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1. 发明申请

US20080144810A1 Factoring Based Modular Exponentiation 有权
标题翻译：基于分数的模块化指数
公开(公告)号：US20080144810A1
公开(公告)日：2008-06-19
申请号：US11610886
申请日：2006-12-14
申请人： Vinodh Gopal , Erdinc Ozturk , Matt Bace , Wajdi Feghali , Robert P. Ottavi
发明人： Vinodh Gopal , Erdinc Ozturk , Matt Bace , Wajdi Feghali , Robert P. Ottavi
IPC分类号： H04L9/30
CPC分类号： G06F7/723
摘要： The present disclosure provides a system and method for performing modular exponentiation. The method may include dividing a first polynomial into a plurality of segments and generating a first product by multiplying the plurality of segments of the first polynomial with a second polynomial. The method may also include generating a second product by shifting the contents of an accumulator with a factorization base. The method may further include adding the first product and the second product to yield a first intermediate result and reducing the first intermediate result to yield a second intermediate result. The method may also include generating a public key based on, at least in part, the second intermediate result. Of course, many alternatives, variations and modifications are possible without departing from this embodiment.
摘要翻译：本公开提供了一种用于执行模幂运算的系统和方法。该方法可以包括将第一多项式划分成多个段，并通过将第一多项式的多个段乘以第二多项式来生成第一乘积。该方法还可以包括通过用因式分解基座移位累加器的内容来产生第二乘积。该方法还可以包括添加第一产物和第二产物以产生第一中间结果并减少第一中间结果以产生第二中间结果。该方法还可以包括至少部分地基于第二中间结果生成公钥。当然，在不脱离本实施例的情况下，可以进行许多替代，变化和修改。

2. 发明授权

US07961877B2 Factoring based modular exponentiation 有权
标题翻译：基于分数的模幂运算
公开(公告)号：US07961877B2
公开(公告)日：2011-06-14
申请号：US11610886
申请日：2006-12-14
申请人： Vinodh Gopal , Erdinc Ozturk , Matt Bace , Wajdi Feghali , Robert P. Ottavi
发明人： Vinodh Gopal , Erdinc Ozturk , Matt Bace , Wajdi Feghali , Robert P. Ottavi
IPC分类号： H04L9/30 , H04L9/28 , H04L9/00 , G06G7/16
CPC分类号： G06F7/723
摘要： The present disclosure provides a system and method for performing modular exponentiation. The method may include dividing a first polynomial into a plurality of segments and generating a first product by multiplying the plurality of segments of the first polynomial with a second polynomial. The method may also include generating a second product by shifting the contents of an accumulator with a factorization base. The method may further include adding the first product and the second product to yield a first intermediate result and reducing the first intermediate result to yield a second intermediate result. The method may also include generating a public key based on, at least in part, the second intermediate result. Of course, many alternatives, variations and modifications are possible without departing from this embodiment.
摘要翻译：本公开提供了一种用于执行模幂运算的系统和方法。该方法可以包括将第一多项式划分成多个段，并通过将第一多项式的多个段乘以第二多项式来生成第一乘积。该方法还可以包括通过用因式分解基座移位累加器的内容来产生第二乘积。该方法还可以包括添加第一产物和第二产物以产生第一中间结果并减少第一中间结果以产生第二中间结果。该方法还可以包括至少部分地基于第二中间结果生成公钥。当然，在不脱离本实施例的情况下，可以进行许多替代，变化和修改。

3. 发明申请

US20100153829A1 RESIDUE GENERATION 失效
标题翻译：残留生成
公开(公告)号：US20100153829A1
公开(公告)日：2010-06-17
申请号：US12336029
申请日：2008-12-16
申请人： Vinodh Gopal , Erdinc Ozturk , Gilbert Wolrich , Wajdi Feghali
发明人： Vinodh Gopal , Erdinc Ozturk , Gilbert Wolrich , Wajdi Feghali
IPC分类号： H03M13/09 , G06F7/72 , G06F11/10
CPC分类号： G06F7/724 , H03M13/091
摘要： In one embodiment, circuitry is provided to generate a residue based at least in part upon operations and a data stream generated based at least in part upon a packet. The operations may include at least one iteration of at least one reduction operation including (a) multiplying a first value with at least one portion of the data stream, and (b) producing a reduction by adding at least one other portion of the data stream to a result of the multiplying. The operations may include at least one other reduction operation including (c) producing another result by multiplying with a second value at least one portion of another stream based at least in part upon the reduction, (d) producing a third value by adding at least one other portion of the another stream to the another result, and (e) producing the residue by performing a Barrett reduction based at least in part upon the third value.
摘要翻译：在一个实施例中，提供电路以至少部分地基于至少部分地基于分组产生的操作和数据流来生成残差。操作可以包括至少一个缩减操作的迭代，包括（a）将第一值与数据流的至少一部分相乘，以及（b）通过添加数据流的至少一个其他部分来产生减少是乘法的结果。所述操作可以包括至少一个其它减少操作，其包括（c）至少部分地基于所述减少，通过与另一个流的至少一部分乘以第二值来产生另一结果，（d）通过至少加入来产生第三值另一个流的另一部分到另一个结果，以及（e）至少部分地基于第三个值执行巴雷特还原来产生残留物。

