CN112468283A

CN112468283A - Method for detecting iFeed [ AES ] algorithm to resist differential fault attack

Info

Publication number: CN112468283A
Application number: CN202011337427.2A
Authority: CN
Inventors: 李玮; 朱晓铭; 蔡天培; 李嘉耀; 张雨希; 张金煜; 汪梦林
Original assignee: Donghua University
Current assignee: Donghua University
Priority date: 2020-11-25
Filing date: 2020-11-25
Publication date: 2021-03-09

Abstract

The invention provides a method for detecting an iFeed [ AES ] algorithm to resist differential fault attack. Firstly, ensuring that an iFeed [ AES ] algorithm is used for encrypting a plaintext under the environment that an experimental environment is not interfered at all, and outputting correct results which are recorded as C and T; then changing the experimental environment by physical means, interfering in the encryption process, inducing the encryption process to generate faults, and obtaining wrong output results which are marked as C 'and T'; the capability of the iFeed [ AES ] algorithm for resisting differential fault attacks is evaluated by calculating the differential value of C and C 'and the differential value of T and T'. If the fault is detected, the specific position of the fault can be deduced, and the effectiveness of the fault position is further judged. The method is simple to operate, quick to implement and high in accuracy, and provides good analysis basis for the capability of the evaluation iFeed [ AES ] algorithm in resisting differential fault attacks.

Description

Method for detecting iFeed [ AES ] algorithm to resist differential fault attack

Technical Field

The invention relates to a method for detecting an iFeed [ AES ] algorithm to resist differential fault attack, and belongs to the technical field of information security.

Background

With the rapid development of modern computer technology, information security problems are gradually highlighted, and problems of network attack, illegal invasion and the like are gradually serious, so that huge potential safety hazards are brought to people in the use process of the internet. The safety and reliability encryption algorithm can ensure the integrity and confidentiality of the message, so the safety problem of the encryption algorithm is always the key point of the research of scholars at home and abroad.

The iFeed AES algorithm was proposed 3 months in 2014 and is a new authentication encryption algorithm, which includes two parts of encryption and authentication, so that the confidentiality and integrity of data can be ensured. ifed AES belongs to symmetric cipher algorithms and faces a significant threat of differential fault attack.

The attack method aims at the structure of a symmetric password and the characteristics of round functions, combines differential analysis, introduces faults during algorithm execution, analyzes the influence of the faults on a ciphertext, and finally obtains key information related to a key so as to recover the key. There is no report published to evaluate the capability of iFeed AES algorithm to resist differential fault attacks, leaving a potential safety hazard for products being packaged using iFeed AES algorithm.

Disclosure of Invention

The purpose of the invention is: a method of assessing the capability of an iFeed [ AES ] algorithm to withstand differential fault analysis is provided.

In order to achieve the above object, the technical solution of the present invention is to provide a method for detecting an iFeed [ AES ] algorithm against a differential fault attack, which is characterized by comprising the following steps:

step 1: randomly generating a message to be processed, and recording the message as M;

step 2: processing the message M to obtain correct output, and recording the output as C and T; processing the message M again and introducing a fault to obtain error output which is marked as C 'and T';

and step 3: calculating the difference between the correct ciphertext and the error ciphertext, recording as delta C and delta T, analyzing the delta C and the delta T, judging whether the algorithm is influenced by differential fault attack, deducing a specific position of a lead-in fault, and analyzing the effectiveness of the lead-in fault, wherein the method comprises the following steps:

calculating a difference

Wherein

Represents exclusive-or operation, Δ C is 128 bits, Δ T is 128 bits, and represents the difference between the two output results of the ninth round, Δ C_iIs the ith byte of Δ C, where i ∈ {0,1, …,15}, in accordance with Δ C_iJudging whether the introduced fault is effective or not according to the ratio of the fault to the fault, wherein the specific method comprises the following steps:

and (3) effective failure:

when Δ C₀To Δ C₁₅All the faults are not 0, and the proportion meets any one of the following conditions, the introduced fault is a valid fault:

case 1) if one of the following equations is satisfied, it can be concluded that the fault was introduced at locations 0, 5, 10, 15; 2 Delta C₀＝ΔC₁＝ΔC₂＝3ΔC₃,

ΔC₄＝ΔC₅＝3ΔC₆＝2ΔC₇,

ΔC₈＝3ΔC₉＝2ΔC₁₀＝ΔC₁₁,

3ΔC₁₂＝2ΔC₁₃＝ΔC₁₄＝ΔC₁₅.

