Hardware Trojan defense method based on game theory

Abstract

The invention discloses a hardware Trojan defense method based on the game theory, and relates to the technical field of integrated circuit safety. The method comprises the following steps: S1, defining participants and a strategy space; s2, establishing a hardware Trojan attack and defense income model; s3, calculating an attack and defense payment matrix; s4, constructing a non-cooperative finite dynamic game model; and S5, determining an optimal defense strategy. According to the method, by simulating strategy selection and income calculation of an attacker and a defender, the attacker and the defender are enabled to confront in multiple rounds in combination with mixed strategy game, optimal response dynamic and strategy probability updating, the strategy can be adjusted in each round, adjustment is performed according to the result of the previous round, the evolution and optimal solution of the strategy are studied, and the optimal solution of the strategy is researched. And whether a stable strategy combination or periodic change exists in long-term confrontation is researched, so that a final optimal defense strategy is determined according to the stable strategy combination or a single strategy.

Description

Technical Field

[0001] The present invention relates to the field of integrated circuit security technology, and in particular to a hardware Trojan defense method based on game theory, which is used to improve the security of the system during the design and manufacture of integrated circuits. Background Art

[0002] With the advancement of semiconductor technology and the trend of globalization, the design, manufacturing, testing and packaging of integrated circuits have gradually separated, and integrated circuit design companies often outsource the manufacturing process to third-party factories. However, untrustworthy third-party foundries may implant malicious circuits (hardware Trojans) into integrated circuits without the knowledge of designers, resulting in changes in system functions, information leakage or denial of service, endangering the security of critical infrastructure such as military systems and financial facilities.

[0003] Hardware Trojans are intentionally implanted by adversaries to achieve some malicious goals. In this case, the adversary is an entity with human intelligence and motivation, and hardware Trojans are one of their means. In addition, adversaries usually understand the hardware Trojan detection methods that defenders may adopt and design more covert Trojans to target these methods. These challenges require defenders to have a formal, reliable, and neutral framework to quickly evaluate the optimal hardware Trojan defense strategy. Summary of the invention

[0004] In view of the problems pointed out in the background technology, the present invention provides a hardware Trojan defense method based on game theory. Based on game theory, the present invention optimizes defense measures by analyzing the strategic interaction between the attacker and the defender, thereby selecting the best defense strategy, reducing the risk of hardware Trojan attacks, and improving the security of the hardware system.

[0005] The technical solution adopted by the present invention is as follows:

[0006] A method for defending against hardware Trojans based on game theory, characterized in that it comprises the following steps:

[0007] S1. Define the participants and strategy space, specifically:

[0008] Define participants Z = {d, a}, where d represents the set of defenders and a represents the set of attackers;

[0009] Define the strategy space of defender and attacker; the defense strategy space includes the known defense strategies d1, d2, …, d N and their corresponding usage probabilities ρ1, ρ2, …, ρ N ; The attack strategy space includes the known attack strategies a1, a2, …, a M and their corresponding usage probabilities σ1, σ2, …, σ M ;

[0010] Each player has a set of strategies to choose from, so the defender's mixed strategy is represented as a probability distribution:

[0011] ρ d =(ρ1,ρ2,...,ρ N )

[0012] And satisfy:

[0013]

[0014] The attacker's mixed strategy is represented as a probability distribution:

[0015] σ a =(σ1,σ2,...,σ M )

[0016] And satisfy:

[0017]

[0018] S2. Establish a hardware Trojan attack and defense profit model, specifically:

[0019] The attacker's successful attack will cause resource loss to the integrated circuit, while the defender's successful defense avoids the resource loss of the integrated circuit. Therefore, both the attack benefit and the defense benefit are expressed in terms of resource loss L:

[0020] L=n IC ·k

[0021] Among them, n IC represents the number of hardware resources of the integrated circuit, and k represents the severity coefficient of the attack;

[0022] The defense cost is composed of the design cost and hardware resources required by the defender to design active defense. The defense cost C d It is expressed as:

[0023] C d =n IC ·k d ·R d

[0024] Among them, k d represents the difficulty of designing defense strategies, R d represents the defense coverage of the integrated circuit, n IC Indicates the number of hardware resources of the integrated circuit;

[0025] The attack cost is composed of the design cost and hardware resources required by the attacker to insert the hardware Trojan. The attack cost C a It is expressed as:

[0026] C a=n HT ·k a

[0027] Among them, k a Indicates the design difficulty coefficient of the hardware Trojan, n HT Indicates the hardware resource cost of the hardware Trojan.

