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11. 发明公开

EP2377268A1 CODAGE DE POINTS D'UNE COURBE ELLIPTIQUE 有权转让
标题翻译： CODE椭圆曲线的点上的
公开(公告)号：EP2377268A1
公开(公告)日：2011-10-19
申请号：EP10706012.1
申请日：2010-01-08
申请人： MORPHO
发明人： ICART, Thomas
IPC分类号： H04L9/32
CPC分类号： H04L9/3066 , H04L2209/30
摘要： The method comprises, in an electronic component, carrying out a cryptographic calculation that includes the step of obtaining points P on an elliptic curve following the equation Y
2 + a
1 XY + a
3 Y = X
3 + a
2 X
2 + a
4 + X + a
6 (1) where a
1 , a
2 , a
3 , a
4 et a
6 are elements of a set A of elements; where A is a ring of modular integers Z/qZ where q is a positive integer resulting from a number I of different prime numbers strictly higher than 3, I being an integer higher than or equal to 2, where A is a finite body Fq with q the power of a prime integer; where X and Y are the coordinates of the points P and are elements of A. The method comprises determining a diameter (11), and obtaining the coordinates X and Y of a point P (13) by applying a function (12) to said parameter. The Euler function φ of A corresponds to the equation φ(A) mod 3 = 1. The function is a reversible and deterministic function expressed by a rational fraction in a
1 , a
2 , a
3 , a
4 and a
6 and in said parameter in A, and reaches at least a number q/4
1 of points P, with I being equal to 1 for a finite body Pq. The method further comprises using the point P in a cryptographic application for ciphering or hashing or signature or authentication or identification.

12. 发明授权

EP2149220B1 PROTECTION D'EXECUTION D'UN CALCUL CRYPTOGRAPHIQUE 有权转让
标题翻译：程序加密计算的实现
公开(公告)号：EP2149220B1
公开(公告)日：2012-02-29
申请号：EP08805766.6
申请日：2008-05-09
申请人： MORPHO
发明人： CHABANNE, Hervé , BRINGER, Julien , ICART, Thomas
IPC分类号： H04L9/32 , H04L9/08 , H04L9/14 , G06F7/38 , G06K19/073
CPC分类号： H04L9/0866 , H04L9/0836 , H04L9/321 , H04L2209/805
摘要： A cryptographic calculation is executed in an electronic component, according to a cryptographic algorithm including at least one application of a one-way function which is disabled upon an intrusion into the electronic component. The one-way function is based on a first affine operation corresponding to a first secret key. The one-way function is applied, by obtaining (11) first and second random values (r, r'), then, by obtaining a first result (13) by applying a second affine operation (σK1), which corresponds to a second secret key, to a first combination (12) of the first and second random values, and, by obtaining (14) thereafter a second result by applying a third affine operation (OK2), which corresponds to a third secret key, to said first result. The combination of the third and second affine operations (σK2 o σK1) corresponds to the first affine operation; and a cryptographic operation is moreover applied (15) to one at least among said second result and a second combination of the first and second random values.

13. 发明公开

EP2449721A1 CRYPTOGRAPHIE PAR PARAMETRISATION SUR UNE COURBE ELLIPTIQUE 有权转让
标题翻译：密码学BY建立一个椭圆曲线
公开(公告)号：EP2449721A1
公开(公告)日：2012-05-09
申请号：EP10745354.0
申请日：2010-06-28
申请人： MORPHO
发明人： ICART, Thomas , CHABANNE, Hervé
IPC分类号： H04L9/30
摘要： A device is controlled by a controller on the basis of a password. A determination is made at the device or at the controller, on the basis of a random value r1, of a point P(X,Y) on an elliptic curve in a finite body Fq, q being an integer, according to: Ea,b(x, y):x3+ax+b=y2. First and second parameters k and k′ are obtained such that P(X,Y)=F(K,k′), where F is a surjective function of Fq×Fq, in Fq. The first and second parameters are obtained in an encrypted format by encryption in accordance with the password. The first and second encrypted parameters are then transmitted to the controller. During the control, the function F is used, such that, whatever the values of z and z′ which are input elements of Fq, F(z,z′) is a point on the elliptic curve and the input elements do not satisfy the equation.