Case 2) if one of the following equations is satisfied, it can be concluded that the fault is directed to

location

3, 4, 9, 14; 3 Delta C₀＝2ΔC₁＝ΔC₂＝ΔC₃,

2ΔC₄＝ΔC₅＝ΔC₆＝3ΔC₇,

ΔC₈＝ΔC₉＝3ΔC₁₀＝2ΔC₁₁,

ΔC₁₂＝3ΔC₁₃＝2ΔC₁₄＝ΔC₁₅.

Case 3) if one of the following equations is satisfied, it can be concluded that the fault is directed to location 2, 7, 8, 13;

ΔC₀＝3ΔC₁＝2ΔC₂＝ΔC₃,

3ΔC₄＝2ΔC₅＝ΔC₆＝ΔC₇,

2ΔC₈＝ΔC₉＝ΔC₁₀＝3ΔC₁₁,

ΔC₁₂＝ΔC₁₃＝3ΔC₁₄＝2ΔC₁₅.

case 4) if one of the following equations is satisfied, it can be concluded that the fault is directed to location 1, 6, 11, 12;

ΔC₀＝ΔC₁＝3ΔC₂＝2ΔC₃,

ΔC₄＝3ΔC₅＝2ΔC₆＝ΔC₇,

3ΔC₈＝2ΔC₉＝ΔC₁₀＝ΔC₁₁,

2ΔC₁₂＝ΔC₁₃＝ΔC₁₄＝3ΔC₁₅.

invalid failure: a fault satisfying one of the following conditions is an invalid fault

Condition 1) when Δ C is 0, it means that the value after the fault is introduced is equal to the original correct value, the difference value is 0, and the fault is an invalid fault;

condition 2) when Δ C ≠ 0, the obtained ciphertext cannot recover the key, or the finally obtained key is not unique, so that the fault is an invalid fault;

condition 3) invalid failure when the failure is introduced before the 8 th round

Judging whether the fault of the delta T is effective or not and a method for leading in the position are the same as a method for judging the delta C;

and 4, step 4: and (3) after the search space of the key is reduced according to the differential value obtained in the step (3), guessing the key by using an exhaustion method and finally cracking the key.

Preferably, in the process of processing the message M by using the iFeed [ AES ] algorithm in the step 2, two experimental environments are controlled, and the specific steps are as follows:

1) inputting a message M, controlling the experimental environment not to be interfered by any other irrelevant objects, and enabling the iFeed [ AES ] algorithm to be correctly carried out, so that a correct output result is obtained and is marked as C and T;

2) and re-inputting the message, processing the message by using the iFeed [ AES ] algorithm again, changing the operating environment by means of other physical equipment, inducing to generate faults to interfere the processing process of the iFed [ AES ] algorithm, and recording the output result as C 'and T'.

Preferably, the method for changing the operating environment to induce the fault comprises the following steps: changing clock, voltage, humidity, radiation, pressure, light and eddy currents.

The method provided by the invention can be used for evaluating the capability of the iFeed [ AES ] algorithm for resisting differential fault attacks. The invention is mainly applied to the evaluation of the safety of the products packaged by the algorithm.

The invention provides a method for detecting that an iFeed [ AES ] algorithm resists differential fault attack, which comprises the steps of firstly processing a certain input message through the iFed [ AES ] algorithm; in the message processing stage, two controls are implemented on the execution environment, one is to ensure that the experimental environment is not interfered, the control processing process runs accurately and records the output results as C and T, and the other is to artificially introduce faults by using some physical means in the process of processing the plaintext message by the algorithm, induce the faults to output wrong results and record the wrong results as C 'and T'. The capability of the iFeed AES algorithm for resisting differential fault attacks is evaluated by calculating differential values delta C and delta T obtained by a correct result and an incorrect result. If the fault is detected, the position of the fault can be deduced, and the effectiveness of the fault position is further judged. The method provided by the invention has the characteristics of simplicity, rapidness, accuracy, easiness in implementation and the like, and provides a good analysis basis for detecting the capability of the iFeed [ AES ] algorithm for resisting differential fault attacks.

Drawings

FIG. 1 is a flow chart of a method for an iFeed [ AES ] algorithm to resist differential fault attacks;

FIG. 2 is a diagram of a differential fault analysis of the iFeed [ AES ] algorithm;

FIG. 3 is a graph of an authentication analysis of the iFeed [ AES ] algorithm;

fig. 4 is a schematic diagram of an experimental environment of the present scheme.

Detailed Description

The invention will be further illustrated with reference to the following specific examples. It should be understood that these examples are for illustrative purposes only and are not intended to limit the scope of the present invention. Further, it should be understood that various changes or modifications of the present invention may be made by those skilled in the art after reading the teaching of the present invention, and such equivalents may fall within the scope of the present invention as defined in the appended claims.