[0028] The attacker's payment value E a for:

[0029] E a =LC a

[0030] Defender's payment value E d for:

[0031] E d =LC d

[0032] S3. Calculate the payment matrix of attack and defense, specifically:

[0033] The attack mode and corresponding use probability, defense mode and corresponding use probability in the strategy space are brought into step S2 to obtain the attack and defense payment matrix; the payment matrix represents the payment value of the attacker and the defender under each strategy combination;

[0034] The attacker's payment matrix P A It is expressed as:

[0035]

[0036] Among them, a nm It means that when the attacker chooses strategy a m＝1,2,3,...,M , the defender chooses strategy d n＝1,2,3,...,N The defender’s payment matrix P is D It is expressed as:

[0037]

[0038] Among them, d mn It means that when the defender chooses strategy d n＝1,2,3,...,N , the attacker chooses strategy a m＝1,2,3,...,M The defender's payment value.

[0039] S4. Construct a non-cooperative finite dynamic game model, specifically:

[0040] In integrated circuit design and manufacturing, the hardware Trojan defense and attack game is divided into multiple rounds, each round is divided into a defense phase and an attack phase; in the defense phase, the defender designs active defense measures, and in the attack phase, the attacker inserts the hardware Trojan;

[0041] In each round of the game, the attacker and defender choose strategies according to their strategy probability distribution:

[0042] s A = random-strategy(σ a )

[0043] s D =random-strategy(ρ d )

[0044] Among them, s A represents the attack strategy chosen by the attacker, s D represents the defense strategy chosen by the defender;

[0045] After selecting a strategy, calculate the payment value under the corresponding strategy according to the payment matrix:

[0046] u A =P A [s A ][s D ]+random-normal(0,1)

[0047] u D =P D [s A ][s D ]+random-normal(0,1)

[0048] Among them, random-normal (0,1) represents the random perturbation introduced when calculating the payment value;

[0049] In each round of the game, since the attacker is acting later, he may observe the active defense measures at this time, so he will choose a reasonable attack strategy; while the defender may detect the attacker's attack strategy in the previous round, so he will adjust the defense strategy;

[0050] The update formula for the probability distribution of the attacker and defender strategies is:

[0051] σ j =σ j +α·u A ·δ i,j

[0052] ρ i =ρ i +α·u D ·δ i,j

[0053] Among them, α is the learning rate, δ i,jis the Kronecker delta function. When i=j, δ i,j =1, otherwise δ i,j =0.

[0054] S5. Determine the best defense strategy;

[0055] Assume that in the tth round, the attacker and defender's payments are u A (t) and u D (t), then the attacker’s cumulative payment is:

[0056]

[0057] The defender's cumulative payout is:

[0058]

[0059] The difference between the attacker's and defender's accumulated payouts is:

[0060] X(t)=U D (t)-U A (t)

[0061] When X(t) reaches its maximum value X max (t), the strategy chosen by the defender at this time is the best defense strategy.

[0062] The present invention simulates the strategy selection and benefit calculation of attackers and defenders, combines mixed strategy game, best response dynamics, and strategy probability update to allow attackers and defenders to confront each other in multiple rounds. The strategy can be adjusted in each round according to the results of the previous round, and the evolution and optimal solution of the strategy are studied. It is also studied whether there is a stable strategy combination or periodic changes in the long-term confrontation, so as to determine the final optimal defense strategy based on the stable strategy combination or a single strategy. BRIEF DESCRIPTION OF THE DRAWINGS

[0063] Figure 1 Schematic diagram of the attack and defense strategy profit model. DETAILED DESCRIPTION

[0064] In order to make the purpose, technical solution and effect of the present invention more clear, the present invention is further described in detail below with reference to the accompanying drawings and embodiments.

