CN112364392B - Proving method of program high-order power consumption side channel safety based on graph isomorphism - Google Patents
Proving method of program high-order power consumption side channel safety based on graph isomorphism Download PDFInfo
- Publication number
- CN112364392B CN112364392B CN202010913876.0A CN202010913876A CN112364392B CN 112364392 B CN112364392 B CN 112364392B CN 202010913876 A CN202010913876 A CN 202010913876A CN 112364392 B CN112364392 B CN 112364392B
- Authority
- CN
- China
- Prior art keywords
- variable
- graph
- observable
- abstract syntax
- directed acyclic
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Active
Links
- 238000000034 method Methods 0.000 title claims abstract description 28
- 230000014509 gene expression Effects 0.000 claims abstract description 40
- 125000002015 acyclic group Chemical group 0.000 claims description 13
- 230000001131 transforming effect Effects 0.000 claims description 2
- 238000012795 verification Methods 0.000 abstract description 11
- 238000002474 experimental method Methods 0.000 abstract description 2
- 238000004364 calculation method Methods 0.000 description 6
- 230000000873 masking effect Effects 0.000 description 2
- 238000012545 processing Methods 0.000 description 2
- 238000011160 research Methods 0.000 description 2
- 238000013459 approach Methods 0.000 description 1
- 230000005540 biological transmission Effects 0.000 description 1
- 238000011161 development Methods 0.000 description 1
- 230000005670 electromagnetic radiation Effects 0.000 description 1
- 238000012986 modification Methods 0.000 description 1
- 230000004048 modification Effects 0.000 description 1
- 238000006467 substitution reaction Methods 0.000 description 1
- 230000009466 transformation Effects 0.000 description 1
Classifications
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F21/00—Security arrangements for protecting computers, components thereof, programs or data against unauthorised activity
- G06F21/70—Protecting specific internal or peripheral components, in which the protection of a component leads to protection of the entire computer
- G06F21/71—Protecting specific internal or peripheral components, in which the protection of a component leads to protection of the entire computer to assure secure computing or processing of information
- G06F21/75—Protecting specific internal or peripheral components, in which the protection of a component leads to protection of the entire computer to assure secure computing or processing of information by inhibiting the analysis of circuitry or operation
- G06F21/755—Protecting specific internal or peripheral components, in which the protection of a component leads to protection of the entire computer to assure secure computing or processing of information by inhibiting the analysis of circuitry or operation with measures against power attack
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F21/00—Security arrangements for protecting computers, components thereof, programs or data against unauthorised activity
- G06F21/60—Protecting data
- G06F21/602—Providing cryptographic facilities or services
-
- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
- Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
- Y02D—CLIMATE CHANGE MITIGATION TECHNOLOGIES IN INFORMATION AND COMMUNICATION TECHNOLOGIES [ICT], I.E. INFORMATION AND COMMUNICATION TECHNOLOGIES AIMING AT THE REDUCTION OF THEIR OWN ENERGY USE
- Y02D10/00—Energy efficient computing, e.g. low power processors, power management or thermal management
Landscapes
- Engineering & Computer Science (AREA)
- Theoretical Computer Science (AREA)
- Computer Hardware Design (AREA)
- Physics & Mathematics (AREA)
- Software Systems (AREA)
- Computer Security & Cryptography (AREA)
- General Engineering & Computer Science (AREA)
- General Physics & Mathematics (AREA)
- Health & Medical Sciences (AREA)
- General Health & Medical Sciences (AREA)
- Bioethics (AREA)
- Mathematical Physics (AREA)
- Stored Programmes (AREA)
- Management, Administration, Business Operations System, And Electronic Commerce (AREA)
Abstract
The application relates to a proving method of program high-order power consumption side channel safety based on graph isomorphism. The method provided by the application judges whether the joint probability distribution of two variable sets is the same or not through isomorphism of the variable type sensitive graph. In the method provided by the application, the following steps are adopted: converting the computing expression of the variable into forms such as abstract syntax tree or directed acyclic graph; when the expression is simplified, in order to ensure that the verification result is not influenced, an equivalent rule in algebra is adopted; for constants in the expression, when the constants are reduced by a method of replacing the sub-expressions, the joint probability distribution of the observable variable set is ensured to be unchanged. Through a plurality of experiments, the method provided by the application can effectively reduce the number of times of model counting and solving, thereby improving the verification efficiency.
