CN101183945A - Bypass operator based elliptical curve anti-bypass attack method - Google Patents

Abstract

The invention discloses an ellipse curve method for anti bypass attack based on the bypass operator, belonging to the technical field of information security, which comprises the following steps: firstly the mistakes of the prior technical proposal are modified to get the correct bypass equivalent execution sequence of the doubled point-point addition operation of the ellipse curve in the finite field Fp and the bypass equivalent execution sequence is expressed as a correct operator module matrix of doubled point-point addition of the ellipse curve; then aiming at the code mechanism of the ellipse curve, an implementation scheme of the C++ software is made, and the core steps of the encryption and decryption of the code mechanism of the ellipse curve is achieved in the software technical proposal, namely, a scalar point multiplication operation of the ellipse curve based on the bypass operator in the finite field. The invention has an advantage of improving the anti bypass-attack ability of the code of the ellipse curve according to adding correct pseudo operation sequence.

Description

Elliptic curve anti-bypass attack method based on the bypass operator

Technical field

The present invention relates to a kind of method of field of information security technology, specifically is a kind of elliptic curve anti-bypass attack method based on the bypass operator.

Background technology

Bypass attack (SCA) is based on the analytical technology of physical features, the assailant can be under the situation that obtains cryptographic algorithm operation carrier (computer, crypto, encryption box, smart card etc.), utilize the characteristic of running environment to attack, thereby obtain key fast, decode whole cryptographic system.Characteristics such as key is short, encryption/decryption speed fast because elliptic curve cryptosystem (ECC) has, low-power consumption, narrow bandwidth and memory space are little such as are applied to move, hand usually at wireless device, and environment for use is abominable relatively, and is very vulnerable.Therefore the high-performance elliptic curve cipher optimisation technique and the implementation thereof of research defence bypass attack technology are extremely urgent.

Find by prior art documents, B.Chevallier-Mames etc. are in " IEEETransactions on Computers " (IEEE Chinese journal of computers) (2004 53 the 6th phases of volume, the 760-768 page or leaf) " the Low Cost Solutions for Preventing Simple Side-Channel Analysis:Side-Channel Atomicity " that delivers (prevents the low-cost solution that simple bypass is analyzed: the bypass operator) proposed the method for bypass operator in order to resist simple power consumption attack, this method has at first defined and can not have been analyzed the operator module of being discerned of equal value by bypass, then by inserting pseudo-operation, one continuous command sequence is expressed as the sequence that repeats of bypass operator, has obtained an elliptic curve times point-plus operator modular matrix.But the elliptic curve dot product operation of carrying out on the prime field by such scheme is wrong, though the middle sequence of carrying out of elliptic curve cipher scalar dot product operation has been upset in the pseudo-operation of adding in this scheme, the execution result of these pseudo-operations is not cancelled each other behind the dot product EO.Cause the reason of described mistake to be: the employed result register of some pseudo-operations is relevant with the arithmetic register that follow-up middle some basic operation of carrying out sequence is used, the result register that is a certain pseudo-operation is the arithmetic register of follow-up some basic operation, make the introducing of pseudo-operation change the intermediate object program of carrying out sequence, and its influence can't finally be eliminated, and has obtained a wrong times point-plus operator modular matrix thus.

Summary of the invention

The objective of the invention is at deficiency of the prior art, a kind of elliptic curve anti-bypass attack method based on the bypass operator is provided, make it revise the mistake of existing scheme in the above-mentioned background technology, under the prerequisite that does not increase computation complexity, effectively take precautions against simple power consumption attack, can be used for fields such as cipher theory, password cracking, safety chip design, smart card designs.