The symbols used in this example are illustrated below:

m: plaintext;

N_i: fault value at the beginning of the ninth round;

c: processing a correct message ciphertext output after the plaintext message M is processed by using iFeed [ AES ];

c': encrypting a plaintext message M and importing an error message ciphertext output after a fault;

Δ C: the difference of C and C';

t: processing the plaintext message M by using iFeed [ AES ] to obtain a correct verification tag;

t': processing a plaintext message M by using an iFeed [ AES ] and introducing a fault to obtain an error verification label;

Δ T: the difference value of T and T';

SB: a byte substitution layer;

SR: performing line shift transformation;

MC: a column obfuscation transformation;

ARK: a key addition layer;

l: importing a set of key candidate values derived after the first failure;

performing exclusive or operation;

K_i: the ith byte of the key K;

jth byte of ith round key k

Pad (A): if the length of A is less than n, then take A |10^n-1-|A|modnAnd if the length of A is n, taking A.

When the same key is used for processing the same message by using the iFeed [ AES ] algorithm, if experimental environments (such as clock, voltage, humidity, radiation, pressure, light, eddy current and the like) are different, an attacker can respectively obtain a correct output and an error output, and respectively calculate the difference values delta C and delta T of the correct output and the error output, so that key information can be deduced. An attacker can induce a fault to occur during the execution of the iFeed AES algorithm, but does not clear the specific location and specific error value of the fault lead-in. Therefore, the specific location of the fault introduction is important, and if important information is to be acquired from the differential value, it is necessary to ensure that the location of the introduced fault is valid, otherwise an attacker cannot acquire the key information from the Δ C.

Fig. 1 is a flowchart of a method for detecting that an iFeed [ AES ] algorithm resists differential fault attack, which is provided by the present invention, and the method for detecting that the iFeed [ AES ] algorithm resists differential fault attack includes the following steps:

step 2: processing the message M to obtain correct output, recording the correct output as C and T, processing the message M again, introducing a fault, and obtaining error output, recording the error output as C 'and T';

and step 3: calculating the difference between the correct ciphertext and the error ciphertext, and respectively recording the result as delta C and delta T;

and 4, step 4: analyzing the delta C and the delta T, judging whether the algorithm is influenced by differential fault attack, deducing a specific position for leading in the fault, and analyzing the effectiveness of leading in the fault;

and 5: after the search space of the key is reduced through the difference proportion, the key is guessed by using an exhaustion method and is finally cracked.

Aiming at the step 2, an iFeed [ AES ] algorithm is used for processing M, and in the experimental process, two different controls are implemented on the operation environment, namely:

1) inputting a message M, controlling the experimental environment not to be interfered by any other irrelevant matters, and enabling the iFeed [ AES ] algorithm to be correctly carried out, so that a correct ciphertext and a correct verification tag are obtained and are marked as C and T;

2) and re-inputting the message, processing the message by using the iFeed [ AES ] algorithm again, changing the operating environment by virtue of other physical equipment, inducing to generate a fault to interfere the processing process of the iFed [ AES ] algorithm, and generating an erroneous output result which is recorded as C 'and T'.

The method for inducing the fault generation in the step 2) comprises the following steps: changing clock, voltage, humidity, radiation, pressure, light and eddy currents, etc.

For step 3, calculate the difference

Wherein

And representing an exclusive-or operation, wherein Δ C is 128 bits, and Δ T is 128 bits, and respectively represent difference values of the two output results of the ninth round.

For step 4, the principle of differential analysis of Δ C and determination of fault location is as follows:

ifed AES is a block cipher that incorporates both encryption and authentication. The design aim is to ensure the low requirement of the algorithm on resources, can process the short message effectively and with low consumption, and can be applied to an embedded system. The packet length of the ifed [ AES ] is 128 bits, ten iterations are required in the encryption and decryption processes, and each iteration except the last iteration is in sequence, and the method comprises four steps: byte substitution, row shifting, column obfuscation, round key addition, the tenth round is similar to the previous nine rounds but without the column obfuscation step.

The key K is derived by fault-importing the algorithm. As shown in fig. 2, after a fault is introduced in the eighth round, a corresponding differential ratio is generated in the ninth round, column aliasing can diffuse a single-byte fault to the whole column, row displacement can diffuse a fault to different columns, and after two rounds of encryption, a fault can be diffused to the whole ciphertext. The method can be used for deriving a fault diffusion diagram and corresponding differential proportion after faults are introduced at other positions. Because the intermediate state output after the ninth round of encryption is equal to the state after the tenth round of decryption, the specific position of fault introduction is deduced by the proportional relation between the correct ciphertext and the error ciphertext output in the tenth round of backward motion and the specific position of fault introduction, so that the candidate value of the key is determined, and finally the key is determined by an exhaustive search method.