[0065] The type of hardware Trojan that an attacker may choose to insert will affect the defender's choice of defensive measures, and vice versa, that is, the choices of the defender and the attacker will determine the rate of return for both parties. In view of this coupling between the actions of the attacker and the defender, non-cooperative finite dynamic game theory provides appropriate modeling and analysis tools to help understand the strategy selection process of the attacker and the defender, and to help the defender choose a specific defense strategy.

[0066] This example proposes a hardware Trojan defense method based on game theory, which includes the following steps: constructing a non-cooperative limited dynamic game model, establishing a hardware Trojan attack and defense profit model, dynamic game process, and determining the best defense strategy.

[0067] S1. Define the participants and strategy space, specifically:

[0068] Define participants Z = {d, a}, where d represents the set of defenders and a represents the set of attackers.

[0069] Define the strategy space of defender and attacker; the defense strategy space includes the known defense strategies d1, d2, …, d N (such as statistical detection, rare event removal, obfuscation, etc.) and their corresponding usage probabilities ρ1, ρ2, …, ρ N ;

[0070] Each player has a set of strategies to choose from, so the defender's mixed strategy is represented as a probability distribution:

[0071] ρ d =(ρ1,ρ2,...,ρ N )

[0072] And satisfy:

[0073]

[0074] The attack strategy space includes the known attack strategies a1, a2, ..., a M (such as FPGA modification Trojans, side channel Trojans, clock Trojans, etc.) and their corresponding usage probabilities σ1, σ2, …, σ M ;

[0075] Therefore, the attacker's mixed strategy is represented as a probability distribution:

[0076] σ a =(σ1,σ2,...,σ M )

[0077] And satisfy:

[0078]

[0079] Table 1 shows the strategy space of defenders and attackers.

[0080] Table 1

[0081]

[0082]

[0083] S2. Both the insertion and active defense of hardware Trojans require the use of integrated circuit resources. The cost is positively correlated with the occupied resources. The intrinsic value and utility of integrated circuits are positively correlated with the resources they possess. Considering that the payment value is the basis of the attack and defense game model and the selection of the optimal defense strategy, an attack and defense benefit model based on integrated circuit resources is needed to calculate the payment value of the attacker and defender to determine the optimal defense strategy.

[0084] Establish a hardware Trojan attack and defense profit model, such as Figure 1 As shown, specifically:

[0085] The attacker's successful attack will cause resource loss to the integrated circuit, while the defender's successful defense avoids the resource loss of the integrated circuit. Therefore, both the attack benefit and the defense benefit are expressed in terms of resource loss L:

[0086] L=n IC ·k

[0087] Among them, n IC represents the number of hardware resources of the integrated circuit, and k represents the severity coefficient of the attack.

[0088] The defense cost is composed of the design cost and hardware resources required by the defender to design active defense. The defense cost C d It is expressed as:

[0089] C d =n IC ·k d ·R d

[0090] Among them, k d represents the difficulty of designing defense strategies, R d represents the defense coverage of the integrated circuit, n IC Indicates the number of hardware resources of an integrated circuit.

[0091] The attack cost is composed of the design cost and hardware resources required for the attacker to insert the HT (hardware Trojan). The attack cost C a It is expressed as:

[0092] C a =n HT ·k a

[0093] Among them, k a Indicates the design difficulty coefficient of the hardware Trojan, n HT Indicates the hardware resource cost of the hardware Trojan.

[0094] The attacker's payment value E a for:

[0095] Ea =LC a

[0096] Defender's payment value E d for:

[0097] E d =LC d

[0098] The purpose of establishing a general return model that includes key factors is to convert the key factors that affect strategy selection into quantitative values ​​related to returns.

[0099] S3. Calculate the payment matrix of attack and defense, specifically:

[0100] The attack methods and corresponding usage probabilities, defense methods and corresponding usage probabilities in the strategy space are brought into S2 to obtain the payment matrix of attack and defense; the payment matrix represents the payment values ​​of the attacker and defender under each strategy combination.

[0101] The attacker's payment matrix P A It is expressed as:

[0102]

[0103] Among them, a nm It means that when the attacker chooses strategy a m＝1,2,3,...,M , the defender chooses strategy d n＝1,2,3,...,N The defender’s payment matrix P is D It is expressed as:

[0104]

[0105] Among them, d mn It means that when the defender chooses strategy d n＝1,2,3,...,N , the attacker chooses strategy a m＝1,2,3,...,M The defender's payment value.

[0106] According to the payment matrix, we can see the payment values ​​of attackers and defenders under different strategy combinations, including positive returns, negative returns and zero returns.

[0107] S4. Construct a non-cooperative finite dynamic game model, specifically:

[0108] In integrated circuit design and manufacturing, the hardware Trojan defense and attack game is divided into multiple rounds, each round is divided into a defense phase and an attack phase; in the defense phase, the defender designs active defense measures, and in the attack phase, the attacker inserts a hardware Trojan, similar to the situation where different batches of integrated circuits are returned from the manufacturer.

[0109] In each round of the game, the attacker and defender choose strategies according to their strategy probability distribution:

[0110] s A = random-strategy(σ a )

[0111] s D =random-strategy(ρ d )

[0112] Among them, s A represents the attack strategy chosen by the attacker, s D Indicates the defense strategy selected by the defender.

[0113] After selecting a strategy, calculate the payment value under the corresponding strategy according to the payment matrix:

[0114] u A =P A [s A ][s D ]+random-normal(0,1)

[0115] u D =P D [s A ][s D ]+random-normal(0,1)

[0116] Among them, random-normal (0,1) represents the random perturbation introduced when calculating the payment value, the purpose of which is to simulate the uncertainty and randomness in reality and make the results more realistic and diverse.

[0117] In each round of the game, since the attacker is acting later, he may observe the active defense measures at this time, so he will choose a reasonable attack strategy. The defender may detect the attacker's attack strategy in the previous round, so he will adjust the defense strategy.

[0118] The update formula for the probability distribution of the attacker and defender strategies is:

[0119] σ j =σ j +α·u A ·δ i,j

[0120] ρ i =ρ i +α·u D ·δ i,j

[0121] Among them, α is the learning rate, δ i,jis the Kronecker delta function. When i=j, δ i,j =1, otherwise δ i,j =0.

[0122] The strategy selection of attackers and defenders is based on probability distribution, which is similar to the strategy frequency in evolutionary game theory. In addition, by introducing randomness, it is possible to avoid a certain strategy being fixedly selected all the time, thereby increasing the diversity of strategy selection.

[0123] S5. Determine the best defense strategy;

[0124] The optimal defense strategy is determined based on the difference in the cumulative payouts of the attacker and the defender.

[0125] Cumulative payoff refers to the total payoff of the attacker and defender over multiple rounds of the game. Assume that in the tth round, the payoffs of the attacker and defender are u A (t) and u D (t), then the attacker’s cumulative payment is:

[0126]

[0127] The defender's cumulative payout is:

[0128]

[0129] By calculating the difference between the attacker's and defender's accumulated payoffs:

[0130] X(t)=U D (t)-U A (t)

[0131] When X(t) reaches its maximum value X max (t), the strategy chosen by the defender at this time is the best defense strategy.

[0132] In summary, the present invention proposes a dynamic and effective defense mechanism to deal with hardware Trojan attacks. By simulating the strategy selection and payment value of the attacker and defender, combining mixed strategy game, strategy probability update and cumulative payment, the final optimal defense strategy can be obtained.

Claims

1. A hardware Trojan defense method based on game theory, characterized in that: The following steps are involved: S1. Define the participants and strategy space; S2. Establish a hardware Trojan attack and defense profit model; S3. Calculate the payment matrix of attack and defense; S4. Construct a non-cooperative limited dynamic game model; S5. Determine the best defense strategy.