The present invention is achieved by the following technical solutions, and the present invention at first revises the mistake of existing scheme, obtains finite field F _pGo up the bypass execution of equal value sequence of a correct elliptic curve times point-add operation, and it is expressed as a correct elliptic curve times point-plus operator modular matrix; Then at elliptic curve cryptosystem efficient, optimize, safety realizes, formulate its C++ software implement scheme, and in this software scenario, realize the core procedure of elliptic curve cryptosystem encryption and decryption---the elliptic curve scalar dot product based on the bypass operator on the finite field is operated.This technical scheme has realized the raising of elliptic curve cipher opposing bypass attack ability by adding correct pseudo-operation sequence.

Described existing scheme is meant that people such as B.Chevallier-Mames in the background technology is in 2004 schemes that propose.

Described finite field F _pGo up the bypass sequence of carrying out of equal value of a correct elliptic curve times point-add operation, be meant: what obtain after reselecting the pseudo-operation sequence and carrying out register operates execution sequence of equal value with basic elliptic curve dot product.Be specially: mask register T ₆Replace the related register in the existing scheme, this is because register T ₆Only carry out assignment by other registers, before this its operation of carrying out all be can be used as pseudo-operation in last some steps of intermediary operation.

A described correct elliptic curve times point-plus operator modular matrix is meant described finite field F _pGo up the bypass matrix notation of carrying out sequence of equal value of a correct elliptic curve times point-add operation, be specially:

Based on the elliptic curve scalar dot product operation of bypass operator, be the basic step that realizes the elliptic curve cryptosystem encryption and decryption on the described finite field, be specially:

Known definition is at large prime field F _pElliptic curve E/F on (P is big prime number) _p: y ²=x ³Some P on the+ax+b ₁=(X ₁, Y ₁, Z ₁), a wherein, b ∈ F _p, X ₁, Y ₁, Z ₁Be respectively a P ₁X, Y, Z sit target value under Jacobi's coordinate system, and well-known key d=(1, d _M-2..., d ₀) ₂, promptly d is the binary system positive integer of m bit, each bit is respectively d _i, i=0 ..., m-1, and d _M-1=1, adopt a described elliptic curve times point-plus operator modular matrix , realize the scalar multiplication P that puts on the elliptic curve _d=dP ₁=(X _d, Y _d, Z _d) process, P wherein _dBe same elliptic curve E/F _pOn point, X _d, Y _d, Z _dBe respectively a P _dX, Y, Z sit target value under Jacobi's coordinate system.

If the register of usefulness is R _j, j=0 ..., 9.At first be each register initialize R ₀=a, R ₁=X ₁, R ₂=Y ₁, R ₃=Z ₁, R ₇=X ₁, R ₈=Z ₁, R ₉=Z ₁, get intermediate variable i, s, and be respectively its initialize i=m-2, s=1.Carry out following register assignment operation then:

K=( s) * (k+1), the k representing matrix

K capable;

s＝d _i×(kdiv?25)+(-d _i)×(kdiv?9)；

$R_{u_{k,0}^{*}}=R_{u_{k,1}^{*}}\×R_{u_{k,2}^{*}};R_{u_{k,3}^{*}}=R_{u_{k,4}^{*}}+R_{u_{k,5}^{*}};$

$R_{u_{k,6}^{*}}=-R_{u_{k,6}^{*}};R_{u_{k,7}^{*}}=R_{u_{k,8}^{*}}+R_{u_{k,9}^{*}};$

U wherein _{K, l} ^*The matrix element of representing the capable l row of k of a described correct elliptic curve times point-plus operator modular matrix.

Value with i becomes i-s afterwards, if above-mentioned register assignment operation is then repeated in i 〉=0, otherwise register R ₁, R ₂, R ₃Value just be respectively a P _dX, Y, Z coordinate, so P _d(X _d, Y _d, Z _d)=(R ₁, R ₂, R ₃).P _dBe P ₁Result after elliptic curve cryptosystem is handled.

The C++ software implement scheme of described elliptic curve cryptosystem, be for guarantee elliptic curve cryptosystem efficient, optimize, safety realizes the C++ software implement scheme formulated.Be specially: the level of at first determining to realize elliptic curve cryptosystem according to the mathematic(al) structure of elliptic curve, the operation of putting on the elliptic curve progressively is decomposed into the operation that CPU can bear, define the data type of each layer from low to high successively by level then, and realize the master data operation of each layer.