Description
Technical Field
The application relates to a proving method of program high-order power consumption side channel safety based on graph isomorphism, which can be applied to verification of random mask high-order power consumption side channel safety.
Background
With the development of information technology, cryptographic algorithms are widely used to protect the transmission and processing of private data. Modern cryptography is based on computational complexity, so that it is difficult to crack keys by brute force attacks. However, kocher, quisquater and Mangard et al propose a side channel attack that can quickly crack keys using physical information such as time, power consumption, electromagnetic radiation, etc. when the system is running.
The random mask is a strategy for effectively defending power consumption side channel attack, so that research and adoption of domestic and foreign scientific research institutions and enterprises are carried out. Random masking random number masking is used to avoid statistical dependencies between physical information and encryption keys. A program employing an n-order mask should ideally be resistant to n-order power consumption side channel attacks. However, the cryptographic algorithm that correctly implements the n-order mask is a complex and error-prone task, and therefore requires an automated verification method to prove the program high-order power-consumption side channel security.
The proving method based on type deduction and the proving method based on model counting solving are sequentially provided for proving the safety of the high-order power consumption side channel. The proving method based on type deduction is efficient, but false positive is caused by false alarm; the proving method based on model counting solving has no false alarm theoretically, but cannot verify the complete program efficiently due to high calculation cost.
Disclosure of Invention
The purpose of the application is that: the number of times of model counting and solving is reduced, and verification efficiency is effectively improved.
In order to achieve the above object, the technical solution of the present application is to provide a method for proving the security of a program high-order power consumption side channel based on graph isomorphism, which is characterized by comprising the following steps:
step 1, inputting programs and variable types thereof, mutually disjoint sets T 1 And T 2 Wherein: any set T 1 The joint statistical distribution of the observable variable sets in (1) is independent of the key, any set T 2 The joint statistical distribution of the observable variable sets in (a) is not independent of the key;
step 2, constructing an intermediate representation form of the input program, wherein the intermediate representation form is an abstract syntax tree or a directed acyclic graph;
for any set t containing d observable variables, the intermediate representation is t abstract syntax trees or directed acyclic graphs; an abstract syntax tree or directed acyclic graph corresponds to a computational expression, intermediate nodes of the abstract syntax tree or directed acyclic graph correspond to operators of the computational expression, and leaf nodes correspond to input variables of the computational expression;
step 3, checking whether the corresponding t abstract syntax trees or directed acyclic graphs contain constants for any set t containing d observable variables, and if so, entering step 4 to simplify and transform the expression; if the constant is not present, the step 6 is entered to perform isomorphism check of the variable type sensitive graph;
step 4, carrying out equivalent transformation on sub-expressions in t abstract syntax trees or directed acyclic graphs, so that the appearance form of each constant c becomesx ☉ c, where x is a variable, ☉ represents any one of the operations of addition, subtraction, exclusive OR, and x can only be x ☉ c, or x ☉ c in the form of t abstract syntax trees or directed acyclic graphs 1 And c 1 Representing other constants than c;
step 5, iteratively executing the following steps 5.1 and 5.2 to reduce constants for all the sub-expressions of x ☉ c in the t abstract syntax trees or the directed acyclic graph:
step 5.1, replacing all sub-expressions x ☉ c with x;
step 5.2, all sub-expressions x ☉ c 1 Replaced by x ☉ c 2 WhereinIf ☉ is an exclusive OR operator, then +.>Representing an exclusive or operator; if ☉ is the plus or minus operator, +.>Representing the minus operator.