2. A method for defending against hardware Trojans based on game theory as claimed in claim 1, characterized in that: In step S1, define participants Z = {d, a}, where d represents the set of defenders and a represents the set of attackers; Define the strategy space of defender and attacker; the defense strategy space includes the known defense strategies d1, d2, …, d N and their corresponding usage probabilities ρ1, ρ2, …, ρ N ; The attack strategy space includes the known attack strategies a1, a2, …, a M and their corresponding usage probabilities σ1, σ2, …, σ M ; Each player has a set of strategies to choose from, so the defender's mixed strategy is represented as a probability distribution: r d =(ρ1,ρ2,...,ρ N ) And satisfy: The attacker's mixed strategy is represented as a probability distribution: s a =(σ1,σ2,...,σ M ) And satisfy:

3. A method for defending against hardware Trojans based on game theory as claimed in claim 2, characterized in that: In step S2, a hardware Trojan attack and defense profit model is established. Specifically: The attacker's successful attack will cause resource loss to the integrated circuit, while the defender's successful defense avoids the resource loss of the integrated circuit. Therefore, both the attack benefit and the defense benefit are expressed in terms of resource loss L: L=n IC ·k Among them, n IC represents the number of hardware resources of the integrated circuit, and k represents the severity coefficient of the attack; The defense cost is composed of the design cost and hardware resources required by the defender to design active defense. The defense cost C d It is expressed as: C d =n IC ·k d ·R d Among them, k d represents the difficulty of designing defense strategies, R d represents the defense coverage of the integrated circuit, n IC Indicates the number of hardware resources of the integrated circuit; The attack cost is composed of the design cost and hardware resources required by the attacker to insert the hardware Trojan. The attack cost C a It is expressed as: C a =n HT ·k a Among them, k a Indicates the design difficulty coefficient of the hardware Trojan, n HT Indicates the hardware resource cost of the hardware Trojan; The attacker's payment value E a for: AND a =LC a Defender's payment value E d for: AND d =LC d 。 4. A method for defending against hardware Trojans based on game theory as claimed in claim 3, characterized in that: In step S2, the payment matrix of attack and defense is calculated, which is: The attack mode and corresponding use probability, defense mode and corresponding use probability in the strategy space are brought into step S2 to obtain the attack and defense payment matrix; the payment matrix represents the payment value of the attacker and the defender under each strategy combination; The attacker's payment matrix P A It is expressed as: Among them, a nm It means that when the attacker chooses strategy a m＝1,2,3,...,M , the defender chooses strategy d n＝1,2,3,...,N The attacker's payment value is The defender's payment matrix P D It is expressed as: Among them, d mn It means that when the defender chooses strategy d n＝1,2,3,...,N , the attacker chooses strategy a m＝1,2,3,...,M The defender's payment value.

5. A method for defending against hardware Trojans based on game theory as claimed in claim 4, characterized in that: In step S4, a non-cooperative finite dynamic game model is constructed, including: In integrated circuit design and manufacturing, the hardware Trojan defense and attack game is divided into multiple rounds, each round is divided into a defense phase and an attack phase; in the defense phase, the defender designs active defense measures, and in the attack phase, the attacker inserts the hardware Trojan; In each round of the game, the attacker and defender choose strategies according to their strategy probability distribution: s A =random-strategy(σ a ) s D =random-strategy(ρ d ) Among them, s A represents the attack strategy chosen by the attacker, s D represents the defense strategy chosen by the defender; After selecting a strategy, calculate the payment value under the corresponding strategy according to the payment matrix: u A =P A [s A ][s D ]+random-normal(0,1) u D =P D [s A ][s D ]+random-normal(0,1) Among them, random-normal (0,1) represents the random perturbation introduced when calculating the payment value; In each round of the game, since the attacker is acting later, he may observe the active defense measures at this time, so he will choose a reasonable attack strategy; while the defender may detect the attacker's attack strategy in the previous round, so he will adjust the defense strategy; The update formula for the probability distribution of the attacker and defender strategies is: s j =s j +a·u A ·d i,j r i =ρ i +a·u D ·d i,j Among them, α is the learning rate, δ i,j is the Kronecker delta function. When i=j, δ i,j =1, otherwise δ i,j =0.

6. A method for defending against hardware Trojans based on game theory as claimed in claim 5, characterized in that: In step S1, the best defense strategy is determined, specifically: Assume that in the tth round, the attacker and defender's payments are u A (t) and u D (t), then the attacker’s cumulative payment is: The defender's cumulative payout is: The difference between the attacker's and defender's accumulated payouts is: X(t)=U D (t)-U A (t) When X(t) reaches its maximum value X max (t), the strategy chosen by the defender at this time is the best defense strategy.

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