The level of described realization elliptic curve cryptosystem is meant: the operation of putting on the elliptic curve is divided into three layers of realization, and top layer is the cryptographic system on the elliptic curve; Middle one deck is the operation of putting on the elliptic curve, comprises the addition put on the elliptic curve and the multiplication of point; The bottom is the operation on the finite field, comprises on subtraction on territory levels, the territory, territory comultiplication, the territory inverting, asking mould etc. on the territory.

Data type of described each layer and master data operation, be meant: for realizing the operation on the described bottom finite field, at first define big integer class, make up mould P integer class then, P is big prime number; Realize prime field F subsequently _pOn master data handle operation, comprise on subtraction on territory levels, the territory, territory comultiplication, the territory and invert, ask mould on the territory; Be the operation of putting on the elliptic curve of realizing described intermediate layer, at first make up affine coordinate mooring points class and Jacobi's coordinate mooring points class, and define its friendly each other metaclass, in these two classes, realize the operation of point subsequently respectively, and in Jacobi's coordinate mooring points class, realizing mutual conversion, mutual operation under the different coordinates, described dot product operation based on the bypass operator also realizes in Jacobi's coordinate points class; Be the cryptographic system on the elliptic curve of realizing described top layer, make up the public private key pair class respectively, realize class of a curve etc.

The present invention can guarantee quick, safe, the correct realization of elliptic curve cryptosystem, adopt the delamination software implementation of elliptic curve cipher system, guaranteed the independence of each layer realization, make change that any one deck realizes can be to other each layer generation too much influence, and the improvement of any one deck, the overall performance of elliptic curve cipher system is improved in the capital, improves the ability that anti-bypass is supplied with.The present invention can be advantageously applied to the optimization realization of elliptic curve cipher system, the applications such as Safety Design of high speed elliptic curve cryptography chip.

Embodiment

Below embodiments of the invention are elaborated: present embodiment is being to implement under the prerequisite with the technical solution of the present invention, provided detailed execution mode and concrete operating process, but protection scope of the present invention is not limited to following embodiment.

If embodiment intends plaintext M, adopt key d to carry out elliptic curve cryptography and handle.According to elliptic curve cryptosystem, at first plaintext M is converted to elliptic curve E/F _p: y ²=x ³Some P on the+ax+b operates Q=dP by the scalar multiplication of implementing to put on the elliptic curve then, obtains the expression Q of the point of the ciphertext on same elliptic curve.When specific implementation, select prime field F _pOn the elliptic curve parameter can fix.Such as getting elliptic curve equation y ²=x ³+ ax+b, a, b ∈ F _pA=0x bb8e5e8f bc115e13 9fe6a814 fe48aaa6f0ada1aa 5df91985, b=0x 1854bebd c31b21b7 aefc80ab 0ecd10d5 b1b3308e6dbf11c1, big prime number p is got 0x bdb6f4fe 3e8b1d9e 0da8c0d4 6f4c318c efe4afe3b6b8551f, basic point x coordinate is taken as 0x 4ad5f704 8de709ad 51236de6 5e4d4b48 2c836dc6e4106640, basic point y coordinate is 0x 02bb3a02 d4aaadac ae24817a 4ca3a1b0 14b5270432db27d2, and basic point rank n is 0x bdb6f4fe 3e8b1d9e 0da8c0d4 0fc96219 5dfae76f56564677.Whole invention adopts the specific implementation process of above-mentioned C++ implementation as follows:

1, for obtaining the point of ciphertext on the elliptic curve,, at first needs to realize finite field F according to the C++ software hierarchy implementation of above-mentioned elliptic curve cryptosystem _pOperation.At finite field F _pDown, the element in the territory all needs to adopt the form of big integer to represent, wherein for any one element m, 0≤m≤(p-1) is arranged all.If

