A hardware Trojan defense method based on game theory

Abstract

The application discloses a hardware Trojan defense method based on game theory and relates to the technical field of integrated circuit security. 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 a payoff matrix of attack and defense; S4, constructing a non-cooperative finite dynamic game model; and S5, determining an optimal defense strategy. The application simulates the strategy selection and income calculation of attackers and defenders, combines mixed strategy game, optimal response dynamics and strategy probability updating, and enables the attackers and the defenders to confront each other in multiple rounds, the strategy can be adjusted in each round, the strategy evolution and optimal solution are researched according to the result of the last round, and whether there is a stable strategy combination or periodic change in long-term confrontation is researched, so that the final optimal defense strategy is determined according to the stable strategy combination or single strategy.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of integrated circuit security technology, and particularly relates to a hardware Trojan defense method based on game theory, which is used to improve the security of a system during integrated circuit design and manufacturing. BACKGROUND

[0002] With the progress of semiconductor technology and the trend of globalization, the design, manufacturing, testing and packaging of integrated circuits are gradually separated, and integrated circuit design companies often outsource the manufacturing process to third-party factories. However, untrusted third-party foundries may implant malicious circuits (hardware Trojans) into integrated circuits without the designer's knowledge, causing system function changes, information leakage or denial of service, endangering the safety of critical infrastructure such as military systems and financial facilities.

[0003] Hardware Trojans are intentionally implanted by an adversary with the goal of achieving some malicious objective. In this case, the adversary is an entity with human intelligence and motivation, and the hardware Trojan is one of its means. In addition, the adversary usually knows the hardware Trojan detection methods that the defender may adopt, and designs more covert Trojans against these methods. These challenges make the defender need a formal, reliable and neutral framework to quickly evaluate the optimal hardware Trojan defense strategy. SUMMARY

[0004] In view of the problems pointed out in the background, the present application provides a hardware Trojan defense method based on game theory. Based on game theory, the present application optimizes the defense measures by analyzing the strategy interaction of the attacker and the defender, so as to select the best defense strategy, reduce the risk of hardware Trojan attack, and improve the security of the hardware system.

[0005] The technical solutions adopted by the present application are as follows:

[0006] A hardware Trojan defense method based on game theory, characterized in that it comprises the following steps:

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

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

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

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

[0011] p d = (p1, p2,..., pn) N

[0012] and satisfies:

[0013]

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

[0015] s a = (s1, s2,..., sn) M

[0016] and satisfies:

[0017]

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

[0019] The attacker's successful attack will cause resource loss to the integrated circuit, while the defender's successful defense avoids resource loss to the integrated circuit, so both attack and defense benefits are represented by resource loss L:

[0020] L = n IC · k

[0021] where 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 consists of the design cost and hardware resources required by the defender to design active defense, and the defense cost C d is represented as:

[0023] C d = n IC · k d · R d

[0024] where k d represents the design difficulty of the defense strategy, R d represents the defense coverage rate of the integrated circuit, and n IC represents the number of hardware resources of the integrated circuit;

[0025] The attack cost consists of the design cost and hardware resources required by the attacker to insert the hardware Trojan, and the attack cost C a is represented as:

[0026] C a ​​= n HT · k a

[0027] wherein k a represents the design difficulty coefficient of the hardware Trojan, n HT represents the hardware resource cost of the hardware Trojan.

[0028] The payment value E a of the attacker is:

[0029] E a = L - C a

[0030] The payment value E d of the defender is:

[0031] E d = L - C d

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

[0033] The attack and defense payment matrix is obtained by bringing the attack mode and the corresponding use probability in the strategy space, the defense mode and the corresponding use probability into step S2; the payment matrix represents the payment value of the attacker and the defender under each strategy combination;

[0034] The payment matrix P A of the attacker represents:

[0035]

[0036] wherein a nm represents the payment value of the attacker when the attacker selects strategy a m＝1,2,3,...,M and the defender selects strategy d n＝1,2,3,...,N . The payment matrix P D of the defender represents:

[0037]

[0038] wherein d mn represents the payment value of the defender when the defender selects strategy d n＝1,2,3,...,N and the attacker selects strategy a m＝1,2,3,...,M .

[0039] S4. Build 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, and 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;

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

[0042] s A =random-strategy(σ a )

[0043] s D =random-strategy(ρ d )

[0044] where s A represents the attack strategy selected by the attacker, and s D represents the defense strategy selected by the defender;

[0045] After the strategies are selected, the payoff value under the corresponding strategy is calculated according to the payoff 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] where random-normal(0,1) represents a random disturbance introduced when calculating the payoff value;

[0049] In each round of the game, since the attacker is the after-action, the attacker can observe the proactive defense measures at this time and will select a reasonable attack strategy; and the defender can detect the attack strategy of the attacker in the last round, and thus will adjust the defense strategy;

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

[0051] σ j =σ j +α·u A ·δ i,j

[0052] ρ i =ρ i +α·u D ·δ i,j

[0053] where α is the learning rate, and 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] Suppose in the tth round, the attacker and the defender's payment are u A (t) and u D (t), then the attacker's cumulative payment is:

[0056]

[0057] The defender's cumulative payment is:

[0058]

[0059] The difference between the attacker and the defender's cumulative payment:

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

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

[0062] The present application simulates the strategy selection and revenue calculation of the attacker and the defender, combines mixed strategy game, best response dynamics, strategy probability update, and makes the attacker and the defender fight in multiple rounds, each round can adjust the strategy, adjusts according to the result of the last round, studies the evolution of the strategy and the optimal solution, and studies whether there is a stable strategy combination or periodic change in the long-term confrontation, so as to determine the final best defense strategy according to the stable strategy combination or single strategy. BRIEF DESCRIPTION OF DRAWINGS

[0063] Figure 1 It is an attack and defense strategy revenue model schematic diagram. DETAILED DESCRIPTION

[0064] In order to make the purpose, technical scheme and effect of the present application more clear, the present application will be further described in detail below in combination with the drawings and examples.

[0065] The type of hardware Trojan that the attacker may choose to insert will affect the defender's choice of defense measures, and vice versa, that is, the choices of the defender and the attacker will determine the yield rate of both parties. In view of this coupling of the actions of the attack and defense parties, the non-cooperative finite dynamic game theory provides a suitable modeling and analysis tool, which helps to understand the strategy selection process of the attack and defense parties and provides help for the defense party to select specific defense strategies.

[0066] The present example proposes a hardware Trojan defense method based on game theory, which comprises the following steps: constructing a non-cooperative finite dynamic game model, establishing a hardware Trojan attack and defense benefit model, dynamic game process, and determining the best defense strategy.

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

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

[0069] Define the strategy space of the defenders and attackers; the defense strategy space includes known defense strategies d1, d2,..., d N , and their corresponding use probabilities ρ1, ρ2,..., ρ N .

[0070] Each participant 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 known attack strategies a1, a2,..., a M , and their corresponding use 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] The strategy space of the defenders and attackers is shown in Table 1.

[0080] Table 1

[0081]

[0082]

[0083] S2. The insertion of hardware trojans and active defense both require integrated circuit resources, the cost of which is positively related to the occupied resources, and the intrinsic value and utility of integrated circuits are positively related to the resources they possess. Considering that the payment value is the basis for attack-defense game model and optimal defense strategy selection, a hardware trojan attack-defense benefit model based on integrated circuit resources is needed to calculate the payment value of attackers and defenders to determine the best defense strategy.

[0084] A hardware trojan attack-defense benefit model is established, as shown in Figure 1 Specifically,

[0085] Successful attacks by attackers will cause resource loss to integrated circuits, while successful defenses by defenders will avoid resource loss to integrated circuits, therefore, both attack benefits and defense benefits are represented by resource loss L:

[0086] L = n IC · k

[0087] Wherein, n IC represents the number of hardware resources of integrated circuits, and k represents the severity coefficient of attacks.

[0088] The defense cost consists of the design cost and hardware resources required by the defender to design active defense, and the defense cost C d is represented as:

[0089] C d = n IC · k d · R d

[0090] Wherein, k d represents the design difficulty of defense strategy, R d represents the defense coverage rate of integrated circuits, and n IC represents the number of hardware resources of integrated circuits.

[0091] The attack cost consists of the design cost and hardware resources required by the attacker to insert HT (hardware trojan), and the attack cost C a is represented as:

[0092] C a = n HT · k a

[0093] Wherein, k a represents the design difficulty coefficient of hardware trojan, and n HT represents the hardware resource cost of hardware trojan.

[0094] The payment value E a of the attacker is:

[0095] Ea = L - C a

[0096] E d is:

[0097] E d = L - C d

[0098] A general payoff model containing key factors is established, which aims to convert the key factors affecting the strategy selection into quantified values related to the payoff.

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

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

[0101] The payoff matrix P A of the attacker is represented as:

[0102]

[0103] wherein a nm represents the payment value of the attacker when the attacker selects strategy a m＝1,2,3,...,M and the defender selects strategy d n＝1,2,3,...,N . The payoff matrix P D of the defender is represented as:

[0104]

[0105] wherein d mn represents the payment value of the defender when the defender selects strategy d n＝1,2,3,...,N and the attacker selects strategy a m＝1,2,3,...,M .

[0106] According to the payoff matrix, the payment values of the attacker and the defender under different strategy combinations can be seen, including positive payoff, negative payoff and zero payoff.

[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, and each round is divided into a defense phase and an attack phase; in the defense phase, the defender designs proactive defense measures, and in the attack phase, the attacker inserts a hardware Trojan, which is similar to the situation of different batches of integrated circuits returning from the manufacturer.

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

[0110] s A = random-strategy(σ a )

[0111] s D = random-strategy(ρ d )

[0112] where s A represents the attack strategy chosen by the attacker, and s D represents the defense strategy chosen by the defender.

[0113] After choosing strategies, the payoff value under the corresponding strategy is calculated according to the payoff 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] where random-normal(0, 1) represents a random disturbance introduced when calculating the payoff value, aiming to simulate the uncertainty and randomness in reality, making the result more realistic and diverse.

[0117] In each round of the game, since the attacker is the second mover, the attacker may observe the proactive defense measures at this time and will choose a reasonable attack strategy. The defender may detect the attack strategy of the attacker in the last round and will adjust the defense strategy.

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

[0119] σ j = σ j + α·u A · δ i,j

[0120] ρ i = ρ i + α·u D · δ i,j

[0121] where α is the learning rate, and δ i,jis the Kronecker delta function, when i = j, δ i,j = 1, otherwise δ i,j = 0.

[0122] The strategy selection of the attacker and the defender is based on the probability distribution, which is similar to the strategy frequency in evolutionary game theory; in addition, by introducing randomness, it can avoid a certain strategy being selected all the time, and increase the diversity of strategy selection.

[0123] S5. Determining the optimal defense strategy;

[0124] The optimal defense strategy is determined according to the difference between the cumulative payments of the attacker and the defender.

[0125] The cumulative payment refers to the total income of the attacker and the defender in multiple game rounds. Assuming that the payments of the attacker and the defender in the tth round are u A (t) and u D (t), the cumulative payment of the attacker is:

[0126]

[0127] The cumulative payment of the defender is:

[0128]

[0129] By calculating the difference between the cumulative payments of the attacker and the defender:

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

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

[0132] In summary, the application proposes a dynamic and effective defense mechanism to cope with hardware Trojan attacks. By simulating the strategy selection and payment value of the attacker and the defender, combining mixed strategy game, strategy probability updating 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 method comprises the following steps: S1. defining participants, a policy space; S2. establishing a hardware Trojan attack and defense benefit model; S3. calculating the payment matrix of attack and defense; S4. constructing a non-cooperative finite dynamic game model; S5. determining the optimal defense strategy; In step S1, the participants Z = {d, a} are defined, wherein d represents a set of defenders, and a represents a set of attackers; define the defender and attacker strategy spaces; the defender strategy space includes known defense strategies d1, d2,..., d N and their corresponding usage probabilities ρ1, ρ2,..., ρ N ; the attacker strategy space includes known attack strategies a1, a2,..., a M and their corresponding usage probabilities σ1, σ2,..., σ M ; Each participant has a set of strategies to choose from, so the mixed strategy of the defender is represented as a probability distribution: p d = (pi, p2,..., p N ) and satisfies: The mixed strategy of the attacker is represented as a probability distribution: σ a = (σ1, σ2,..., σ M ) and satisfies: In step S2, the hardware Trojan attack and defense benefit model is established, specifically: Successful attacks by the attacker will cause resource loss to the integrated circuit, and successful defense by the defender will avoid resource loss of the integrated circuit, so the attack benefit and the defense benefit are both represented by resource loss L: L = n IC • k wherein n IC represents the number of hardware resources of the integrated circuit, and k represents the severity coefficient of the attack; The defense cost consists of the design cost and hardware resources required for the defender to design the active defense, and the defense cost C d is represented as: C d = n IC · k d · R d wherein, k d represents the design difficulty of the defense strategy, R d represents the defense coverage of the integrated circuit, n IC represents the number of hardware resources of the integrated circuit; The attack cost C is composed of the design cost and hardware resources required by the attacker to insert the hardware Trojan horse. a is represented as: C a = n HT · k a wherein, k a represents the design difficulty coefficient of the hardware Trojan, n HT represents the hardware resource cost of the hardware Trojan; The payment value E of the attacker a is: E a = L-C a The defender's payment value E d is: E d = L - C d In step S3, the payment matrix of attack and defense is calculated, specifically: The attack and defense payment matrix is obtained by bringing the attack method and the corresponding use probability in the policy space, the defense method and the corresponding use probability into step S2; the payment matrix represents the payment value of the attacker and the defender under each strategy combination; The payment matrix P of the attacker A is represented as: where a nm represents the payoff value of the attacker 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 D is represented as: where d mn represents the defender's payoff value when the defender chooses strategy d n＝1,2,3,...,N , the attacker chooses strategy a m＝1,2,3,...,M . 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 a hardware Trojan; In each round of the game, the attacker and the defender select strategies according to their strategy probability distribution: s A = random-strategy(σ a ) s D = random-strategy(p d ) where s A represents the attack strategy selected by the attacker, s D represents the defense strategy selected by the defender; After selecting the strategy, the payment value under the corresponding strategy is calculated 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) Wherein, random-normal(0,1) represents a random disturbance introduced when calculating the payment value; In each round of the game, since the attacker is the after-action, the attacker may observe the active defense measures at this time, and will select a reasonable attack strategy; and the defender may detect the attack strategy of the attacker in the last round, and will adjust the defense strategy; The update formula of the strategy probability distribution of the attacker and the defender is: σ j = σ j + α · u A · δ i,j p i = p i + a · u D · δ i,j where a is the learning rate, d i,j is the Kronecker delta function, d i,j = 1 when i = j, and d i,j = 0 otherwise. In step S5, the optimal defense strategy is determined, specifically: Let us denote the payoffs of the attacker and the defender in the tth round by u A (t) and u D (t), respectively. Then the cumulative payoff of the attacker is: The cumulative payment of the defender is: The difference between the cumulative payments of the attacker and the defender is: X(t) = U D (t) - U A (t) When X(t) takes the maximum value X max (t), the strategy selected by the defender is the best defense strategy.

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