Symmetric white-box encryption implementation security enhancement method based on partial adder

Abstract

The invention belongs to the technical field of data encryption, and particularly relates to a symmetric white-box encryption implementation security enhancement method based on a partial adder, which comprises the following steps of: 1, designing a partial adder generation algorithm; step 2, designing a partial adder subsequent lookup table adaptation algorithm; and step 3, when the method is applied to symmetric white-box encryption implementation, a white-box attack success condition is destroyed through a fuzzy partial adder and a calculation boundary of a subsequent lookup table, so that a security enhancement effect is obtained. According to the method, the white-box attack success condition is destroyed through the fuzzy partial adder and the calculation boundary of the subsequent lookup table, so that various white-box attacks can be effectively resisted, and a new design normal form is provided for constructing safe white-box encryption.

Description

Technical Field

[0001] This invention belongs to the field of data encryption technology, specifically relating to a method for enhancing security through symmetric white-box encryption based on partial adders. Background Technology

[0002] In the context of the ongoing digital transformation, the need for secure storage, processing, and transmission of information is becoming increasingly prominent. The widespread application of services such as mobile payments, digital content protection, multimedia communication, smart homes, and ride-sharing further underscores the crucial role of information security. Secure network transmission typically requires ensuring multiple attributes of information, including confidentiality, integrity, and availability. Confidentiality is often achieved through encryption technologies, such as symmetric and asymmetric encryption. Among various encryption technologies, symmetric encryption is frequently used as the core cryptographic component in data encryption due to its high efficiency, ease of standardization, and adaptability to various software and hardware platforms.

[0003] While the security of symmetric encryption technologies, primarily AES, is widely recognized under traditional attack models, its security in practical deployments can still face various challenges. With the widespread use of mobile terminals and IoT devices, the operating environment of encryption algorithms is becoming increasingly open and complex. In some cases, attackers can completely control the device's execution environment, including directly reading algorithm code, monitoring its running status, and obtaining intermediate computation results. In scenarios such as mobile payments and digital content protection, algorithms perform encryption and decryption operations on sensitive information within terminal devices. Since the security of the software execution environment is difficult to guarantee absolutely, attackers may use reverse engineering, dynamic debugging, binary tracing, or static analysis to directly extract key information from the device's memory. The security assumptions in traditional cryptanalysis cannot fully cover such extreme scenarios, prompting academia to focus on more severe attack models known as white-box attack models. White-box attack models assume that the attacker has ultimate control over the execution device. Under this assumption, the keys of traditional symmetric encryption are directly exposed to the attacker, posing a significant threat to its security.

[0004] White-box cryptography aims to build key protection technologies suitable for software environments. By protecting the execution flow of cryptographic algorithms, it prevents key leakage under white-box attack models. This concept was initially proposed by Chow et al. in 2002 to address the security needs of cryptographic algorithms running in untrusted environments. In traditional security assumptions, encryption algorithms are generally executed in a controlled environment, with attackers only having access to the algorithm's inputs and outputs. However, with the development of applications such as mobile internet and the Internet of Things, attackers may gain complete control over the algorithm's runtime environment, including source code, execution flow, and stored data. Under such extreme conditions, attackers can directly access and analyze the internal implementation of encryption algorithms, rendering traditional security assumptions inapplicable. The goal of white-box cryptography is to design encryption schemes that can withstand such threats, making it difficult for attackers to recover keys or compromise algorithm security even if they have complete control over the runtime environment. The main purpose of white-box cryptographic design is to maintain key and algorithm security in untrusted environments. Symmetric white-box encryption, as a white-box implementation for protecting the security of symmetric encryption keys, ensures that key information is not exposed in white-box attack models, thereby maintaining the overall security of the cryptographic algorithm.

[0005] The main idea of ​​existing white-box cryptography schemes is to break down each round of the encryption algorithm into several sub-operations, with the result of each sub-operation stored in an independent lookup table. During program execution, the results of each sub-operation are obtained by looking up the table, and then the results are added together using an adder table to recover the correct output of that round. To prevent attackers from directly obtaining the results of the operations, the designers apply random linear and non-linear encoding to the input and output of each lookup table, thereby increasing the difficulty of the attack. The role of the adder is to merge the intermediate results of the outputs of multiple sub-operation lookup tables, so that they can be reconstructed into the data required for subsequent rounds of operations.

[0006] Based on the above main ideas, the characteristics of subsequent security improvement schemes can be mainly divided into three categories: 1. Adjusting the organization of the original lookup table, changing the number of lookup tables, the connection order, or the local combination form; 2. Inserting additional table components or redundant wheels into the wheel structure, that is, adding several additional steps that do not change the final encryption result but will change the intermediate execution path, making it more difficult for attackers to directly correspond the implementation process to the wheel steps of the standard encryption algorithm; 3. Introducing perturbation components or alternative structures into the lookup table network, that is, adding some components or structures that simulate real operations but are actually used for interference analysis, making the tables in different positions less distinguishable in appearance.

[0007] However, the existing symmetric white-box encryption schemes and subsequent improvements by various scholars share a common problem: existing schemes typically only ensure that a single lookup table does not directly reveal key information, but they do not structurally eliminate the composability between lookup tables. The wheel boundaries and component combination relationships in the lookup table network remain relatively clear, especially the merging paths formed by adder table connections, which have clear structural characteristics. Therefore, attackers can first identify connection boundaries with clear functional meanings in the lookup table network, then gradually piece these local combinations together into an interpretable wheel structure, thereby stripping away the encoding protection and recovering the key. Attackers can still use multi-table joint analysis to identify the internal computational logic and use algebraic attacks and structural analysis to break existing schemes. Summary of the Invention

[0008] This invention proposes a security enhancement method for symmetric white-box encryption based on partial adders. This method improves the security of white-box encryption schemes built on existing frameworks under white-box attack environments. The core of this method is to replace the adder table, which originally performed addition and merging operations all at once, with a partial adder table. This prevents the entire result from being calculated at once, instead calculating only a portion and passing the incomplete portion to a subsequent lookup table in a protected encoded form. Furthermore, the subsequent lookup table directly connected to the partial adder table is appropriately modified to complete all addition and merging calculations and obtain the final result. Essentially, this approach makes it difficult for attackers to clearly define functional boundaries, as is the case with traditional schemes, thus breaking the conditions for successful white-box attacks that rely on clear boundaries. Since the partial adders and their subsequent lookup tables still implement complete functionality, the overall encryption function of the white-box encryption implementation remains unchanged, and the final output ciphertext is consistent with the original scheme. This improves security while maintaining compatibility and replaceability with existing decryption processes.

[0009] The technical solution of this invention is as follows: A method for enhancing security through symmetric white-box encryption based on partial adders, characterized by the following steps: Step 1: Design a partial adder generation algorithm; Step 2: Design a successor lookup table adaptation algorithm for some adders; Step 3 applies the algorithms from Step 1 and Step 2 to the implementation of symmetric white-box encryption. By blurring the computational boundaries of the adder and its subsequent lookup table, the conditions for a successful white-box attack are broken, thus effectively resisting various white-box attacks.

[0010] Furthermore, step 1 includes: Step 1.1 Execute the partial adder generation algorithm, named Used to generate partial adders: its input parameters nThis refers to the number of inputs to a partial adder, which should be the same as the number of inputs to the original adder to be replaced, and its input parameters. This refers to the number of bits per input of a partial adder, which should be the same as the number of bits per input of the original adder to be replaced. Its input parameters... For some adders, the actual addition operation is performed on each input. The number of bits (i.e., each input has 100 bits) The bits were actually added together, and each input had a remaining bit. (Bits not added) Specifically, it includes: Step 1.1.1 Generate a random permutation mapping As part of the adder's output encoding, Indicates containing Galois field of elements; Step 1.1.2 Indicates a partial adder n Each input corresponds to a corresponding input decoder, and this input decoder should be matched with the original adder to be replaced. n Each input has the same input decoding, among which Indicates containing Galois field of elements; let This represents the input of a partial adder, where Indicates containing Galois field of elements; let This represents the value of a portion of the adder's input after input decoding. These represent the first two values ​​of the decoded value. q Bits and the remainder t - q Bit; First, the first value of each input after input decoding is... q Add the bits together to get the result. ,in Indicates the addition operation; Next, we will add the results of partial addition. d The remainder of each input after decoding tq The bits are concatenated to obtain a concatenated length of... n ( tq ) +q The result of the number of bits Where || denotes a bit concatenation operation; Finally, the spliced ​​result e Perform output encoding to obtain the output of a partial adder. .

[0011] Step 1.1.3 Output the generated partial adder; Step 1.2 Replace the original adder in the white-box encryption implementation with the generated partial adder.

[0012] Furthermore, step 2 involves executing a partial adder successor lookup table adaptation algorithm, named... This is used to adjust the successor lookup table of some adders, enabling them to complete addition operations that some adders have not yet completed and continue executing the original operations of the lookup table, thus ensuring the correctness of the encryption process; its input parameters The number of adder outputs received by the subsequent lookup table is... The output of each partial adder becomes the input to the subsequent lookup table, whose input parameters... n The number of inputs to a partial adder, its input parameters This refers to the number of bits per input of a partial adder, which should be the same as the number of bits per input of the original adder to be replaced. Its input parameters... For some adders, the actual addition operation is performed on each input. The number of bits (i.e., each input has 100 bits) The bits were actually added together, and each input had a remaining bit. (Bits not added) Specifically, it includes: Step 2.1 For this successor lookup table The first input The inverse operation of the partial adder output encoding corresponding to this input is used as the input decoding, which is... ,in , Indicates containing Galois field of elements; Step 2.2 Decoding each input A new operation is then inserted to complete the addition operations that were not completed by the corresponding adder. make For this successor lookup table The first input One, of which Indicates containing Galois field of elements; let For this successor lookup table The first input Input decoded The value after that, for To split into a length of q Bit fragments ,as well as n A length of tq Bit fragments ,in ; First of all n A length of tq Bit fragments Perform addition to obtain the result. ; Then add the results p With length q Bit fragments By splicing, a length of [length missing] is obtained. t The result of bits , where || represents the bit concatenation operation; Step 2.3 Keep the rest of the subsequent lookup table unchanged and output the adapted lookup table.

[0013] A security enhancement method for symmetric white-box encryption based on partial adders is proposed. The implementation of this technical solution involves replacing the adder table with a partial adder table in a lookup table network, and adapting and modifying the subsequent lookup table of this partial adder table. This allows the merging calculation, which was originally completed in one step by the adder table, to be completed jointly by the partial adder and its subsequent lookup table. This blurs the clear functional boundaries in the lookup table network, disrupting the conditions under which attackers rely on clear boundaries to perform structural splicing, structural analysis, and key extraction from the lookup table network. Consequently, the security of the symmetric white-box encryption scheme constructed based on the lookup table network is improved in a white-box attack environment, providing a new design paradigm for constructing secure white-box encryption implementations.

[0014] The beneficial effects of this invention are as follows: 1. It has reliable security. Through anti-attack analysis and experimental verification, insecure white-box encryption implementations, after applying the method proposed in this invention, can resist all existing white-box attacks.

[0015] 2. It has broad applicability. The method proposed in this invention can be adapted to all white-box encryption schemes with adders, providing a more secure implementation for these schemes.

[0016] 3. Excellent performance. Performance experiments have verified that the security enhancement algorithm using this invention exhibits excellent encryption efficiency, lookup table generation time, and energy consumption on various experimental devices. Attached Figure Description

[0017] Figure 1 This is a schematic diagram of the process of the present invention; Figure 2 This is a schematic diagram of a sub-process of step 1 of the present invention; Figure 3 This is a schematic diagram of the original adder; Figure 4 This is a schematic diagram of a partial adder proposed in this invention; Figure 5 This is a schematic diagram of a sub-process of step 2 of the present invention; Figure 6 To demonstrate the white-box encryption efficiency of this invention on various experimental devices under different round and group length configurations of substitution-linear transformation networks; Figure 7 To apply this invention to the white-box AES-128 encryption algorithm developed by Chow et al., and to compare the encryption efficiency, lookup table generation time, and energy consumption of existing white-box AES-128 implementations on various experimental devices; Figure 8 To apply this invention to the white-box AES-128 encryption algorithm developed by Chow et al. and integrate it into a wireless communication protocol, comparative experiments were conducted on various experimental devices to evaluate the average power consumption, average CPU utilization, and data transmission rate. Detailed Implementation

[0018] The technical solution provided in this application will be further described below with reference to specific embodiments and accompanying drawings. The advantages and features of this application will become clearer from the following description.

[0019] A security enhancement method based on partial adders for symmetric white-box encryption is proposed, which mainly includes two steps and two algorithms running in these two steps.

[0020] The following section first explains the symbols and design concepts used in the invention, then introduces the partial adder step and the partial adder successor lookup table adaptation step in the white-box encryption implementation, and then introduces the partial adder generation algorithm and the partial adder successor lookup table adaptation algorithm.

[0021] The symbols used in this invention are explained in Table 1.

[0022] Table 1. Symbols used in this invention like Figure 1 As shown, a method for enhancing security through symmetric white-box encryption based on partial adders includes the following steps: like Figure 2 As shown: Step 1: Design a partial adder generation algorithm Used to generate a partial adder, its input parameters n This refers to the number of inputs to a partial adder, which should be the same as the number of inputs to the original adder to be replaced, and its input parameters. This refers to the number of bits per input of a partial adder, which should be the same as the number of bits per input of the original adder to be replaced. Its input parameters... For some adders, the actual addition operation is performed on each input. The number of bits (i.e., each input has 100 bits) The bits were actually added together, and each input had a remaining bit. (Bits, not added) A schematic diagram of the original adder is shown below. Figure 3 As shown, a schematic diagram of a partial adder is as follows: Figure 4 As shown; like Figure 5 As shown: Step 2: Design a successor lookup table adaptation algorithm for partial adders. Its input parameters The number of adder outputs received by the subsequent lookup table is... The output of each partial adder becomes the input to the subsequent lookup table, whose input parameters... n The number of inputs to a partial adder, its input parameters This refers to the number of bits per input of a partial adder, which should be the same as the number of bits per input of the original adder to be replaced. Its input parameters... For some adders, the actual addition operation is performed on each input. The number of bits (i.e., each input has 100 bits) The bits were actually added together, and each input had a remaining bit. (Bits not added) Step 3 includes: Step 3.1: Implement a symmetric white-box encryption method with enhanced security as needed. Select the vulnerable original adders and replace the adders in the original white-box encryption implementation with the adders generated by the algorithm in Step 1. Step 3.2: Execute the partial adder successor lookup table adaptation algorithm from Step 2 to adjust the successor lookup table of the partial adders so that it can complete the addition operations that the partial adders have not completed and continue to execute the original operations of the lookup table, thus ensuring the correctness of the encryption process. This concludes the steps of the entire plan.

[0023] The above process includes the following two algorithms: Algorithm 1: Partial adder generation algorithm, named Used to generate a partial adder, its input parameters n This refers to the number of inputs to a partial adder, which should be the same as the number of inputs to the original adder to be replaced, and its input parameters. This refers to the number of bits per input of a partial adder, which should be the same as the number of bits per input of the original adder to be replaced. Its input parameters... For some adders, the actual addition operation is performed on each input. The number of bits (i.e., each input has 100 bits) The bits were actually added together, and each input had a remaining bit. (bits not added), the output is the generated partial adder; Algorithm 2: Partial adder successor lookup table adaptation algorithm, named This is used to adjust the successor lookup table of some adders, enabling them to complete addition operations that some adders have not yet completed and continue executing the original operations of the lookup table, thus ensuring the correctness of the encryption process; its input parameters The number of adder outputs received by the subsequent lookup table is... The output of each partial adder becomes the input to the subsequent lookup table, whose input parameters... n The number of inputs to a partial adder, its input parameters This refers to the number of bits per input of a partial adder, which should be the same as the number of bits per input of the original adder to be replaced. Its input parameters... For some adders, the actual addition operation is performed on each input. The number of bits (i.e., each input has 100 bits) The bits were actually added together, and each input had a remaining bit. (Bits not added); the output is the adapted successor lookup table.

[0024] Test effect verification The security enhancement method for symmetric white-box encryption based on partial adders proposed in this invention has been tested on cloud servers, personal computers, smartphones, Raspberry Pi 5 development boards, and UP Nezha development boards. The experimental equipment is shown in Table 2.

[0025] Table 2 Experimental Equipment like Figure 6 As shown, under different rounds and block length configurations of the substitution-linear transformation network, the encryption efficiency of this invention exhibits an approximately inverse relationship with the changes in block length and rounds. Furthermore, when this invention is applied to the SHARK and PRESENT algorithms, its performance is consistent with our overall evaluation conclusions regarding the substitution-linear transformation network configuration.

[0026] like Figure 7As shown, this invention is applied to the white-box AES-128 encryption algorithm developed by Chow et al., and compared with existing white-box AES-128 implementations in terms of encryption efficiency, lookup table generation time, and energy consumption. This invention, as the only implementation with white-box security, achieves encryption efficiency comparable to other solutions on various devices. Specifically, the lookup table generation time of this invention ranges from 178.32 to 2504.97 ms, the encryption speed ranges from 0.18 to 3.29 MB / s, the lookup table generation energy consumption ranges from 534.12 to 2947.27 J, and the encryption power consumption ranges from 1.11 to 3.77 W.

[0027] like Figure 8 As shown, this invention was applied to the white-box AES-128 encryption algorithm developed by Chow et al. and integrated into three widely used wireless communication protocols: BLE, LoRaWAN, and Zigbee. Compared with traditional AES-128, the performance of each protocol was compared. The average power consumption increased by 2.6% to 4.0%, and the average CPU utilization increased by 0.6% to 1.1%, while the data transmission rate remained unchanged. This indicates that in scenarios where it is integrated into wireless communication protocols, compared to the traditional AES-128 version, this invention has a smaller impact on data transmission rate, power consumption, and CPU utilization, while providing stronger security.

[0028] Experimental results show that the symmetric white-box encryption implementation protected by this invention has good performance on various experimental platforms.

[0029] The above description is merely a description of preferred embodiments of this application and is not intended to limit the scope of this application in any way. Any modifications or alterations made by those skilled in the art based on the above-disclosed technical content should be considered equivalent and valid embodiments, and all fall within the scope of protection of the technical solution of this application.

Claims

1. A method for enhancing security through symmetric white-box encryption based on partial adders, characterized in that, Includes the following steps: Step 1: Design a partial adder generation algorithm; Step 2: Design a successor lookup table adaptation algorithm for some adders; Step 3: The algorithms from Step 1 and Step 2 are applied to the implementation of symmetric white-box encryption. By blurring the computational boundaries of the adder and its subsequent lookup table, the conditions for a successful white-box attack are broken, thus effectively resisting various white-box attacks.

2. The method for enhancing security through symmetric white-box encryption based on partial adders as described in claim 1, characterized in that, Step 1 includes: Step 1.1 Execute the partial adder generation algorithm, named Used to generate partial adders: its input parameters n This refers to the number of inputs to a partial adder, which should be the same as the number of inputs to the original adder to be replaced, and its input parameters. This refers to the number of bits per input of a partial adder, which should be the same as the number of bits per input of the original adder to be replaced. Its input parameters... For some adders, the actual addition operation is performed on each input. The number of bits (i.e., each input has 100 bits) The bits were actually added together, and each input had a remaining bit. (Bits not added) Step 1.2 Replace the original adder in the white-box encryption implementation with the generated partial adder.

3. The method for enhancing security through symmetric white-box encryption based on partial adders as described in claim 1, characterized in that, Step 1.1 specifically includes: Step 1.1.1 Generate a random permutation mapping As part of the adder's output encoding, Indicates containing Galois field of elements; Step 1.1.2 Let Indicates a partial adder n Each input corresponds to a corresponding input decoder, and this input decoder should be matched with the original adder to be replaced. n Each input has the same input decoding, among which Indicates containing Galois field of elements; let This represents the input of a partial adder, where Indicates containing Galois field of elements; let This represents the value of a portion of the adder's input after input decoding. These represent the first two values ​​of the decoded value. q Bits and the remainder t - q Bit; First, the first value of each input after input decoding is... q Add the bits together to get the result. ,in Indicates the addition operation; Next, we will add the results of partial addition. d The remainder of each input after decoding tq The bits are concatenated to obtain a concatenated length of... n ( tq ) +q The result of the number of bits Where || denotes a bit concatenation operation; Finally, the spliced ​​result e Perform output encoding to obtain the output of a partial adder. ; Step 1.1.3 Output the generated partial adder.

4. The method for enhancing security through symmetric white-box encryption based on partial adders as described in claim 1, characterized in that, Step 2 includes: executing a partial adder successor lookup table adaptation algorithm, named... This is used to adjust the successor lookup table of some adders, enabling them to complete addition operations that some adders have not yet completed and continue executing the original operations of the lookup table, thus ensuring the correctness of the encryption process; its input parameters The number of adder outputs received by the subsequent lookup table is... The output of each partial adder becomes the input to the subsequent lookup table, whose input parameters... n The number of inputs to a partial adder, its input parameters This refers to the number of bits per input of a partial adder, which should be the same as the number of bits per input of the original adder to be replaced. Its input parameters... For some adders, the actual addition operation is performed on each input. The number of bits (i.e., each input has 100 bits) The bits were actually added together, and each input had a remaining bit. (Bits not added).

5. The method for enhancing security through symmetric white-box encryption based on partial adders as described in claim 1, characterized in that, Step 2 specifically includes: Step 2.1 For this successor lookup table The first input The inverse operation of the partial adder output encoding corresponding to this input is used as the input decoding, which is... ,in , Indicates containing Galois field of elements; Step 2.2 Decoding each input A new operation is then inserted to complete the addition operations that were not completed by the corresponding adder. make For this successor lookup table The first input One, of which Indicates containing Galois field of elements; let For this successor lookup table The first input Input decoded The value after that, for To split into a length of q Bit fragments ,as well as n A length of tq Bit fragments ,in ; First of all n A length of tq Bit fragments Perform addition to obtain the result. ; Then add the results p With length q Bit fragments By splicing, a length of [length missing] is obtained. t The result of bits , where || represents the bit concatenation operation; Step 2.3 Keep the rest of the subsequent lookup table unchanged and output the adapted lookup table.

6. The method for enhancing security through symmetric white-box encryption based on partial adders as described in claim 1, characterized in that, Step 3: When applied in the implementation of symmetric white-box encryption, the addition operation is completed jointly by a partial adder and a subsequent lookup table. By blurring the computational boundary between the partial adder and the subsequent lookup table, the security of the symmetric white-box encryption implementation is improved.

Images