Therefore, field element can be stored in the word of forming by t 32 bits: a=(a _T-1..., a ₂, a ₁, a ₀).The definition bottom big integer class class BIGINT6 and mould prime number class class Pint.The definition example of concrete data type and basic operation thereof is as follows:

class?BIGINT6

{

friend?int?operator＞＝(const?BIGINT6?&?A，const?BIGINT6?&?B)；

friend?int?operator＞(const?BIGINT6?&?A，const?BIGINT6?&?B)；

friend?int?operator＜＝(const?BIGINT6?&?A，const?BIGINT6?&?B)；

friend?int?operator＜(const?BIGINT6?&?A，const?BIGINT6?&?B)；

friend?int?operator＝＝(const?BIGINT6?&?A，const?BIGINT6?&?B)；

friend?WORD32_sub(const?WORD32*pa，const?WORD32*pb，WORD32*dest)；

friend?WORD32_add(const?WORD32*pa，const?WORD32*pb，WORD32*dest)；

friend?ostream&operator＜＜(ostream&output，const?BIGINT6&N)；

public：

BIGINT6(void)；

BIGINT6(const?int?N)；

BIGINT6(const?WORD32?N)；

BIGINT6(const?WORD32?wor[])；

BIGINT6(const?BIGINT6&aBig)；

public：

~BIGINT6(void)；

/* We?use?a?word?as?the?smallest?cell?to?avoid?little-endia?or?big-endia?problem.

* data；store?192?bit?BIGINT

* The?represent?struct：

* data[5]||?data[4]||?data[3]||?data[2]||?data[1]||data[0]

* most?significant?word least?significant?word*/

WORD32?data[6]；

}；

class?PInt

{

friend?PInt?&?operator+(const?PInt?&?PA，const?PInt?&?PB)；

friend?PInt?&?operator-(const?PInt?&?PA，const?PInt?&?PB)；

friend?PInt?&?operator*(const?PInt?&?PA，const?PInt?&?PB)；

friend?int?operator＞＝(const?PInt?&?A，const?PInt?&?B)；

friend?int?operator＞(const?PInt?&?A，const?PInt?&?B)；

friend?int?operator＜＝(const?PInt?&?A，const?PInt?&?B)；

friend?int?operator＜(const?PInt?&?A，const?PInt?&?B)；

friend?int?operator＝＝(const?PInt?&?A，const?PInt?&?B)；

friend?int NAF(const?PInt?A，char*trsf_result)；

friend?int BINARY(const?PInt?A，char*trsf_result)；

friend?void?SHIFTRIGHT(PInt?&?l，unsigned?int?amt)；

friend?ostream?&?operator＜＜(ostream?&?output，const?PInt?&?N)；

friend?PInt?&?operator％(const?PInt?&?P，const?PInt?&?N)；

friend?PInt?&?ranBigInt(void)；

public：

PInt(void)；

PInt(const?BIGINT6?&?big)；

PInt(const?WORD32?wor[])；

PInt(const?PInt?&?P)；

PInt(const?WORD32?N)；

PInt(const?int?N)；

PInt?&?operator~(void)const；

PInt?&?operator-(void)const；

static?int?setPri_N(void)；

stat?ic?int?setPri_P(void)；

stat?ic?PInt?&?getPrime(void)；

public：

~PInt(void)；

private：

BIGINT6?pInt；

static?BIGINT6?pri；

}；

2, according to above-mentioned C++ software hierarchy implementation, in the basic operation that realizes the point of elliptic curve on the prime field on above-mentioned 1 the basis.At first define the some class on the elliptic curve, comprise affine coordinate mooring points class class APoint and Jacobi's coordinate mooring points class class JPoint, the friendly each other metaclass of two classes; Secondly, mutual conversion, the mutual operation under the realization different coordinates in Jacobi's coordinate mooring points class.The definition example of data type and operation thereof is as follows:

class?APoint

{

friend?class?JPoint；

friend?APoint?&?operator+(const?APoint?&?LP，const?APoint?&?RP)；/////ADDITION//////////

friend?APoint?&?operator-(const?APoint?&?LP，const?APoint?&?RP)；//////////////SUBTRATION//

friend?APoint?&?operator*(const?PInt?&?k，const?APoint&P)；/////POINT?MULTIPLY////////

friend?APoint?&?operator*(const?APoint?&?P，const?PInt?&?k)；

friend?ostream?&?operator＜＜(ostream&output，const?APoint?&?P)；///////////DISPLAY//////

public：

APoint(void)；

APoint(const?APoint?&?P)；

APoint(const?PInt?&?x，const?PInt?&?y)；

APoint(const?int?x，const?int?y)；

APoint(const?JPoint?&?P)；

APoint?&?operator-(void)const；//////////////////NEGTIVE?POINT////////////

int?operator＝＝(const?APoint&rP)?const；////////////////COMPARE//////////////////

int?operator||(const?APoint&rP)const；///////is_Couple？no-＞0；yes-＞1this＝rP///////

int?operator！(void)const?；/////////is?infinite？no-＞0；yes-＞1////////////

int?is_on_curve?(void)?const；/////////is?on?the?curve？no-＞0；yes-＞1//?////////

public：

~APoint(void)；

private：

PInt?Px；

PInt?Py；

}；

class?JPoint

{

friend?class?APoint；

//////////////////////////////////////////ADDITION////////////////////////////////////////

friend?JPoint?&?operator+(const?JPoint?&?L，const?JPoint?&?R)；

//BETWEEN**************************************************************

friend?JPoint?&?operator+(const?JPoint?&?LP，const?APoint?&?RP)；

friend?JPoint?&?operator+(const?APoint?&?LP，const?JPoint?&?RP)；

friend?JPoint?&?PointAddition(const?JPoint?&?p1，const?JPoint?&?p2)；

friend?JPoint?&?Doubling(const?JPoint?&?p)；

/////////////////////////////////////SUBTRATION///////////////////////////////////////////

friend?JPoint?&?operator-(const?JPoint?&?L，const?JPoint?&?R)；

//BETWEEN**************************************************************

friend?JPoint?&?operator-(const?JPoint?&?LP，const?APoint?&?RP)；

friend?JPoint?&?operator-(const?APoint?&?LP，const?JPoint?&?RP)；

//////////////////////////////////////POINT?MULTIPLY//////////////////////////////////////

friend?JPoint?&?operator*(const?JPoint?&?P，const?PInt?&?D)；

friend?JPoint?&?operator*(const?PInt?&?D，const?JPoint?&?P)；

///////////////////////////////////////////DISPLAY///////////////////////////////////////

friend?ostream?&?operator＜＜(ostream?&?output，const?JPoint?&?P)；

public：

JPoint(void)；

JPoint(const?PInt?&?x，const?PInt?&?y，const?PInt?&?z)；

JPoint(const int?x，const?int?y，const int?z)；

JPoint(const?JPoint?&?P)；

JPoint(const?APoint?&?P)；

//////////////////////////////////////////NEGTIVE?POINT////////////////////////////////////

JPoint?&?operator-(void)const；

////////////////////////////////////////COMPARE////////////////////////////////////?////////

int?operator＝＝(const?JPoint?&?P)const；

/////////////////////////////////////////is_Couple？no-＞0；yes-＞1this＝-rP///////////////

int?operator||(const?JPoint?&?rP)const；

//////////////////////////////////////////is?infinite？no-＞0；yes＞1////////////////////////

int?operator！(void)const；

public：

~JPoint(void)；

private：

PInt?PX；

PInt?PY；

PInt?PZ；

}；

3, for improving the anti-bypass attack ability of elliptic curve cryptosystem, its key operation---elliptic curve scalar dot product adopts on the above-mentioned finite field elliptic curve scalar dot product scheme based on the bypass operator.Concrete, on above-mentioned 2 basis, at the function JPoint of JPoint class ﹠amp; Operator* (JPoint ﹠amp; P, PInt ﹠amp; D) realize in.Concrete steps are:

At first define a described times of point-plus operator modular matrix

int?u?[26]?[10]＝

{{4，1，1，5，4，4，3，4，4，5}， {5，3，3，1，1，1，3，6，1，3}， {5，5，5，1，1，3，3，1，L?3}， {5，0，5，4，4，5，3，5，2，2}，

{3，3，5，1，1，3，3，1，1，3}， {2，2，2，2，2，2，4，6，1，3}， {5，1，2，1，1，5，5，1，1，5}， {1，4，4，1，?1，5，4，1，1，5}，

{2，2，2，2，2，2，3，5，1，5}， {4，4，5，2，2，4，2，4，4，5}， {4，9，9，5，1，5，5，5，1，5}， {1，1，4，5，1，5，5，5，1，5}，

{4，4，9，5，1，5，5，5，1，5}，{2，2，4，5，1，5，5，5，1，5}，{4，3，3，5，1，5，5，5，1，5}，{5，4，7，6，2，5，5，5，1，5}，

{4，3，4，6，2，5，6，6，5，6}，{4，4，8，6，5，6，4，4，2，4}，{3，3，9，6，5，6，6，6，5，6}，{3，3，5，6，5，6，6，6，5，6}，

{6，5，5，6，3，6，3，6，3，6}，{1，1，6，1，1，4，4，1，1，4}，{5，5，6，6，1，2，2，6，2，6}，{1，4，4，1，1，5，6，1，1，6}，

{2，2，5，1，1，6，3，6，1，6}，{4，4，6，2，2，4，6，6，1，6}}；

Secondly, realize on the finite field elliptic curve scalar dot product based on the bypass operator.If the some P=(X of plaintext M correspondence ₁, Y ₁, Z ₁), X ₁, Y ₁, Z ₁Be respectively a P X, Y, Z under Jacobi's coordinate system and sit target value; If key d is the binary system positive integer of m bit, promptly d=(1, d _M-2..., d ₀) ₂, d _M-1=1; If the point that obtains after dot product is handled is Q=(X _d, Y _d, Z _d), X _d, Y _d, Z _dBe respectively a Q X, Y, Z under Jacobi's coordinate system and sit target value; If the register that uses in the scheme implementation is R _j, j=0 ..., 9.Detailed process is:

(1). each register initialize R ₀=a, R ₁=X ₁, R ₂=Y ₁, R ₃=Z ₁, R ₇=X ₁, R ₈=Y ₁, R ₉=Z ₁

(2). get intermediate variable i, s, and be respectively its initialize i=m-2, s=1;

(3). carry out following register assignment operation:

(3.1) k=( s) * (k+1), the k representing matrix

K capable;

(3.2)s＝d _i×(kdiv?25)+(-d _i)×(kdiv?9)；

$\left(3.3\right),R_{u_{k,0}^{*}}=R_{u_{k,1}^{*}}\×R_{u_{k,2}^{*}};$

$\left(3.4\right),R_{u_{k,3}^{*}}=R_{u_{k,4}^{*}}+R_{u_{k,5}^{*}};$

$\left(3.5\right),R_{u_{k,6}^{*}}=-R_{u_{k,6}^{*}};$

$\left(3.6\right),R_{u_{k,7}^{*}}=R_{u_{k,8}^{*}}+R_{u_{k,9}^{*}};$

(3.7)i＝i-s，

(4) if. i 〉=0, then repeated execution of steps 3; Otherwise register R ₁, R ₂, R ₃Value just be respectively X, Y, the Z coordinate of a Q, so Q=(X _d, Y _d, Z _d)=(R ₁, R ₂, R ₃).