The obtained difference results have the following four difference results by analysis, wherein N is₁、N₂、N₃、N₄The difference result in the table is the difference result output after the ninth round of encryption, and is also the state after the tenth round of decryption is finished.

1) If the difference ratios are shown in table 1, for example, it can be inferred that the fault is introduced at positions 0, 5, 10, and 15;

2N₁	N₄	N₃	3N₂
				N₁	N₄	3N₃	2N₂
N₁	3N₄	2N₃	N₂
				3N₁	2N₄	N₃	N₂

TABLE 1 first Difference attack

2) If the difference ratios are shown in table 2, for example, it can be inferred that the fault is introduced at

positions

3, 4, 9, and 14;

3N₂	2N₁	N₄	N₃
				2N₂	N₁	N₄	3N₃
N₂	N₁	3N₄	2N₃
				N₂	3N₁	2N₄	N₃

TABLE 2 second Difference attack

3) If the difference ratios are shown in table 3, for example, it can be inferred that the failure is introduced at positions 2, 7, 8, and 13;

N₃	3N₂	2N₁	N₄
				3N₃	2N₂	N₁	N₄
2N₃	N₂	N₁	3N₄
				N₃	N₂	3N₁	2N₄

TABLE 3 third differential attack

4) If the difference ratio table 4 shows that the fault is introduced to the positions 1, 6, 11 and 12;

N₄	N₃	3N₁	2N₁
				N₄	3N₃	2N₂	N₁
3N₄	2N₃	N₂	N₁
				2N₄	N₃	N₂	3N₁

TABLE 4 fourth differential attack

Taking the first differential case as an example, the following differential equation follows the lead-in of the first fault:

when a fault is introduced, the input difference of the S-box in the ninth round can be obtained by using the correct ciphertext and the error ciphertext obtained in the tenth round according to the encryption algorithm and the propagation path of the fault, and the sub-key in the ninth round is replaced by using the sub-key presumed in the tenth round, so as to reduce the search space of the sub-key. The relationship between the ninth round key and the tenth round key is as follows:

from the ninth and tenth round key relationships and the differential ratio, one can derive the ninth round S-box input as follows:

where C and C' are known, we can find the K value satisfying the above equation by exhaustive method, and put all candidate values into L. If not by a proportional relationship, a possible result of obtaining the value of K by exhaustion is 2¹²⁸Now, according to the differential relation, each time a fault is introduced, a key satisfying an equation has 2⁸As a possible result, there are four equations in total, so there is 2 in total¹⁰And (4) carrying out the following steps. The guessing space of the tenth round key can be further reduced by changing the plaintext and repeating the above-mentioned processes of introducing faults and analyzing, and finally the correct sub-key is obtained. Then according to iFeed [ AES ]]And (4) a key arrangement scheme of the algorithm, and deriving an original key.

The effectiveness of the fault analysis is specifically analyzed as follows:

and (3) effective failure:

when Δ C₀To Δ C₁₅All the faults are not 0, and the proportion meets any one of the following conditions, the introduced fault is effective.

Case 1) if one of the following equations is satisfied, it can be concluded that the fault was introduced at locations 0, 5, 10, 15;

2ΔC₀＝ΔC₁＝ΔC₂＝3ΔC₃,

ΔC₄＝ΔC₅＝3ΔC₆＝2ΔC₇,

ΔC₈＝3ΔC₉＝2ΔC₁₀＝ΔC₁₁,

3ΔC₁₂＝2ΔC₁₃＝ΔC₁₄＝ΔC₁₅.

location

3, 4, 9, 14;

3ΔC₀＝2ΔC₁＝ΔC₂＝ΔC₃,

2ΔC₄＝ΔC₅＝ΔC₆＝3ΔC₇,

ΔC₈＝ΔC₉＝3ΔC₁₀＝2ΔC₁₁,

ΔC₁₂＝3ΔC₁₃＝2ΔC₁₄＝ΔC₁₅.

ΔC₀＝3ΔC₁＝2ΔC₂＝ΔC₃,

3ΔC₄＝2ΔC₅＝ΔC₆＝ΔC₇,

2ΔC₈＝ΔC₉＝ΔC₁₀＝3ΔC₁₁,

ΔC₁₂＝ΔC₁₃＝3ΔC₁₄＝2ΔC₁₅.