Step 6, in the set T 1 Sum set T 2 Find out whether there is an observable variable set t 1 Such that set t and observable variable set t 1 Is a graph isomorphism that is variable type sensitive, i.e., satisfies the following two conditions simultaneously:
condition one) observable variable set t 1 The size of the set t is the same as that of the set t;
condition two) observable variable set t 1 A one-to-one correspondence h is formed between the set t and the set t, namely t1→t, so that an abstract syntax tree or a directed acyclic graph of any pair of variables (x, h (x)) is graph isomorphic, the types of corresponding variables in the graph isomorphic are the same, and h (x) is a corresponding relation function;
step 7, if in set T 1 Find a set t of observable variables as described in step 6 1 The joint statistical distribution of the attestation set t is independent of the key; if at set T 2 Find one ofThe observable variable set t of step 6 1 The joint statistical distribution of the proof set t is not independent of the key; if set T 1 Sum set T 2 None of the set of observable variables t described in step 6 1 It cannot be determined whether the joint statistical distribution of the set t is independent of the key.
Preferably, in step 1, the variable types include a key variable, a plaintext variable, and a random variable.
Preferably, in step 2, the intermediate representation of the input program is constructed by a lexical analyzer and a syntax analyzer of the compilation technique.
Preferably, in step 4, the sub-expressions in the t abstract syntax trees or directed acyclic graphs are equivalently transformed according to equivalence rules in algebra, such as a combination law, a switching law, an allocation law, etc.
The method provided by the application judges whether the joint probability distribution of two variable sets is the same or not through isomorphism of the variable type sensitive graph. In the method provided by the application, the following steps are adopted: converting the computing expression of the variable into forms such as abstract syntax tree or directed acyclic graph; when the expression is simplified, in order to ensure that the verification result is not influenced, an equivalent rule in algebra is adopted; for constants in the expression, when the constants are reduced by a method of replacing the sub-expressions, the joint probability distribution of the observable variable set is ensured to be unchanged. Through a plurality of experiments, the method provided by the application can effectively reduce the number of times of model counting and solving, thereby improving the verification efficiency.
Drawings
FIG. 1 shows the steps of the present application;
FIG. 2 is an exemplary abstract syntax tree in which leaf nodes are variables and constants and intermediate nodes are operators;
FIG. 3 is an abstract syntax tree of an example in which the computational expressions for variables y and z are reduced by the expressions;
FIG. 4 is an abstract syntax tree of the example after step 5 of the computational expressions for variables y and z.
Detailed Description
The application will be further illustrated with reference to specific examples. It is to be understood that these examples are illustrative of the present application and are not intended to limit the scope of the present application. Furthermore, it should be understood that various changes and modifications can be made by one skilled in the art after reading the teachings of the present application, and such equivalents are intended to fall within the scope of the application as defined in the appended claims.
The application provides a proving method of program high-order power consumption side channel safety based on graph isomorphism, which comprises the following steps:
step 1, inputting a program and variable types thereof, wherein the variable types comprise three types: key variable, plaintext variable and random variable, mutually exclusive set T 1 And T 2 Wherein: any set T 1 The joint statistical distribution of the observable variable sets in (1) is independent of the key, any set T 2 The joint statistical distribution of the observable variable sets in (a) is not independent of the key;
step 2, constructing an intermediate representation form of the input program through a lexical analyzer and a grammar analyzer of a compiling technology, wherein the intermediate representation form is an abstract grammar tree or a directed acyclic graph;
for any set t containing d observable variables, the intermediate representation is t abstract syntax trees or directed acyclic graphs; an abstract syntax tree or directed acyclic graph corresponds to a computational expression, intermediate nodes of the abstract syntax tree or directed acyclic graph correspond to operators of the computational expression, and leaf nodes correspond to input variables of the computational expression;
step 3, checking whether the corresponding t abstract syntax trees or directed acyclic graphs contain constants for any set t containing d observable variables, and if so, entering step 4 to simplify and transform the expression; if the constant is not present, the step 6 is entered to perform isomorphism check of the variable type sensitive graph;
step 4, equivalently transforming sub-expressions in t abstract syntax trees or directed acyclic graphs according to an equivalence rule in algebra to enable the appearance form of each constant c to be changed into x ☉ c, wherein x is a variable, ☉ represents any one operator of addition, subtraction and exclusive or, and x is tThe abstract syntax tree or directed acyclic graph can appear only in x ☉ c, or x ☉ c 1 And c 1 Representing other constants than c.