14. 发明公开

EP2443789A2 CRYPTOGRAPHIE SUR UNE COURBE ELLIPTIQUE SIMPLIFIEE 有权转让
标题翻译：加密的简化椭圆曲线上
公开(公告)号：EP2443789A2
公开(公告)日：2012-04-25
申请号：EP10738014.9
申请日：2010-06-15
申请人： MORPHO
发明人： ICART, Thomas
IPC分类号： H04L9/30 , G06F7/72 , H04L9/28 , G06F17/10 , G06F7/58
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.

15. 发明公开

EP2443787A2 CRYPTOGRAPHIE SUR UNE COURBE ELLIPTIQUE 有权转让
标题翻译：加密椭圆曲线上
公开(公告)号：EP2443787A2
公开(公告)日：2012-04-25
申请号：EP10738013.1
申请日：2010-06-15
申请人： MORPHO
发明人： ICART, Thomas , CORON, Jean-Sébastien
IPC分类号： H04L9/28 , G06F7/58 , G06F17/10
CPC分类号： G06F7/725 , G06F2207/7261 , H04L9/3066
摘要： A cryptographic calculation is performed in an electronic component, comprising the step of obtaining a point P(X,Y) from a parameter t on an elliptical curve of equation: Y
2 = f(X); and from polynomials X
1 (t), X
2 (t), X
3 (t) and U(t) satisfying the equality: f(X
1 (t)).f(X
2 (t)).f(X
3 (t))=U(t)
2 in Fq, with q = 3 mod 4. Firstly a value of the parameter t is obtained. Next, the point P is determined by carrying out the following substeps: (i) X
1 = X
1 (t), X
2 = X
2 (t), X
3 = X
3 (t) and U=U(t) are calculated; (ii) if the term f(X
1 ).f(X
2 ) is a square, then it is tested whether the term f(X
3 ) is a square in F
q and if so the square root of f(X
3 ) is calculated, in order to obtain the point P(X
3 ); (iii) otherwise, it is tested whether the term f(Xι) is a square and, if so, the square root of f(X
1 ) is calculated, in order to obtain the point P(X
1, ); (iv) otherwise, the square root of f(X
2 ) is calculated in order to obtain the point P(X
2 ). This point P can then be used in a cryptographic application.

16. 发明授权

EP2443787B1 Cryptographie sur une courbe elliptique 有权转让
标题翻译：加密椭圆曲线上
公开(公告)号：EP2443787B1
公开(公告)日：2013-10-02
申请号：EP10738013.1
申请日：2010-06-15
申请人： MORPHO
发明人： ICART, Thomas , CORON, Jean-Sébastien
IPC分类号： G06F7/72 , H04L9/28 , G06F7/58 , G06F17/10
CPC分类号： G06F7/725 , G06F2207/7261 , H04L9/3066

17. 发明公开

EP2225849A1 CONTROLE D'UNE ENTITE A CONTROLER PAR UNE ENTITE DE CONTROLE 审中-公开
标题翻译： STEUERUNG EINER VON EINER STEUEREINHEIT ZU STEUERNDEN EINHEIT
公开(公告)号：EP2225849A1
公开(公告)日：2010-09-08
申请号：EP08864656.7
申请日：2008-12-10
申请人： MORPHO
发明人： CHABANNE, Hervé , BRINGER, Julien , ICART, Thomas
IPC分类号： H04L9/32
摘要： A control entity (11) communicates with an entity to be controlled (12) so as to effect a control, a secret key being associated with the control entity. These entities share public parameters (g, gv), a second public parameter (gv) being a combination of a first public parameter (g) of the said plurality with the secret key (v). At the level of the entity to be controlled, a random value (r1) is generated, a first message is transmitted to the control entity, this first message comprising at least one value (x) obtained by combining the first public parameter (g) with the random value; and a second message is transmitted to the control entity, this second message comprising at least one value (y) obtained by combining the first random value (r1), a secret key of the entity to be controlled (s) and a value received from the control entity (C). One of the values included in the first or the second message is based on the second public parameter (gv).
摘要翻译：控制实体与要被控制的实体进行通信，以便实现控制，秘密密钥与控制实体相关联。这些实体共享公共参数，第二公共参数是所述多个的第一公共参数与秘密密钥的组合。在要被控制的实体的级别，生成随机值，将第一消息发送到控制实体，该第一消息包括通过将第一公共参数与随机值组合而获得的至少一个值; 并且第二消息被发送到控制实体，该第二消息包括通过组合第一随机值，要被控制的实体的秘密密钥和从控制实体接收的值而获得的至少一个值。包含在第一或第二消息中的值之一是基于第二公共参数。

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