Method for enabling elliptic curve cryptography to defend differential power attack

A differential power attack, elliptic curve cryptography technology, applied in the direction of the public key of secure communication, can solve the problems of meaningless mapping, multi-time, cannot be taken as 1, etc., to achieve defense against differential power attack, low cost Effect

Active Publication Date: 2012-07-04
SHANGHAI HUAHONG INTEGRATED CIRCUIT
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Problems solved by technology

But here θ is a random non-zero point in a finite field, and it cannot be taken as 1, otherwise the mapping is meaningless
Since θ≠1, the Z coordinate of P′ is not equal to 1, so in the process of calculating mP′, only the general point addition formula can be called, and the time-consuming is 13M+4S
Therefore, using the projective coordinate randomization method to defend against differential power consumption attacks also requires sacrificing more time

Method used

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  • Method for enabling elliptic curve cryptography to defend differential power attack
  • Method for enabling elliptic curve cryptography to defend differential power attack
  • Method for enabling elliptic curve cryptography to defend differential power attack

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Embodiment Construction

[0066] see figure 1 and combine figure 2 , the present invention provides a scalar multiplication calculation process using a method for defending against differential power consumption attacks to illustrate specific implementation details of the present invention.

[0067] The National Institute of Standards and Technology (NIST) recommends 15 sets of parameters for elliptic curve cryptography. One set of parameters is adopted in this embodiment, which is as follows:

[0068] E: y 2 +xy=x 3 +x 2 +b

[0069] p(t)=t 163 +t 7 +t 6 +t 3 +1

[0070] r=5846006549323611672814742442876390689256843201587

[0071] b=0x2 0a601907 b8c953ca 1481eb10 512f7874 4a3205fd

[0072] P x = 0x3 f0eba162 86a2d57e a0991168 d4994637 e8343e36

[0073] P y = 0x0 d51fbc6c 71a0094f a2cdd545 b11c5c0c 797324f1

[0074] The elliptic curve E( ) in n=163, now take the hexadecimal integer m, m=0xe4040cf925d6ff9b8be31e8263dcf0b831bd55ed, randomly select the hexadecimal integer f=0x8, and u=1,...

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Abstract

The invention discloses a method for enabling elliptic curve cryptography to defend differential power attack. The method comprises the following steps: step 1) selecting a non-zero point P=(X:Y:1) on an elliptic curve E(F2<n>) and giving any integer m; step 2) calculating isomorphic mapping phi (P)=(fuX:fvY:1), recording P'=(X': Y': 1)=phi (P); step 3) calculating scalar multiplication mP', and recording a point R=mP'=(X'':Y'':Z''); and step 4), calculating isomorphic and inverse mapping phi<-1> (R)=(fvX'':fv+2uY'':fv+uZ'')=mP. The differential power attack can be defended with very low time cost by utilizing the method.

Description

technical field [0001] The invention relates to a method for defending against differential power consumption attacks, in particular to a method for defending against differential power consumption attacks for elliptic curve cryptography. Background technique [0002] In López Dahab projective coordinates, the elliptic curve E( )It can be expressed as [0003] Y 2 +XYZ=X 3 Z+a 2 x 2 Z 2 +a 6 Z 4 [0004] Define the point at infinity ∞=(1:0:0). When Z 1 ≠0, A point in Dahab projective coordinates (X 1 :Y 1 :Z 1 ) corresponding to a point in affine coordinates is Let the elliptic curve E( ) on any two points P, Q, when P, Q are represented by López Dahab projective coordinates, if R=P+Q, the coordinates of R are calculated by the following formula: [0005] If P=∞ then R=∞+Q=Q; [0006] If Q=∞ then R=P+∞=P; [0007] Let us now assume that P≠∞ and Q≠∞. [0008] Note P=(X 1 :Y 1 :Z 1 ), Q=(X 2 :Y 2 :Z 2 ), R=(X 3 :Y 3 :Z 3 ). [0009] If P≠Q, th...

Claims

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Application Information

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Patent Type & Authority Applications(China)
IPC IPC(8): H04L9/30
Inventor 顾海华
Owner SHANGHAI HUAHONG INTEGRATED CIRCUIT
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