Step 5, iteratively executing the following steps 5.1 and 5.2 to reduce constants for all the sub-expressions of x ☉ c in the t abstract syntax trees or the directed acyclic graph:
step 5.1, replacing all sub-expressions x ☉ c with x;
step 5.2, all sub-expressions x ☉ c 1 Replaced by x ☉ c 2 WhereinIf ☉ is an exclusive OR operator, then +.>Representing an exclusive or operator; if ☉ is the plus or minus operator, +.>Representing the minus operator.
Step 6, in the set T 1 Sum set T 2 Find out whether there is an observable variable set t 1 Such that set t and observable variable set t 1 Is a graph isomorphism that is variable type sensitive, i.e., satisfies the following two conditions simultaneously:
condition one) observable variable set t 1 The size of the set t is the same as that of the set t;
condition two) observable variable set t 1 A one-to-one correspondence h is formed between the set t and the set t, namely t1→t, so that an abstract syntax tree or a directed acyclic graph of any pair of variables (x, h (x)) is graph isomorphic, the types of corresponding variables in the graph isomorphic are the same, and h (x) is a corresponding relation function;
step 7, if in set T 1 Find a set t of observable variables as described in step 6 1 The joint statistical distribution of the attestation set t is independent of the key; if at set T 2 Find a set t of observable variables as described in step 6 1 Then prove the joint statistical distribution of the set tNot independent of the key; if set T 1 Sum set T 2 None of the set of observable variables t described in step 6 1 It cannot be determined whether the joint statistical distribution of the set t is independent of the key.
According to the technical scheme of the application, the implementation emphasis is that the verification result cannot be influenced when simplifying the expression and reducing the constant, and the result of the graph isomorphic method cannot cause false alarm. The application is further described in detail, and a specific embodiment of the application is shown in fig. 1.
In observable variable set t= { x, y, z } and t 1 ＝{x,y 1 ,z 1 For example, x, y, z, y therein 1 And z 1 The calculated expression of (2) is as follows:
the calculation expression of x is x;
the calculation expression of y is
The calculated expression of z is
y 1 The calculated expression of (2) is
z 1 The calculated expression of (2) is
Wherein the method comprises the steps ofK and k are exclusive-or operators 1 As key variables, x, r and r 1 Is a random variable. After processing by compiling technology (i.e. step 2), the observable variables x, y, z, y 1 And z 1 Is shown in fig. 2.
Let it be assumed that the set t is known 1 ＝{x,y 1 ,z 1 The joint probability distribution of the key variable k is independent of 1 T, i.e 1 ＝{t 1 }。
The reduction of expressions and the reduction of constants must be ensured that the result of verification is not affected
In order to ensure that the result of verification is not affected when the expression is simplified, equivalent rules in algebra, such as a combination law, a switching law, a distribution law and the like, must be adopted; or other substitution rules that can ensure that the joint probability distribution is unchanged.
In the above example, step 3 finds that the calculated expression in the set t= { x, y, z } contains constants 1 and 2, and after the expression reduction (i.e. step 4): the calculation expression of y isAnd z has the calculation expression +.>The abstract syntax tree is shown in fig. 3. The result of verification is not affected by the bond law guarantee when simplifying the expression.
In step 5, consider the sub-expressionWill->Is replaced by k; the sub-expression is then +.>Replaced byWherein->That is, the calculation expression of y becomes +.>And z becomes +.>The variation of the expression here ensures that the joint probability distribution is unchanged.
The result of the graph isomorphism-based approach does not lead to false positives.
In order to ensure that the result of the graph isomorphism-based method does not cause false alarm, the corresponding variables in the graph isomorphism must be ensured to have the same type while the graph isomorphism is satisfied.
In the above example, the abstract syntax tree of the expressions of variables y and z after step 5 is shown in fig. 4. It can find the expression abstract syntax tree of x, y and z and x, y 1 、z 1 The expression abstract syntax tree of (a) is a graph isomorphism once, and the corresponding variable types in the graph isomorphism are the same. It can thus be determined that the set t= { x, y, z } joint probability distribution is independent of the key variable k. The key here is k and k 1 Isomorphism in the figure is a corresponding variable and is a key variable; similarly, r and r 1 Isomorphism in the graph is a corresponding variable and is the same type and is a random variable; other in-graph isomorphism is that the corresponding constant values must be equal.
