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Random point generation method suitable for elliptic curve cryptography (ECC) safety protection

An elliptic curve cryptography and security protection technology, which is applied in the field of random point generation suitable for elliptic curve cryptography security protection, and can solve the problem of large time cost of modular multiplication operations.

Inactive Publication Date: 2011-06-29
SHANGHAI HUAHONG INTEGRATED CIRCUIT
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  • Abstract
  • Description
  • Claims
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AI Technical Summary

Problems solved by technology

It can be seen that the time cost of a large number of modular multiplication operations required by the traditional method of generating random points on the elliptic curve is too large

Method used

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  • Random point generation method suitable for elliptic curve cryptography (ECC) safety protection
  • Random point generation method suitable for elliptic curve cryptography (ECC) safety protection

Examples

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Embodiment Construction

[0059] The following is an example of generating random points on an elliptic curve using the method of the present invention.

[0060] In the embodiment of the present invention, the given finite field is F p , the elliptic curve equation used is y 2 =x 3 -3x+b, the scalar multiplication coordinate system uses Jacobian projective coordinates, the scalar multiplication adopts the binary method from left to right, and the method of judging the point at infinity is whether the Z coordinate of the midpoint of the projective coordinates is 0.

[0061] Such as figure 1 As shown, the steps of generating random points on the specific elliptic curve of the present invention are as follows:

[0062] Step 1, get the elliptic curve y 2 =x 3 A fixed point P on -3x+b. The fixed point P can be any fixed point on the elliptic curve except the point at infinity.

[0063] Step 2, choose a random number r65 , a random number r of 64 bits or less can be randomly selected.

[0064] In ste...

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Abstract

The invention discloses a random point generation method suitable for elliptic curve cryptography (ECC) safety protection. The method comprises the following steps: (1) finding a fixed point P on a certain elliptic curve except an infinite point; (2) selecting a random number r; (3) calculating scalar multiplication of r and P to obtain a calculation result Q; (4) determining whether Q is the infinite point, if yes, returning to the step (2), and otherwise, executing the step (5); and (5) obtaining the random point Q on the certain elliptic curve. The method can obviate the large amount of modular multiplication by obviating the evolution of large numbers or the operation for solving a quadratic equation with one unknown. Therefore, the method provided by the invention can greatly improve the operation speed and reduce the time for generating the random point on the elliptic curve.

Description

technical field [0001] The invention relates to a method for masking points on an elliptic curve in ECC (elliptic curve cryptography) security protection, in particular to a method for generating random points suitable for ECC security protection, especially for the application of chips containing ECC algorithms . Background technique [0002] ECC (Elliptic Curve Cryptography) algorithm is vulnerable to DPA (Differential Power Analysis) attack. One defense against this attack is to use a random point on the elliptic curve to mask the input point of the calculation during the public key generation process. Use the masked point and scalar to calculate the public key, then restore the calculation result, and finally get the correct public key. In this way, the power consumption public key of the chip will change randomly every time the public key is generated, eliminating the correlation between power consumption and the key, and achieving the purpose of protecting the key. ...

Claims

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Application Information

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IPC IPC(8): G06F7/72
Inventor 马博包斯刚
Owner SHANGHAI HUAHONG INTEGRATED CIRCUIT
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