The C++ realization example of above process is as follows:

JPoint?&?operator*(JPoint?&?P，PInt?&?D)

{

static?JPoint?res；

if((！P)||(D＝＝0))

res＝INFINITE_POINT；

else{

char*d＝new?char[200]；

int?N＝BINARY(D，d)；

PInt?R[10]；

int?i，s，k；

R[0]＝coeA；

R[1]＝P.PX；

R[2]＝P.PY；

R[3]＝P.PZ；

R[7]＝P.PX；

R[8]＝P.PY；

R[9]＝P.PZ；

i＝N-2；

s＝1；

while(i＞＝0)

{

if(s＝＝1)

k＝0；

else?if(s＝＝0)

k＝k+1；

if(d[i]＝＝0)

s＝k/9；

else?if(d[i]＝＝1)

s＝k/25；

R[u[k][0]]＝R[u[k][1]]*R[u[k][2]]；

R[u[k][3]]＝R[u[k][4]]+R[u[k][5]]；

R[u[k][6]]＝-R[u[k][6]]；

R[u[k][7]]＝R[u[k][8]]+R[u[k][9]]；

i＝i-s；

}

res.PX＝R[1]；

res.PY＝R[2]；

res.PZ＝R[3]；

delete[]d；}

return?res；

}

4,, finished the C++ software hierarchy of elliptic curve cryptosystem and realized through above-mentioned 3 steps.For obtaining the some Q of ciphertext on elliptic curve in the present embodiment, only need in main program, call on the above-mentioned finite field elliptic curve scalar dot product function JPoint::JPoint﹠amp based on the bypass operator; Operator* (JPoint ﹠amp; P, PInt﹠amp; D), get final product Q=P*d.

5, at last again with this Q according to the elliptic curve cryptosystem recompile, get final product the hexadecimal string of ciphertext, by adding correct pseudo-operation sequence, realized the raising of elliptic curve cipher opposing bypass attack ability.

Above embodiment shows, the present invention is based on bypass operator anti-bypass attack method and can improve the ability that elliptic curve cryptosystem is taken precautions against simple power consumption attack, adopt the delamination software implementation of elliptic curve cipher system, guaranteed the independence of each layer realization, effectively improved systematic function.

Claims (7)

1. the elliptic curve anti-bypass attack method based on the bypass operator is characterized in that, at first revises the mistake of existing scheme, obtains finite field F _pGo up the bypass sequence of carrying out of equal value of a correct elliptic curve times point-add operation, and it is expressed as a correct elliptic curve times point-plus operator modular matrix, formulate its C++ software implement scheme at elliptic curve cryptosystem then, and realize that in this software scenario the elliptic curve scalar dot product based on the bypass operator is operated on the finite field, thereby, realize the raising of elliptic curve cipher opposing bypass attack ability by adding correct pseudo-operation sequence.

2. the elliptic curve anti-bypass attack method based on the bypass operator according to claim 1 is characterized in that, described finite field F _pGo up the bypass sequence of carrying out of equal value of a correct elliptic curve times point-add operation, be meant: what obtain after reselecting the pseudo-operation sequence and carrying out register operates execution sequence of equal value, i.e. mask register T with basic elliptic curve dot product ₆Replace the related register in the existing scheme.

3. the elliptic curve anti-bypass attack method based on the bypass operator according to claim 1 is characterized in that, a described correct elliptic curve times point-plus operator modular matrix is specially:

4. the elliptic curve anti-bypass attack method based on the bypass operator according to claim 1 is characterized in that, based on the elliptic curve scalar dot product operation of bypass operator, is specially on the described finite field:

Known definition is at large prime field F _pOn elliptic curve E/F _p: y ²=x ³Some P on the+ax+b ₁=(X ₁, Y ₁, Z ₁), P is big prime number, a wherein, b ∈ F _p, X ₁, Y ₁, Z ₁Be respectively a P ₁X, Y, Z sit target value under Jacobi's coordinate system, and well-known key d=(1, d _M-2..., d ₀) ₂, promptly d is the binary system positive integer of m bit, each bit is respectively d _i, i=0 ..., m-1, and d _M-1=1, adopt a described elliptic curve times point-plus operator modular matrix

