CN106788978B - Argument decomposition threshold mask method - Google Patents

Abstract

The invention discloses a new method of argument decomposition threshold mask, which is characterized in that in the S box replacement process of a block cipher, the multiplication operation in a sum domain is realized by using the idea of TI mask, thus the requirement of additional new random numbers in the multiplication process can be reduced, and the independence between data can be achieved. The basic framework of the DOM mask adopted by other operations in the sum domain can achieve the purpose of saving chip resources, thereby effectively achieving the purposes of reducing randomness and saving the use area of a chip, and simultaneously ensuring the confidentiality and the safety of data and effectively resisting power consumption attack and side channel cube attack.

Description

Argument decomposition threshold mask method

Technical Field

The invention relates to the field of information security, in particular to a new method for decomposing a threshold mask by using a variable element.

Background

Various security chips are indispensable hardware carriers for information security technology. With the development of science and technology, security chips have become popular. The security chip reveals various bypass information during operation, and the information has close correlation with the key of the cryptographic algorithm. The side channel attack is to attack the security chip by using the correlation. Among side channel attacks, the most effective attack method is Differential Power Attack (DPA). One new security challenge is: in an open environment of the security chip device, how to cancel the correlation between various bypass information leaked out by the security chip in the operation process and the key of the cryptographic algorithm. In response to this problem, professor Svelta Nikova at the university of luxen, belgium proposed ti (threshold expressions) technology. The technology is provided on the basis of key sharing, threshold encryption and a multi-party security computing protocol. The basic design idea of the TI technique is: the intermediate data of the encryption algorithm in the running process is randomized by using a key sharing mechanism, so that no direct correlation exists between the intermediate state data of the encryption process and the power consumption of the intermediate state data, and an attacker cannot guess the key of the corresponding cryptographic algorithm after extracting the leaked bypass information. TI the intermediate state data of this technique is masked by a plurality of random data, so that the masking technique requires too many random numbers and the computational complexity is high as the order against DPA increases. Hannes Gross proposes a DOM (domain-oriented masking) mechanism. The basic design idea of the mask scheme is to make components of each argument operate in its own domain, so that the components in all domains are independent from the components in other domains, thereby realizing the resistance to power consumption attack. This masking scheme can achieve the effect of resisting power consumption attack, and it requires few chips and random numbers and can be applied to a protected circuit of any order, but it is vulnerable to side channel cube attack.

Disclosure of Invention

Aiming at the technical defects, the invention provides a new method for the variable element decomposition threshold mask, and a new mask method is designed by combining the mask algorithms of TI and DOM.

The technical scheme for realizing the purpose of the invention is as follows:

the new method of the argument decomposition threshold mask comprises the following steps:

1) carrying out masking component on 8-bit sensitive variables input by an S box in the running process of a cryptographic algorithm by using a key sharing mechanism;

2) mapping the 8-bit random mask component in step 1) to GF (2)⁴) Above, are respectively X₁＝A₁x+A₀，X₂＝B₁x+B₀，X₃＝C₁x+C₀…；

3) Under GF (2)⁴) Are respectively multipliedOperation, inversion operation and squaring operation;

4) under GF (2)⁴) The multiplication operation is realized by a mask mode of 3 input and 3 output in the TI mask, and in order to meet the uniformity, an additional random number needs to be added to each output component result;

5) the components of each squaring operation and the components of the multiplication result are XOR-ed, thus being at GF (2)⁴) The value in the domain that needs to be inverted;

6) returning to step 2) to remove GF (2)⁴) Inv in (1)₁，Inv₂，Inv₃Mapping to GF (2)²) Upper, is Inv respectively₁＝Inv_1ax+Inv_1b，Inv₂＝Inv_2ax+Inv_2b，Inv₃＝Inv_3ax+Inv_3b…；

7) Then, using the steps 3) and 4) to obtain GF (2)²) The result of the squaring and multiplication operations in the domain, due to GF (2)²) The inversion operation and the squaring operation in the domain are the same, so the result of the inversion can be solved by using the squaring operation;

8) using GF (2)²) The result in the domain is mapped reversely;

9) inverse mapping is performed using the result of 8) to obtain the input of multiplication 5 and multiplication 6, and GF (2) is obtained by multiplication 5 and multiplication 6⁸) The inversion result of X in (1);

10) using the result of 9) to perform inverse mapping to obtain the mask component at GF (2)⁸) The final result in (1).