4. 发明申请

US20080148011A1 Carry/Borrow Handling 审中-公开
标题翻译：携带/借款处理
公开(公告)号：US20080148011A1
公开(公告)日：2008-06-19
申请号：US11610897
申请日：2006-12-14
申请人： Vinodh Gopal , Gilbert M. Wolrich , Gunnar Gaubatz , Daniel Cutter , Wajdi Feghali , Kaan Yuksel , Erdinc Ozturk
发明人： Vinodh Gopal , Gilbert M. Wolrich , Gunnar Gaubatz , Daniel Cutter , Wajdi Feghali , Kaan Yuksel , Erdinc Ozturk
IPC分类号： G06F9/30
CPC分类号： G06F9/3001
摘要： The present disclosure provides a system and method for performing carry/borrow handling. A method according to one embodiment may include generating a first result having a first carry or borrow from a first mathematical operation and storing the first carry or borrow and a first pointer address in a temporary register. The method may further include generating a second result having a second carry or borrow from a second mathematical operation and calling a subroutine configured to perform carry and borrow handling. The method may also include copying the first pointer address from the temporary register into a global variable. Of course, many alternatives, variations and modifications are possible without departing from this embodiment.
摘要翻译：本公开提供了用于执行进位/借用处理的系统和方法。根据一个实施例的方法可以包括从第一数学运算产生具有第一进位或借位的第一结果，并将第一进位或借位以及第一指针地址存储在临时寄存器中。该方法还可以包括从第二数学运算产生具有第二进位或借位的第二结果，并调用被配置为执行进位和借位处理的子程序。该方法还可以包括将第一指针地址从临时寄存器复制到全局变量中。当然，在不脱离本实施例的情况下，可以进行许多替代，变化和修改。

5. 发明申请

US20080144811A1 Method for Simultaneous Modular Exponentiations 有权
标题翻译：同时模块化指标的方法
公开(公告)号：US20080144811A1
公开(公告)日：2008-06-19
申请号：US11610919
申请日：2006-12-14
申请人： Vinodh Gopal , Erdinc Ozturk , Kaan Yuskel , Gunnar Gaubatz , Wajdi Feghali , Gilbert M. Wolrich
发明人： Vinodh Gopal , Erdinc Ozturk , Kaan Yuskel , Gunnar Gaubatz , Wajdi Feghali , Gilbert M. Wolrich
IPC分类号： H04L9/30
CPC分类号： G06F7/723 , H04L9/302
摘要： The present disclosure provides a method for performing modular exponentiation. The method may include generating a first remainder (xp) based on an encrypted message (X) modulo a first prime number (p) and generating a second remainder (xq) based on the encrypted message (X) modulo a second prime number (q). The method may further include generating a third remainder(v1) based on the first remainder (xp) raised to a first private key number (d1) modulo the first prime number (p) and simultaneously generating a fourth remainder (v2) based on the second remainder (xq) raised to a second private key number (d2) modulo the second prime number(q). The method may also include subtracting the fourth remainder (v2) from the third remainder (v1) to yield a result (v1−v2) and multiplying the result (v1−v2) by a constant (c) to produce a second result. The method may additionally include generating a sixth remainder (h) by taking the second result modulo the first prime number (p) and multiplying the sixth remainder (h) by the second prime number (q) to produce a third result. The method may further include adding the third result and the fourth remainder (v2) to yield a final result (Y) and generating, at least in part, a public key based on the final result (Y). Of course, many alternatives, variations and modifications are possible without departing from this embodiment.
摘要翻译：本公开提供了一种用于执行模幂运算的方法。该方法可以包括基于第一素数（p）模数的加密消息（X）生成第一余数（xp），并且基于加密消息（X）生成第二余数（xq），第二素数（q））。该方法还可以包括：基于第一余数（xp）产生第三余数（v1），所述第一余数（xp）基于所述第一余数（xp）生成第一素数（p）的第一私钥数（d1）并同时生成第四余数第二余数（xq）升至第二素数（q）的第二私钥号（d2）。该方法还可以包括从第三余数（v1）中减去第四余数（v2）以产生结果（v1-v2）并将结果（v1-v2）乘以常数（c）以产生第二结果。该方法可以另外包括通过将第二结果以第一素数（p）取模并将第六余数（h）乘以第二素数（q）产生第三结果来产生第六余数（h）。该方法还可以包括添加第三结果和第四余数（v2）以产生最终结果（Y），并且至少部分地基于最终结果（Y）生成公钥。当然，在不脱离本实施例的情况下，可以进行许多替代，变化和修改。

6. 发明申请

US20110106872A1 Method and apparatus for providing an area-efficient large unsigned integer multiplier 审中-公开
标题翻译：用于提供面积效率大的无符号整数乘法器的方法和装置
公开(公告)号：US20110106872A1
公开(公告)日：2011-05-05
申请号：US12157074
申请日：2008-06-06
申请人： William Hasenplaugh , Gilbert Wolrich , Vinodh Gopal , Gunnar Gaubatz , Erdinc Ozturk , Wajdi Feghali
发明人： William Hasenplaugh , Gilbert Wolrich , Vinodh Gopal , Gunnar Gaubatz , Erdinc Ozturk , Wajdi Feghali
IPC分类号： G06F7/487
CPC分类号： G06F7/5324 , G06F7/72
摘要： An area efficient multiplier having high performance at modest clock speeds is presented. The performance of the multiplier is based on optimal choice of a number of levels of Karatsuba decomposition. The multiplier may be used to perform efficient modular reduction of large numbers greater than the size of the multiplier.
摘要翻译：提出了一种在适度的时钟速度下具有高性能的区域有效乘法器。乘数的表现是基于对Karatsuba分解的多个水平的最佳选择。乘法器可用于执行大于乘数大小的大数量的有效的模块化减少。

7. 发明申请

US20090158132A1 Determining a message residue 有权
标题翻译：确定消息残差
公开(公告)号：US20090158132A1
公开(公告)日：2009-06-18
申请号：US12291621
申请日：2008-11-12
申请人： Vinodh Gopal , Gilbert Wolrich , Wajdi Feghali , Erdinc Ozturk , Shay Gueron
发明人： Vinodh Gopal , Gilbert Wolrich , Wajdi Feghali , Erdinc Ozturk , Shay Gueron
IPC分类号： H03M13/09 , G06F7/72 , G06F17/14 , G06F11/10 , G06F5/01
CPC分类号： G06F7/724 , H03M13/091
摘要： In one aspect, circuitry to determine a modular remainder with respect to a polynomial of a message comprised of a series of segment. In another aspect, circuitry to access at least a portion of a first number having a first endian format, determine a second number based on a bit reflection and shift of a third number having an endian format opposite to that of the first endian format, and perform a polynomial multiplication of the first number and the at least a portion of the first number.
摘要翻译：在一个方面，用于确定相对于包括一系列段的消息的多项式的模块余数的电路。在另一方面，访问具有第一末端格式的第一号码的至少一部分的电路基于具有与第一末端格式相反的端格式的第三号码的位反射和位移来确定第二号码，以及执行第一数字和第一数字的至少一部分的多项式相乘。

8. 发明授权

US08042025B2 Determining a message residue 有权
标题翻译：确定消息残差
公开(公告)号：US08042025B2
公开(公告)日：2011-10-18
申请号：US12291621
申请日：2008-11-12
申请人： Vinodh Gopal , Gilbert Wolrich , Wajdi Feghali , Erdinc Ozturk , Shay Gueron
发明人： Vinodh Gopal , Gilbert Wolrich , Wajdi Feghali , Erdinc Ozturk , Shay Gueron
IPC分类号： H03M13/03
CPC分类号： G06F7/724 , H03M13/091
摘要： In one aspect, circuitry to determine a modular remainder with respect to a polynomial of a message comprised of a series of segment. In another aspect, circuitry to access at least a portion of a first number having a first endian format, determine a second number based on a bit reflection and shift of a third number having an endian format opposite to that of the first endian format, and perform a polynomial multiplication of the first number and the at least a portion of the first number.
摘要翻译：在一个方面，用于确定相对于包括一系列段的消息的多项式的模块余数的电路。在另一方面，访问具有第一末端格式的第一号码的至少一部分的电路基于具有与第一末端格式相反的端格式的第三号码的位反射和位移来确定第二号码，以及执行第一数字和第一数字的至少一部分的多项式相乘。