, realize the scalar multiplication P that puts on the elliptic curve _d=dP ₁=(X _d, Y _d, Z _d) process, P wherein _dBe same elliptic curve E/F _pOn point, X _d, Y _d, Z _dNot Wei the some P _dX, Y, Z sit target value under Jacobi's coordinate system;

If the register of usefulness is R _j, j=0 ..., 9, at first be each register initialize R ₀=a, R ₁=X ₁, R ₂=Y ₁, R ₃=Z ₁, R ₇=X ₁, R ₈=Y ₁, R ₉=Z ₁, get intermediate variable i, s, and be respectively its initialize i=m-2, s=1, carry out following register assignment operation then:

K=( s) * (k+1), the k representing matrix

K capable,

s＝d _i×(kdiv?25)+(-d _i)×(kdiv?9)，

$R_{u_{k,0}^{*}}=R_{u_{k,1}^{*}}\×R_{u_{k,2}^{*}};R_{u_{k,3}^{*}}=R_{u_{k,4}^{*}}+R_{u_{k,5}^{*}},$

$R_{u_{k,6}^{*}}=-R_{u_{k,6}^{*}};R_{u_{k,7}^{*}}=R_{u_{k,8}^{*}}+R_{u_{k,9}^{*}},$

U wherein _{K, l} ^*The matrix element of representing the capable l row of k of a described correct elliptic curve times point-plus operator modular matrix;

Value with i becomes i-s afterwards, if above-mentioned register assignment operation is then repeated in i 〉=0, otherwise register R ₁, R ₂, R ₃Value just be respectively a P _dX, Y, Z coordinate, so P _d=(X _d, Y _d, Z _d)=(R ₁, R ₂, R ₃), P _dBe P ₁Result after elliptic curve cryptosystem is handled.

5. the elliptic curve anti-bypass attack method based on the bypass operator according to claim 1, it is characterized in that, the C++ software implement scheme of described elliptic curve cryptosystem, be specially: the level of at first determining to realize elliptic curve cryptosystem according to the mathematic(al) structure of elliptic curve, the operation of putting on the elliptic curve progressively is decomposed into the operation that CPU can bear, define the data type of each layer from low to high successively by level then, and realize the master data operation of each layer.

6. the elliptic curve anti-bypass attack method based on the bypass operator according to claim 5, it is characterized in that, the level of described realization elliptic curve cryptosystem, be meant: the operation of putting on the elliptic curve is divided into three layers of realization, top layer is the cryptographic system on the elliptic curve, middle one deck is the operation of putting on the elliptic curve, comprise the addition put on the elliptic curve and the multiplication of point, the bottom is the operation on the finite field, comprises on subtraction on territory levels, the territory, territory comultiplication, the territory inverting, asking mould on the territory.

7. the elliptic curve anti-bypass attack method based on the bypass operator according to claim 5, it is characterized in that, data type of described each layer and master data operation, be meant: for realizing the operation on the described bottom finite field, at first define big integer class, then make up mould P integer class, P is big prime number, realizes prime field F subsequently _pOn master data handle operation, comprise on subtraction on territory levels, the territory, territory comultiplication, the territory and invert, ask mould on the territory; Be the operation of putting on the elliptic curve of realizing described intermediate layer, at first make up affine coordinate mooring points class and Jacobi's coordinate mooring points class, and define its friendly each other metaclass, in these two classes, realize the operation of point subsequently respectively, and in Jacobi's coordinate mooring points class, realize mutual conversion, mutual operation under the different coordinates, described dot product operation based on the bypass operator also realizes in Jacobi's coordinate points class, be the cryptographic system on the elliptic curve of realizing described top layer, make up the public private key pair class respectively, realize class of a curve.