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    • 36. 发明申请
    • Cryptographic Processing Apparatus
    • 密码处理装置
    • US20070291937A1
    • 2007-12-20
    • US11791283
    • 2005-11-15
    • Masanobu KatagiToru AkishitaIzuru KitamuraTsuyoshi Takagi
    • Masanobu KatagiToru AkishitaIzuru KitamuraTsuyoshi Takagi
    • H04L9/30
    • G06F7/725G06F2207/7261
    • An apparatus and a method for performing a hyperelliptic curve cryptography process at a high speed in a highly secure manner are provided. A base point D is produced such that the base point D and one or more of precalculated data in addition to the base point used in a scalar multiplication operation based on a window algorithm are degenerate divisors with a weight smaller than genus g of a hyperelliptic curve. An addition operation included in the scalar multiplication operation based on the window algorithm is accomplished by performing an addition operation of adding a degenerate divisor and a non-degenerate divisor, whereby a high-speed operation is achieved without causing degradation in security against key analysis attacks such as SPA.
    • 提供了一种以高度安全的方式高速执行超椭圆曲线密码处理的装置和方法。 产生基点D,使得除了基于窗口算法的标量乘法运算中使用的基点之外,基点D和预先计算的数据中的一个或多个是具有小于超椭圆曲线的g的权重的简并因数 。 基于窗口算法的标量乘法运算中包含的加法运算通过执行加法简并因子和非简并因数的加法运算来实现,从而实现高速运算,而不会导致安全性降低密钥分析攻击 如SPA。
    • 37. 发明授权
    • Cryptographic processing apparatus
    • 加密处理装置
    • US07957527B2
    • 2011-06-07
    • US11791283
    • 2005-11-15
    • Masanobu KatagiToru AkishitaIzuru KitamuraTsuyoshi Takagi
    • Masanobu KatagiToru AkishitaIzuru KitamuraTsuyoshi Takagi
    • H04L9/28H04L9/30
    • G06F7/725G06F2207/7261
    • An apparatus and a method for performing a hyperelliptic curve cryptography process at a high speed in a highly secure manner are provided. A base point D is produced such that the base point D and one or more of precalculated data in addition to the base point used in a scalar multiplication operation based on a window algorithm are degenerate divisors with a weight smaller than genus g of a hyperelliptic curve. An addition operation included in the scalar multiplication operation based on the window algorithm is accomplished by performing an addition operation of adding a degenerate divisor and a non-degenerate divisor, whereby a high-speed operation is achieved without causing degradation in security against key analysis attacks such as SPA.
    • 提供了一种以高度安全的方式高速执行超椭圆曲线密码处理的装置和方法。 产生基点D,使得除了基于窗口算法的标量乘法运算中使用的基点之外,基点D和预先计算的数据中的一个或多个是具有小于超椭圆曲线的g的权重的简并因数 。 基于窗口算法的标量乘法运算中包含的加法运算通过执行加法简并因子和非简并因数的加法运算来实现,从而实现高速运算,而不会导致安全性降低密钥分析攻击 如SPA。
    • 39. 发明申请
    • Cryptographic Computation Method, Cryptographic System, and Computer Program
    • 加密计算方法,加密系统和计算机程序
    • US20080095357A1
    • 2008-04-24
    • US11576305
    • 2005-09-26
    • Izuru KitamuraMasanobu KatagiTsuyoshi Takagi
    • Izuru KitamuraMasanobu KatagiTsuyoshi Takagi
    • H04L9/28
    • G06F7/725H04L9/3066
    • A system and method for achieving secure and fast computation in hyperelliptic cryptography is realized. Fast scalar multiplication is achieve by executing computing operations including halving as computing processing in scalar multiplication with respect to a divisor D in hyperelliptic curve cryptography. For example, computing operations including halving are executed in scalar multiplication with respect to a divisor D on a hyperelliptic curve of genus 2 in characteristic 2 having h(x)=x2+x+h0, f4=0 as parameters, a hyperelliptic curve of genus 2 in characteristic 2 having h(x)=x2+h1x+h0, f4=0 as parameters, or a hyperelliptic curve of genus 2 in characteristic 2 having h(x)=x as a parameter. Further, reduced complexity and faster computation are realized through the application of a table that records which of k1, k1′, (k0, k0′) is correct on the basis of a computed value of [½iD] with respect to a fixed divisor D, and through a reduction in the number of inversion operations.
    • 实现了在超椭圆密码学中实现安全快速计算的系统和方法。 通过执行计算操作来实现快速标量乘法,包括在超椭圆曲线密码学中相对于除数D的标量乘法中的计算处理减半。 例如,包括减号的计算操作在具有h(x)= x2 + x + h 的特征2中的类2的超椭圆曲线上相对于除数D的标量乘法执行, 0,f 4,= 0作为参数,特征2中具有h(x)= x2 + h1的特征2的超椭圆曲线 或作为参数的特征2中的属2的超椭圆曲线,其中h(x)= x作为参数,x + h <0>,f 4 。 此外,降低的复杂度和更快的计算是通过应用一个表来实现的,该表记录了k 1,k 1,..., 基于相对于固定除数D的计算值,对于固定除数D,通过减少数量 反演操作。
    • 40. 发明授权
    • Cryptographic computation method, cryptographic system, and computer program
    • 加密计算方法,加密系统和计算机程序
    • US08014521B2
    • 2011-09-06
    • US11576305
    • 2005-09-26
    • Izuru KitamuraMasanobu KatagiTsuyoshi Takagi
    • Izuru KitamuraMasanobu KatagiTsuyoshi Takagi
    • H04L9/28
    • G06F7/725H04L9/3066
    • A system and method for achieving secure and fast computation in hyperelliptic cryptography is realized. Fast scalar multiplication is achieve by executing computing operations including halving as computing processing in scalar multiplication with respect to a divisor D in hyperelliptic curve cryptography. For example, computing operations including halving are executed in scalar multiplication with respect to a divisor D on a hyperelliptic curve of genus 2 in characteristic 2 having h(x)=x2+x+h0, f4=0 as parameters, a hyperelliptic curve of genus 2 in characteristic 2 having h(x)=x2+h1x+h0, f4=0 as parameters, or a hyperelliptic curve of genus 2 in characteristic 2 having h(x)=x as a parameter. Further, reduced complexity and faster computation are realized through the application of a table that records which of k1, k1′, (k0, k0′) is correct on the basis of a computed value of [½iD] with respect to a fixed divisor D, and through a reduction in the number of inversion operations.
    • 实现了在超椭圆密码学中实现安全快速计算的系统和方法。 通过执行计算操作来实现快速标量乘法,包括在超椭圆曲线密码学中相对于除数D的标量乘法中的计算处理减半。 例如,在具有h(x)= x2 + x + h0,f4 = 0作为参数的特征2中,对于属性2的超椭圆曲线上的除数D进行标量乘法的标量乘法执行计算操作,作为参数的超椭圆曲线 具有h(x)= x2 + h1x + h0,f4 = 0作为参数的特征2中的属2,或者具有h(x)= x作为参数的特征2中的属2的超椭圆曲线。 此外,通过应用基于相对于固定除数D的[½iD]的计算值来记录k1,k1',(k0,k0')中的哪一个是正确的表来实现降低的复杂度和更快的计算 ,并且通过减少反演操作次数。