130054991A1 PROCESSOR WITH DIFFERENTIAL POWER ANALYSIS ATTACK PROTECTION 有权
标题翻译：具有差分功率分析攻击保护的处理器
公开(公告)号：US20130054991A1
公开(公告)日：2013-02-28
申请号：US13521541
申请日：2010-11-15
申请人： Uri Kaluzhny
发明人： Uri Kaluzhny
IPC分类号： G06F1/26
CPC分类号： G06F7/00 , G06F21/14 , G06F21/75 , G06F21/755 , G06F2207/7261
摘要： A device including a processor to perform an operation yielding a result, the processor including a register including bit it storage elements and including a first and second section, each element being operative to store a bit value, and a power consumption mask module to determine whether the whole result can be completely written in half or less than half of the register, determine a balancing entry if the result can be completely written in half or less than half of the register, a write module to perform a single write operation to the register including writing the result and the balancing entry to the first and second section, respectively, if the result can be completely written in half or less than half of the register else writing the result of the operation across at least part of the first and second section. Related apparatus and methods are also described.
摘要翻译：一种包括处理器，用于执行产生结果的操作的处理器，所述处理器包括包括位存储元件的寄存器，并且包括第一和第二部分，每个元件可操作以存储位值，以及功耗掩模模块，以确定是否整个结果可以完全写入寄存器的一半或少于一半，如果结果可以完全写入寄存器的一半或少于一半，则确定平衡条目，写入模块对寄存器执行单个写操作包括将结果和平衡条目分别写入第一和第二部分，如果结果可以被完全写入寄存器的一半或少于一半，否则写入操作结果跨越第一和第二部分的至少一部分。还描述了相关装置和方法。

5. 发明授权

US08369517B2 Fast scalar multiplication for elliptic curve cryptosystems over prime fields 有权
标题翻译：椭圆曲线密码系统在素数场上的快速标量乘法
公开(公告)号：US08369517B2
公开(公告)日：2013-02-05
申请号：US12190539
申请日：2008-08-12
申请人： Alexandre Venelli , Francois Dassance
发明人： Alexandre Venelli , Francois Dassance
IPC分类号： H04L1/00 , H04L9/00 , H40K9/00
CPC分类号： G06F7/725 , G06F2207/7261 , H04L9/003 , H04L9/004 , H04L9/3066
摘要： Fast scalar multiplication operations are disclosed for use in an elliptic curve cryptographic system The operations use binary representations of a secret key and points on an elliptic curve defined over a prime field expressed in a coordinate system (e.g., Jacobian coordinates). The operations can be based on a modified Montgomery ladder that uses modified Meloni addition formulas. The operations can be more efficient than a double-and-add operation, and can be more resistant to side-channel attacks by hackers.
摘要翻译：公开了用于椭圆曲线加密系统中的快速标量乘法运算。该操作使用秘密密钥的二进制表示和在坐标系中表示的素数场（例如，雅可比坐标）上定义的椭圆曲线上的点。操作可以基于使用改良的Meloni加成配方的修改后的Montgomery梯子。操作可以比双重添加操作更有效，并且可以更好地抵御黑客的侧向通道攻击。

6. 发明授权

US08243920B2 Method for scalar multiplication in elliptic curve groups over binary polynomial fields for side-channel attack-resistant cryptosystems 有权
标题翻译：用于侧向通道攻击抵抗密码系统的二进制多项式字段中的椭圆曲线组中的标量乘法的方法
公开(公告)号：US08243920B2
公开(公告)日：2012-08-14
申请号：US12084009
申请日：2005-10-28
申请人： Jovan Golic
发明人： Jovan Golic
IPC分类号： H04L9/30
CPC分类号： G06F7/726 , G06F7/725 , G06F2207/7261
摘要： A method for transforming data with a secret parameter in an elliptic curve cryptosystem based on an elliptic curve defined over an underlying binary polynomial field, includes multiplying a point of the elliptic curve, and representing the data to be transformed by a scalar representing the secret parameter, wherein the multiplying includes performing at least one point addition operation and at least one point doubling operation on points of the elliptic curve. The point addition operation includes a first sequence of elementary field operations, and the point doubling operation includes a second sequence of elementary field operations, both the first and the second sequences of elementary field operations including a field inversion of coordinates of the elliptic curve points. A representation of the elliptic curve points in affine coordinates is provided and the first and second sequences of elementary field operations are balanced. The field inversion of coordinates is performed by the extended Euclidean algorithm and the balancing includes balancing the extended Euclidean algorithm by adding at least one dummy operation.
摘要翻译：一种用于基于在下面的二进制多项式域上定义的椭圆曲线在椭圆曲线密码系统中用秘密参数进行数据变换的方法，包括：将椭圆曲线的点相乘，并将要变换的数据代表表示秘密参数的标量，其中所述相乘包括对所述椭圆曲线的点执行至少一个点加法运算和至少一个加倍运算。点加法运算包括基本场运算的第一序列，点加倍运算包括基本场运算的第二序列，基本场运算的第一和第二序列包括椭圆曲线点的坐标的场反转。提供了仿射坐标中的椭圆曲线点的表示，并且基本场操作的第一和第二序列是平衡的。通过扩展的欧几里得算法进行坐标的场反转，平衡包括通过添加至少一个虚拟操作来平衡扩展的欧几里得算法。