And 4) performing multiplication operation, wherein the multiplication operation is non-linear operation and takes the requirement of the security of the encryption algorithm into consideration, and the multiplication operation does not use the multiplication operation of a finite field but performs the multiplication operation by adopting a TI mask implementation mode. Since the TI threshold mask method requires much fewer additional random numbers than the DOM mask algorithm in performing the multiplication operation, the number of random numbers is reduced.

Compared with the prior art, the invention discloses a new method for decomposing the threshold mask by the argument,during S-box permutation of block ciphers, at GF (2)⁴) And GF (2)²) The multiplication operation in the domain uses the idea of TI mask to realize the multiplication operation, so that the requirement of additional new random numbers in the multiplication process can be reduced, and the independence between data can be achieved. At GF (2)⁴) And GF (2)²) The basic framework of the DOM mask adopted by other operations in the domain can achieve the purpose of saving chip resources, thereby effectively achieving the purposes of reducing randomness and saving the use area of the chip, and simultaneously ensuring the confidentiality and the safety of data and effectively resisting power consumption attack and side channel cube attack.

Drawings

FIG. 1 is a flow diagram of a new method of argument decomposition threshold masking according to an embodiment.

Detailed Description

The invention will be further elucidated with reference to the drawing, without being limited thereto.

Example (b):

referring to fig. 1, a new method of argument decomposition threshold masking based on AES against first order DPA:

1) in the running process of the cryptographic algorithm, 8-bit sensitive variables input by an S box are divided into 3 random mask components with 8 bits by using a key sharing mechanism, namely X is equal to X₁+X₂+X₃；

2) 3 random mask components X with 8 bits in the step 1)₁，X₂，X₃Mapping to GF (2)⁴) Above, are respectively X₁＝A₁x+A₀，X₂＝B₁x+B₀，X₃＝C₁x+C₀；

3) Under GF (2)⁴) The square operation is performed, and the corresponding results of square 1, square 2, and square 3 in FIG. 1 are

A_1xorA₀＝(A₁+A₀)²(1)

B_1xorB₀＝(B₁+B₀)²(2)

C_1xorC₀＝(C₁+C₀)²(3)

4) Under GF (2)⁴) The multiplication operation is carried out, and because the multiplication operation is a nonlinear operation and the requirement of the security of the encryption algorithm is considered, the multiplication operation does not use the multiplication operation of a finite field, but adopts a TI implementation mode to carry out the multiplication operation. To achieve uniformity in the nature of TI, we add a random mask to each component function. Since the TI threshold mask method requires much fewer additional random numbers than the DOM mask algorithm in performing the multiplication operation, the number of random numbers is reduced. The specific calculation formula for the multiply 1 operation in FIG. 1 is as follows:

Q_mul1＝B₁B₀+B₁C₀+C₁B₀+Z₀(4)

Q_mul2＝C₁C₀+A₁C₀+C₁A₀+Z₁(5)

Q_mul3＝A₁A₀+A₁B₀+B₁A₀+Z₀+Z₁(6)

5) taking the outputs of steps 3) and 4) as the inputs in this step, the components of each squaring operation and the components of the multiplication result are exclusive-ored, thus resulting in GF (2)⁴) The domain needs to be inverted, and the specific calculation formula is as follows:

Inv₁＝A_1xorA₀+Q_mul1(7)

Inv₂＝B_1xorB₀+Q_mul2(8)

Inv₃＝C_1xorC₀+Q_mul3(9)

6) returning to step 2) to remove GF (2)⁴) 3 of the inverse components Inv₁，Inv₂，Inv₃Mapping to GF (2)²) Upper, is Inv respectively₁＝Inv_1ax+Inv_1b，Inv₂＝Inv_2ax+Inv_2b，Inv₃＝Inv_3ax+Inv_3b；