9. 发明授权

US08312363B2 Residue generation 失效
标题翻译：残留代
公开(公告)号：US08312363B2
公开(公告)日：2012-11-13
申请号：US12336029
申请日：2008-12-16
申请人： Vinodh Gopal , Erdinc Ozturk , Gilbert Wolrich , Wajdi Feghali
发明人： Vinodh Gopal , Erdinc Ozturk , Gilbert Wolrich , Wajdi Feghali
IPC分类号： G06F11/00
CPC分类号： G06F7/724 , H03M13/091
摘要： In one embodiment, circuitry is provided to generate a residue based at least in part upon operations and a data stream generated based at least in part upon a packet. The operations may include at least one iteration of at least one reduction operation including (a) multiplying a first value with at least one portion of the data stream, and (b) producing a reduction by adding at least one other portion of the data stream to a result of the multiplying. The operations may include at least one other reduction operation including (c) producing another result by multiplying with a second value at least one portion of another stream based at least in part upon the reduction, (d) producing a third value by adding at least one other portion of the another stream to the another result, and (e) producing the residue by performing a Barrett reduction based at least in part upon the third value.
摘要翻译：在一个实施例中，提供电路以至少部分地基于至少部分地基于分组产生的操作和数据流来生成残差。操作可以包括至少一个缩减操作的迭代，包括（a）将第一值与数据流的至少一部分相乘，以及（b）通过添加数据流的至少一个其他部分来产生减少是乘法的结果。所述操作可以包括至少一个其它减少操作，其包括（c）至少部分地基于所述减少，通过与另一个流的至少一部分乘以第二值来产生另一结果，（d）通过至少加入来产生第三值另一个流的另一部分到另一个结果，以及（e）至少部分地基于第三个值执行巴雷特还原来产生残留物。

10. 发明授权

US07925011B2 Method for simultaneous modular exponentiations 有权
标题翻译：同时采用模幂分析的方法
公开(公告)号：US07925011B2
公开(公告)日：2011-04-12
申请号：US11610919
申请日：2006-12-14
申请人： Vinodh Gopal , Erdinc Ozturk , Kaan Yuksel , Gunnar Gaubatz , Wajdi Feghali , Gilbert M. Wolrich
发明人： Vinodh Gopal , Erdinc Ozturk , Kaan Yuksel , Gunnar Gaubatz , Wajdi Feghali , Gilbert M. Wolrich
IPC分类号： H04L9/00
CPC分类号： G06F7/723 , H04L9/302
摘要： The present disclosure provides a method for performing modular exponentiation. The method may include generating a first remainder (xp) based on an encrypted message (X) modulo a first prime number (p) and generating a second remainder (xq) based on the encrypted message (X) modulo a second prime number (q). The method may further include generating a third remainder (v1) based on the first remainder (xp) raised to a first private key number (d1) modulo the first prime number (p) and simultaneously generating a fourth remainder (v2) based on the second remainder (xq) raised to a second private key number (d2) modulo the second prime number (q). The method may also include subtracting the fourth remainder (v2) from the third remainder (v1) to yield a result (v1−v2) and multiplying the result (v1−v2) by a constant (c) to produce a second result. The method may additionally include generating a sixth remainder (h) by taking the second result modulo the first prime number (p) and multiplying the sixth remainder (h) by the second prime number (q) to produce a third result. The method may further include adding the third result and the fourth remainder (v2) to yield a final result (Y) and generating, at least in part, a public key based on the final result (Y). Of course, many alternatives, variations and modifications are possible without departing from this embodiment.
摘要翻译：本公开提供了一种用于执行模幂运算的方法。该方法可以包括基于第一素数（p）模数的加密消息（X）生成第一余数（xp），并且基于加密消息（X）生成第二余数（xq），第二素数（q））。该方法还可以包括：基于第一余数（xp）产生第三余数（v1），所述第一余数（xp）基于所述第一余数（xp）生成第一素数（p）的第一私钥数（d1）并同时生成第四余数第二余数（xq）升至第二素数（q）的第二私钥号（d2）。该方法还可以包括从第三余数（v1）中减去第四余数（v2）以产生结果（v1-v2）并将结果（v1-v2）乘以常数（c）以产生第二结果。该方法可以另外包括通过将第二结果以第一素数（p）取模并将第六余数（h）乘以第二素数（q）产生第三结果来产生第六余数（h）。该方法还可以包括添加第三结果和第四余数（v2）以产生最终结果（Y），并且至少部分地基于最终结果（Y）生成公钥。当然，在不脱离本实施例的情况下，可以进行许多替代，变化和修改。

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