7. 发明授权

US08150029B2 Detection of a disturbance in a calculation performed by an integrated circuit 有权
标题翻译：检测由集成电路执行的计算中的干扰
公开(公告)号：US08150029B2
公开(公告)日：2012-04-03
申请号：US11647114
申请日：2006-12-28
申请人： Thierry Huque , Jean-Louis Modave
发明人： Thierry Huque , Jean-Louis Modave
IPC分类号： G06F21/00
CPC分类号： G06F7/723 , G06F7/725 , G06F2207/7261 , G06F2207/7271
摘要： A method for detecting a disturbance of a calculation, by an electronic circuit, of a result of an integral number of applications of an internal composition law on elements of an abelian group, by successive iterations of different steps according to the even or odd character of a current coefficient of a polynomial representation of said integral number, the degree of which determines the number of iterations, each iteration including: in case of an odd current coefficient, updating at least one first variable intended to contain the result at the end of the calculation; and in case of an even current coefficient, of updating a second variable and a comparison of this second variable with an expected value.
摘要翻译：一种用于通过电子电路计算由abelian组的元素组成的内部组成定律的整体数量的结果的方法，通过根据偶数或奇数特征的不同步骤的连续迭代来检测所述积分数的多项式表示的当前系数，其度数确定迭代次数，每次迭代包括：在奇数电流系数的情况下，更新旨在包含结果的结果的至少一个第一变量计算; 并且在均匀电流系数的情况下，更新第二变量和将该第二变量与期望值的比较。

8. 发明授权

US08090957B2 Information security device, information security method, computer program, computer-readable recording medium, and integrated circuit 有权
标题翻译：信息安全装置，信息安全方法，计算机程序，计算机可读记录介质和集成电路
公开(公告)号：US08090957B2
公开(公告)日：2012-01-03
申请号：US12088028
申请日：2006-10-18
申请人： Natsume Matsuzaki , Yuichi Futa
发明人： Natsume Matsuzaki , Yuichi Futa
IPC分类号： H04L29/06
CPC分类号： G06F7/728 , G06F2207/7223 , G06F2207/7261 , H04L9/003 , H04L9/302 , H04L9/3249 , H04L2209/08 , H04L2209/127 , H04L2209/60
摘要： The present invention aims to provide an information security apparatus that counters a simple power analysis attack (SPA) on an information security apparatus such as an RSA cryptosystem. The information security apparatus uses a multiplication with 1 in a Montgomery domain. 1 in the Montgomery domain is determined depending on a modulus and an integer k, which is greater than a number of bits of a modulus p. Therefore, it is hard for attackers who do not know p or k to analyze. Also, even if an analyzer can predict the Hamming weight, it is possible to further improve the safety against the SPA by modifying k or the modulus at random.
摘要翻译：本发明旨在提供一种在诸如RSA密码系统的信息安全装置上对简单功率分析攻击（SPA）进行计数的信息安全装置。信息安全设备在Montgomery域中使用与1相乘的信息。根据模数和大于模数p的位数的整数k确定蒙哥马利域中的1。因此，不知道p或k的攻击者很难分析。此外，即使分析仪可以预测汉明重量，也可以通过随机修改k或模数来进一步提高针对SPA的安全性。

9. 发明授权

US08065531B2 Decryption method 有权
标题翻译：解密方法
公开(公告)号：US08065531B2
公开(公告)日：2011-11-22
申请号：US12295995
申请日：2007-02-15
申请人： Wolfgang Tobergte
发明人： Wolfgang Tobergte
IPC分类号： G06F11/30 , G06F12/14 , G06F13/00
CPC分类号： G06F7/723 , G06F7/725 , G06F2207/7261 , G06F2207/7271 , H04L9/004 , H04L9/005 , H04L9/302
摘要： The invention relates to a method of determining a plaintext M on the basis of a cipher C and using a secret key d, wherein the secret key d is used in binary form, wherein the plaintext M is determined in each iteration step i for the corresponding bit di and a security variable Mn is determined in parallel therewith, and then a verification variable x is determined by means of a bit-compatible exponent of the secret key d.
摘要翻译：本发明涉及一种基于密码C确定明文M并使用秘密密钥d的方法，其中秘密密钥d以二进制形式使用，其中明文M在每个迭代步骤i中被确定为相应的位di和安全变量Mn与其并行确定，然后通过秘密密钥d的位兼容指数来确定验证变量x。

10. 发明授权

US07739521B2 Method of obscuring cryptographic computations 失效
标题翻译：掩盖加密计算的方法
公开(公告)号：US07739521B2
公开(公告)日：2010-06-15
申请号：US10666632
申请日：2003-09-18
申请人： Ernie F. Brickell
发明人： Ernie F. Brickell
IPC分类号： H04L9/00
CPC分类号： G06F7/723 , G06F2207/7233 , G06F2207/7261
摘要： Obscuring cryptographic computations may be accomplished by performing modular exponentiation of an exponent in a cryptographic computation such that memory accesses are independent of the exponent bit pattern, thereby deterring timing attacks.
摘要翻译：模糊加密计算可以通过在密码计算中执行指数的模幂运算来实现，使得存储器访问独立于指数位模式，从而阻止定时攻击。

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