7) Then, using the steps 3) and 4) to obtain GF (2)²) The result of the squaring and multiplication operations in the domain, due to GF (2)²) The inversion operation and the squaring operation in the domain are the same, so the result of the inversion can be obtained by using the squaring operation, and the specific expressions are respectively:

the specific calculation formula of the square 4, square 5 and square 6 operations is as follows:

Inv_1axorInv_1b＝(Inv_1a+Inv_1b)²(10)

Inv_2axorInv_2b＝(Inv_2a+Inv_2b)²(11)

Inv_3axorInv_3b＝(Inv_3a+Inv_3b)²(12)

the result of the multiply 2 operation:

Q₁＝Inv_2aInv_2b+Inv_2aInv_3b+Inv_3aInv_2b+Z₀(13)

Q₂＝Inv_3aInv_3b+Inv_1aInv_3b+Inv_3aInv_1b+Z₁(14)

Q₃＝Inv_1aInv_1b+Inv_1aInv_2b+Inv_2aInv_1b+Z₀+Z₁(15)

the specific calculation formula of the operations of inversion 1, inversion 2 and inversion 3 is as follows:

8) using GF (2)²) DomainObtaining GF (2) by inverse mapping of the result of (1)⁴) The result of inversion is obtained by obtaining A_l21,A_l22,A_l23In time, the xor operation can expose the sensitive data, so an extra random number needs to be added to mask the sensitive data, with the corresponding result:

the corresponding result of the multiply 3 operation is:

the corresponding result of the multiply 4 operation is:

9) inverse mapping is performed using the result of 8) to obtain the input of multiplication 5 and multiplication 6, and GF (2) is obtained by multiplication 5 and multiplication 6⁸) The result of inversion of X in (1) is similarly obtained by obtaining A_l41，A_l42， A_l43An extra random number is needed to mask sensitive data, with the corresponding result as follows:

the inputs to the multiply 5 and multiply 6 operations are:

the corresponding result of the multiply 5 operation is:

the corresponding result of the multiply 6 operation is:

10) using the result of 9) to perform inverse mapping to obtain the mask component at GF (2)⁸) The specific expression of the final result in (1) is as follows:

Claims (1)

1. the argument decomposition threshold mask method is characterized by comprising the following steps:

1) carrying out masking component on 8-bit sensitive variables input by an S box in the running process of a cryptographic algorithm by using a key sharing mechanism;

2) mapping the 8-bit random mask component in step 1) to GF (2)⁴) Above, are respectively X₁＝A₁x+A0，X₂＝B₁x+B0， X₃＝C₁x+C0；

3) Under GF (2)⁴) Respectively carrying out multiplication operation, inversion operation and squaring operation;

4) under GF (2)⁴) The multiplication operation is realized by a mask mode of 3 input and 3 output in the TI mask, and in order to meet the uniformity, an additional random number needs to be added to each output component result;

5) XOR-ing the components of each squaring operation with the components of the multiplication result, at GF (2)⁴) Solving an inverse value in the domain;

6) returning to step 2) to remove GF (2)⁴) Inv in (1)₁，Inv₂，Inv₃Mapping to GF (2)²) Upper, is Inv respectively₁＝Inv₁ax+ Inv₁b，Inv₂＝Inv₂ax+ Inv₂b，Inv₃＝Inv₃ax+ Inv₃b；

7) Then, using the steps 3) and 4) to obtain GF (2)²) The result of the squaring and multiplication operations in the domain, due to GF (2)²) The inversion and squaring operations in the domain are the same, so the values are inverted with a squaring operation;

8) using GF (2)²) The result in the domain is mapped reversely;

9) inverse mapping is performed using the result of 8) to obtain the input of multiplication 5 and multiplication 6, and GF (2) is obtained by multiplication 5 and multiplication 6⁸) The inversion result of X in (1);

10)using the result of 9) to perform inverse mapping to obtain the mask component at GF (2)⁸) The final result in (1).

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