ΔC₀＝ΔC₁＝3ΔC₂＝2ΔC₃,

ΔC₄＝3ΔC₅＝2ΔC₆＝ΔC₇,

3ΔC₈＝2ΔC₉＝ΔC₁₀＝ΔC₁₁,

2ΔC₁₂＝ΔC₁₃＝ΔC₁₄＝3ΔC₁₅.

invalid failure, which is an invalid failure when one of the following conditions is satisfied

Condition 1) when Δ C is 0, it means that the value after the fault is introduced is equal to the original correct value, the difference value is 0, and the fault is an invalid fault.

Condition 2) when Δ C ≠ 0, the obtained ciphertext cannot recover the key, or the finally obtained key is not unique, so that the fault is an invalid fault.

Condition 3) is an invalid fault when the fault lead-in precedes the eighth round.

For the above execution steps, selecting an experimental environment as shown in fig. 4, where the computer is used to generate an input message M of iFeed [ AES ] and analyze the output result; the device encapsulated with the iFeed [ AES ] algorithm is used for processing input messages; the equipment generating the fault is used for changing the experiment execution environment, and aims to interfere the processing process of the input message, so that the function of introducing the fault is realized, and an error output result is generated.

By using the analysis method, the invention adopts Java language programming to simulate the fault import and message processing processes under an Eclipse development tool on a computer with an AMD R74800U CPU 1.8GHz 16GB memory, and the fault import and message processing processes are repeatedly executed for 2000 times, and the experimental result shows that the detection method is accurate. The method provides a sufficient theoretical basis for evaluating the safety of the iFeed [ AES ] algorithm, and the method is simple to operate and accurate in calculation result.

Claims

1. A method for detecting the resistance of an iFeed [ AES ] algorithm to differential fault attacks is characterized by comprising the following steps:

calculating differences Δ C ═ C ≦ C ', Δ T ≦ T', where ≦ represents an exclusive or operation, Δ C is 128 bits, Δ T is 128 bits, and each of the differences represents a difference between the results of the ninth round of two outputs, and Δ C represents a difference between the results of the ninth round of two outputs_iIs the ith byte of Δ C, where i ∈ {0,1, …,15}, in accordance with Δ C_iJudging whether the introduced fault is effective or not according to the ratio of the fault to the fault, wherein the specific method comprises the following steps:

and (3) effective failure:

2ΔC₀＝ΔC₁＝ΔC₂＝3ΔC₃,

ΔC₄＝ΔC₅＝3ΔC₆＝2ΔC₇,

ΔC₈＝3ΔC₉＝2ΔC₁₀＝ΔC₁₁,

3ΔC₁₂＝2ΔC₁₃＝ΔC₁₄＝ΔC₁₅.

case 2) if one of the following equations is satisfied, it can be concluded that the fault is directed to location 3, 4, 9, 14;

3ΔC₀＝2ΔC₁＝ΔC₂＝ΔC₃,

2ΔC₄＝ΔC₅＝ΔC₆＝3ΔC₇,

ΔC₈＝ΔC₉＝3ΔC₁₀＝2ΔC₁₁,

ΔC₁₂＝3ΔC₁₃＝2ΔC₁₄＝ΔC₁₅.

ΔC₀＝3ΔC₁＝2ΔC₂＝ΔC₃,

3ΔC₄＝2ΔC₅＝ΔC₆＝ΔC₇,

2ΔC₈＝ΔC₉＝ΔC₁₀＝3ΔC₁₁,

ΔC₁₂＝ΔC₁₃＝3ΔC₁₄＝2ΔC₁₅.

ΔC₀＝ΔC₁＝3ΔC₂＝2ΔC₃,

ΔC₄＝3ΔC₅＝2ΔC₆＝ΔC₇,

3ΔC₈＝2ΔC₉＝ΔC₁₀＝ΔC₁₁,

2ΔC₁₂＝ΔC₁₃＝ΔC₁₄＝3ΔC₁₅.

2. The method for detecting the defense of the iFeed [ AES ] algorithm function against the differential fault attack as claimed in claim 1, wherein in the process of processing the message M by using the iFed [ AES ] algorithm in the step 2, two experimental environments are controlled, and the specific steps are as follows:

3. The method of claim 2, wherein the method of detecting the ifed [ AES ] algorithm function against differential fault attacks comprises changing the surrounding physical environment by a physical device such that the ifed [ AES ] algorithm is disturbed, the method of changing the operating environment to induce a fault comprising: changing clock, voltage, humidity, radiation, pressure, light and eddy currents.