Claims (4)
1. The proving method of the program high-order power consumption side channel safety based on graph isomorphism is characterized by comprising the following steps:
step 1, inputting programs and variable types thereof, mutually disjoint sets T 1 And T 2 Wherein: any set T 1 The joint statistical distribution of the observable variable sets in (1) is independent of the key, any set T 2 The joint statistical distribution of the observable variable sets in (a) is not independent of the key;
step 2, constructing an intermediate representation form of the input program, wherein the intermediate representation form is an abstract syntax tree or a directed acyclic graph;
for any set t containing d observable variables, the intermediate representation is t abstract syntax trees or directed acyclic graphs; an abstract syntax tree or directed acyclic graph corresponds to a computational expression, intermediate nodes of the abstract syntax tree or directed acyclic graph correspond to operators of the computational expression, and leaf nodes correspond to input variables of the computational expression;
step 3, checking whether the corresponding t abstract syntax trees or directed acyclic graphs contain constants for any set t containing d observable variables, and if so, entering step 4 to simplify and transform the expression; if the constant is not present, the step 6 is entered to perform isomorphism check of the variable type sensitive graph;
step 4, equivalently transforming sub-expressions in t abstract syntax trees or directed acyclic graphs to change the appearance form of each constant c into x ☉ c, wherein x is a variable, ☉ represents any one operator of addition, subtraction and exclusive OR, and x can only be x ☉ c or x ☉ c in the t abstract syntax trees or directed acyclic graphs 1 And c 1 Representing other constants than c;
step 5, iteratively executing the following steps 5.1 and 5.2 to reduce constants for all the sub-expressions of x ☉ c in the t abstract syntax trees or the directed acyclic graph:
step 5.1, replacing all sub-expressions x ☉ c with x;
step 5.2, all sub-expressions x ☉ c 1 Replaced by x ☉ c 2 WhereinIf ☉ is an exclusive OR operator, then +.>Representing an exclusive or operator; if ☉ is the plus or minus operator, +.>Representing a minus operator;
step 6, in the set T 1 Sum set T 2 Find out whether there is an observable variable set t 1 Such that set t and observable variable set t 1 Is a graph isomorphism that is variable type sensitive, i.e., satisfies the following two conditions simultaneously:
condition one) Observable variable set t 1 The size of the set t is the same as that of the set t;
condition two) observable variable set t 1 A one-to-one correspondence h is formed between the set t and the set t, namely t1→t, so that an abstract syntax tree or a directed acyclic graph of any pair of variables (x, h (x)) is graph isomorphic, the types of corresponding variables in the graph isomorphic are the same, and h (x) is a corresponding relation function;
step 7, if in set T 1 Find a set t of observable variables as described in step 6 1 The joint statistical distribution of the attestation set t is independent of the key; if at set T 2 Find a set t of observable variables as described in step 6 1 The joint statistical distribution of the proof set t is not independent of the key; if set T 1 Sum set T 2 None of the set of observable variables t described in step 6 1 It cannot be determined whether the joint statistical distribution of the set t is independent of the key.
2. The method for proving the security of a program high-order power consumption side channel based on graph isomorphism according to claim 1, wherein in step 1, the variable types include a key variable, a plaintext variable and a random variable.
3. The method for proving the high-order power consumption side channel security of a program based on graph isomorphism according to claim 1, wherein in step 2, an intermediate representation of the input program is constructed by a lexical analyzer and a syntax analyzer of a compiling technique.
4. The method for proving the security of the program high-order power consumption side channel based on graph isomorphism as recited in claim 1, wherein in step 4, the sub-expressions in the t abstract syntax trees or directed acyclic graphs are equivalently transformed according to equivalence rules in algebra.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202010913876.0A CN112364392B (en) | 2020-09-03 | 2020-09-03 | Proving method of program high-order power consumption side channel safety based on graph isomorphism |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202010913876.0A CN112364392B (en) | 2020-09-03 | 2020-09-03 | Proving method of program high-order power consumption side channel safety based on graph isomorphism |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN112364392A CN112364392A (en) | 2021-02-12 |
| CN112364392B true CN112364392B (en) | 2023-12-15 |
Family
ID=74516444
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN202010913876.0A Active CN112364392B (en) | 2020-09-03 | 2020-09-03 | Proving method of program high-order power consumption side channel safety based on graph isomorphism |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN112364392B (en) |
Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN103647639A (en) * | 2013-12-03 | 2014-03-19 | 北京中电华大电子设计有限责任公司 | Method for symmetric cryptographic algorithm to resist side-channel analysis |
| CN108521325A (en) * | 2018-03-27 | 2018-09-11 | 林喆昊 | A kind of anti-side-channel attack algorithm suitable for system data Life cycle |
| CN108809622A (en) * | 2018-06-15 | 2018-11-13 | 上海科技大学 | A kind of anti-power consumption side-channel attack countermeasure verification method |
Family Cites Families (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US7764785B2 (en) * | 2004-11-08 | 2010-07-27 | King Fahd University Of Petroleum And Minerals | Method for communicating securely over an insecure communication channel |
-
2020
- 2020-09-03 CN CN202010913876.0A patent/CN112364392B/en active Active
Patent Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN103647639A (en) * | 2013-12-03 | 2014-03-19 | 北京中电华大电子设计有限责任公司 | Method for symmetric cryptographic algorithm to resist side-channel analysis |
| CN108521325A (en) * | 2018-03-27 | 2018-09-11 | 林喆昊 | A kind of anti-side-channel attack algorithm suitable for system data Life cycle |
| CN108809622A (en) * | 2018-06-15 | 2018-11-13 | 上海科技大学 | A kind of anti-power consumption side-channel attack countermeasure verification method |
Non-Patent Citations (2)
| Title |
|---|
| Verifying and Quantifying Side-channel Resistance of Masked Software Implementations;Pengfei Gao, et al.;ACM DIGITAL LIBRARY;第28卷(第3期);全文 * |
| 基于软件指令定位的新型高阶侧信道分析方法;郭志鹏;唐明;胡晓波;李煜光;彭国军;张焕国;;计算机学报(第05期);全文 * |
Also Published As
| Publication number | Publication date |
|---|---|
| CN112364392A (en) | 2021-02-12 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| TWI837103B (en) | Computer-implemented method and system | |
| Bayrak et al. | Sleuth: Automated verification of software power analysis countermeasures | |
| Eldib et al. | SMT-based verification of software countermeasures against side-channel attacks | |
| Chandy et al. | Cyberattack detection using deep generative models with variational inference | |
| Wang et al. | Mitigating power side channels during compilation | |
| CN111460472A (en) | Encryption algorithm identification method based on deep learning graph network | |
| Namjoshi et al. | On the completeness of compositional reasoning methods | |
| Li et al. | Optimal filter design for cyber‐physical systems under stealthy hybrid attacks | |
| CN108809622B (en) | Power consumption side channel attack resisting strategy verification method | |
| Mukhtar et al. | Edge enhanced deep learning system for IoT edge device security analytics | |
| WO2024173599A2 (en) | Systems and methods for state minimization and unlinkable transactions | |
| CN112364392B (en) | Proving method of program high-order power consumption side channel safety based on graph isomorphism | |
| Paiva et al. | Cryptanalysis of the binary permuted kernel problem | |
| Xu et al. | A minimum defense cost calculation method for attack defense trees | |
| Chen et al. | Blockchain and trustworthy systems | |
| Larraia et al. | How to Redact the Bitcoin Backbone Protocol | |
| Zhang et al. | BiAn: smart contract source code obfuscation | |
| Li | Security and Risk Analysis of Financial Industry Based on the Internet of Things | |
| Ahmad et al. | Formal modeling and analysis of security schemes of RPL protocol using colored Petri nets | |
| Chadha et al. | The complexity of quantitative information flow in recursive programs | |
| Lin et al. | An axiom system for sequence-based specification | |
| He et al. | GraphSA: Smart Contract Vulnerability Detection Combining Graph Neural Networks and Static Analysis | |
| Kiraz et al. | How to Redact the Bitcoin Backbone Protocol | |
| Firsov et al. | The Ouroboros of ZK: Why Verifying the Verifier Unlocks Longer-Term ZK Innovation | |
| Chu et al. | Counting algorithms for recognizable and algebraic series |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant |