Introduction
In the field of information security, cryptographic algorithms are the core technology for protecting data security. As cyber security threats become increasingly complex, it is particularly important to evaluate the ability of cryptographic algorithms to resist various attacks. This research report aims to comprehensively analyze the key metrics for assessing the resistance of cryptographic algorithms against attacks, helping relevant researchers and practitioners better understand the security evaluation standards of cryptographic algorithms.
Key Length and Key Space
The key length is an important metric for evaluating the strength and reliability of cryptographic algorithms. The longer the key length, the larger the number of possible key combinations (i.e., key space), making brute-force attacks more difficult.
The size of the key space is calculated using the formula: 2^key length. For example, a 128-bit key has a key space containing 2^128 possible combinations, which is computationally enormous, making brute-force attacks impractical.
In practical applications, the choice of key length directly affects the security strength of the cryptographic algorithm. According to NIST (National Institute of Standards and Technology), as of 2014, the minimum required security strength for processing or creating new data is 112 bits, which means that the cryptographic algorithm must provide at least 112 bits of security strength [18].
Security Strength
Security strength is a metric that measures the ability of a cryptographic algorithm to resist brute-force attacks, usually expressed in “bits”. The higher the security strength, the fewer possible keys an attacker needs to try, making brute-force attacks harder to succeed.
For example, a security strength of 112 bits means that a brute-force attack would require approximately 2^112 operations, which is computationally infeasible. Similarly, a security strength of 128 bits provides even higher security assurance, requiring more computational resources.
Security strength is related to key length but is not entirely equivalent to key length. For symmetric cryptographic algorithms, security strength is typically equal to key length; whereas for asymmetric cryptographic algorithms, due to their basis in specific mathematical problems (such as integer factorization or discrete logarithm problems), security strength is usually less than key length.
Resistance to Cryptanalysis Attacks
Cryptanalysis is a key step in evaluating the strength of cryptographic algorithms, involving various methods to examine the performance of cryptographic algorithms, including the ability to resist different types of cryptanalysis attacks [6].
Common types of cryptanalysis attacks include:
Known-Plaintext Attack (KPA)
The attacker has both the plaintext and its corresponding ciphertext. To evaluate the resistance of a cryptographic algorithm to KPA, it is necessary to check whether the algorithm can prevent the inference of the key from known plaintext-ciphertext pairs.
Chosen-Plaintext Attack (CPA)
The attacker can choose the plaintext to be encrypted and observe the results. To evaluate the resistance of a cryptographic algorithm to CPA, it is necessary to check whether the algorithm can prevent the inference of the key from chosen plaintext-ciphertext pairs.
Adaptive Chosen-Plaintext Attack (aCPA)
The attacker can choose the plaintext to be encrypted in response to previous encryption results. This is a stronger attack model that requires the cryptographic algorithm to remain secure even when the attacker can adaptively choose plaintext.
Chosen-Ciphertext Attack (CCA)
The attacker can choose the ciphertext to be decrypted and observe the results. To evaluate the resistance of a cryptographic algorithm to CCA, it is necessary to check whether the algorithm can prevent the inference of the key from chosen ciphertext-plaintext pairs.
Adaptive Chosen-Ciphertext Attack (aCCA)
The attacker can choose the ciphertext to be decrypted in response to previous decryption results. This is a stronger attack model, requiring the cryptographic algorithm to remain secure even when the attacker can adaptively choose ciphertext.
In cryptography, there are formal security definitions to measure the resistance of cryptographic algorithms to these attacks. For example, IND-CPA (Indistinguishability against Chosen-Plaintext Attack) security means that a cryptographic scheme is secure against chosen-plaintext attacks if no polynomial-time attacker can distinguish the encrypted ciphertext from a random string.
Confusion and Diffusion
Confusion and diffusion are two main principles of well-designed cryptographic algorithms and are important metrics for evaluating their resistance to attacks.
Confusion
Confusion ensures that the relationship between the ciphertext and the key is as complex as possible, making it difficult to infer the key from the ciphertext. High-quality confusion means that each bit in the ciphertext is closely related to multiple bits of the key, and this relationship is nonlinear.
Diffusion
Diffusion ensures that a change in a single bit of the plaintext results in changes in many bits of the ciphertext, thus preventing statistical attacks. High-quality diffusion means that small changes in the plaintext produce significant and predictable propagation in the ciphertext.
Diffusion is typically assessed using metrics such as Pixel Change Rate (PC) and Unified Average Change Intensity (UACI). These metrics are used to measure the sensitivity of the cryptographic algorithm to input changes [29].
Randomness
Randomness is an important metric for evaluating the ability of cryptographic algorithms to resist statistical attacks. A secure cryptographic algorithm should produce ciphertext that appears random, such that even if the attacker knows the detailed structure of the cryptographic algorithm, they cannot infer any information about the plaintext or key from the ciphertext.
Randomness is typically assessed using statistical test suites (such as the NIST Randomness Test Suite). These tests include frequency tests, run tests, variance tests, etc., to check whether the statistical properties of the ciphertext conform to those of an ideal random number.
Security Properties
Security properties are the abilities of cryptographic algorithms to remain secure under specific attack models, including:
Indistinguishability
Indistinguishability means that the ciphertext generated by the cryptographic algorithm is statistically indistinguishable from random strings. This is an important metric for evaluating the resistance of cryptographic algorithms to passive attacks.
Forward Security
Forward security means that even if long-term keys are compromised, previously encrypted ciphertext remains secure. This property is crucial for protecting the security of historical communications.
Backward Security
Backward security means that if short-term keys are compromised, long-term keys remain secure. This property is crucial for protecting the security of long-term keys.
Mathematical Foundations and Their Difficulty
Many modern cryptographic algorithms are based on specific mathematical problems, such as the integer factorization problem, discrete logarithm problem, or elliptic curve discrete logarithm problem. The computational difficulty of these mathematical problems is the foundation of the security of cryptographic algorithms.
One important metric for evaluating the resistance of cryptographic algorithms to attacks is the strength of their mathematical foundations. The harder the mathematical problem is to solve, the more secure the cryptographic algorithm based on that problem is.
For example, the security of the RSA encryption algorithm is based on the difficulty of the integer factorization problem. For an n-bit modulus, the time required for factorization grows exponentially with n, making RSA secure with sufficiently large keys.
Security Margin or Security Buffer
The security margin or security buffer refers to the difference between the security of the cryptographic algorithm and the security required against brute-force attacks. A higher security margin indicates a greater security buffer.
For example, if a cryptographic algorithm has a 128-bit key but requires 2^120 operations to resist cryptanalysis attacks, then the security margin is 8 bits. This indicates that even if cryptanalysis attacks are 2^8 times faster than brute-force attacks, it would still require 2^120 operations, which is computationally infeasible.
Resistance to Specific Types of Attacks (e.g., Brute-Force Attacks, Dictionary Attacks, Statistical Attacks)
One important metric for evaluating the resistance of cryptographic algorithms to attacks is their resistance to specific types of attacks, including:
Brute-Force Attacks
Brute-force attacks involve trying all possible keys to find the correct key. The ability to resist brute-force attacks is primarily measured by key length and key space. A larger key space makes brute-force attacks more difficult.
Dictionary Attacks
Dictionary attacks target cases where common words or phrases are used as passwords. The ability to resist dictionary attacks depends on the strength of the key generation method. Using strong key generation methods and avoiding common passwords can enhance resistance to dictionary attacks.
Statistical Attacks
Statistical attacks exploit statistical properties in plaintext or ciphertext. The ability to resist statistical attacks depends on the cryptographic algorithm’s ability to hide or randomize these statistical properties. High-quality confusion and diffusion can effectively resist statistical attacks.
Security and Robustness
Security and robustness are two important metrics for image encryption algorithms, measuring the reliability and attack resistance of the cryptographic algorithm [25].
Security ensures that the cryptographic algorithm can prevent unauthorized access, while robustness ensures that the cryptographic algorithm can maintain functionality under various conditions (such as noise, errors, etc.). These two metrics together determine the overall security of the cryptographic algorithm.
Attack Resistance Metrics
According to TC260 (National Information Technology Standardization Technical Committee), the attack resistance metrics refer to the ability to evaluate the normal operation of algorithms in the face of attacks, including resistance to digital world attacks, physical world attacks, black-box attacks, backdoor attacks, etc. [28].
These metrics provide a framework for evaluating the ability of cryptographic algorithms to resist various attacks, including:
Digital World Attacks
Digital world attacks refer to attacks on cryptographic algorithms conducted through digital means (such as network attacks). Evaluating the resistance to digital world attacks requires considering the cryptographic algorithm’s resistance to various cryptanalysis attacks.
Physical World Attacks
Physical world attacks refer to attacks on cryptographic algorithms conducted through physical means (such as side-channel attacks). Evaluating the resistance to physical world attacks requires considering the physical security of the cryptographic algorithm’s implementation.
Black-Box Attacks
Black-box attacks refer to attacks where the attacker only knows the input and output, without knowledge of the internal workings of the cryptographic algorithm. Evaluating the resistance to black-box attacks requires considering the black-box security of the cryptographic algorithm.
White-Box Attacks
White-box attacks refer to attacks where the attacker knows the complete implementation of the cryptographic algorithm, including the algorithm structure and keys. Evaluating the resistance to white-box attacks requires considering the security of the cryptographic algorithm under complete transparency.
Backdoor Attacks
Backdoor attacks refer to attacks conducted through vulnerabilities in design or implementation. Evaluating the resistance to backdoor attacks requires considering whether there are intentional or unintentional backdoors in the design and implementation of the cryptographic algorithm.
Side-Channel Analysis and Evaluation
Side-channel analysis is an important method for evaluating the resistance of cryptographic products to side-channel attacks. According to research published in the Journal of Electronics and Information Technology, side-channel analysis evaluation methods analyze the ability of cryptographic products to resist side-channel attacks from different perspectives, including side-channel attack testing, information leakage-based general evaluation, and formal evaluation [13].
Side-channel attacks exploit physical characteristics such as timing and power consumption of the cryptographic implementation, so evaluating the resistance of cryptographic algorithms to side-channel attacks requires considering the physical security of their implementation.
Ciphertext Analysis Methods for Chaotic Image Encryption Systems
For chaotic image encryption systems, ciphertext analysis is an important method for evaluating their resistance to attacks. According to research published in the Journal of Image and Graphics, ciphertext analysis methods can measure the ability of a cryptographic algorithm to resist attacks based on specific circumstances [11].
In the ciphertext analysis of chaotic image encryption systems, in addition to traditional metrics such as PSNR (Peak Signal-to-Noise Ratio) and SSIM (Structural Similarity Index), new metrics such as maximum PSNR have been proposed to more comprehensively evaluate the performance of cryptographic algorithms.
Security Assessment
Security assessment is a core metric for evaluating the resistance of cryptographic algorithms to attacks. According to discussions on Zhihu, security assessment includes evaluating the attack possibilities, resistance, and randomness of cryptographic algorithms [27].
Security assessment typically involves the following steps:
Identifying potential attacks: Determining the types of attacks that may target the cryptographic algorithm.
Assessing attack feasibility: Evaluating the feasibility and complexity of these attacks.
Assessing resistance: Evaluating the resistance of the cryptographic algorithm to these attacks.
Quantifying security: Quantifying the security of the cryptographic algorithm, usually expressed in terms of security strength (in bits).
Conclusion
The metrics for evaluating the resistance of cryptographic algorithms against attacks are multifaceted, covering basic metrics such as key length and key space, to design principles like confusion and diffusion, randomness, and security properties, as well as evaluations of resistance to cryptanalysis attacks and specific types of attacks.
These metrics together form a comprehensive framework for assessing the strength and reliability of cryptographic algorithms in the face of various attacks. In practical applications, it is necessary to select appropriate metrics for evaluation based on specific security needs and threat models.
As cyber security threats continue to evolve, the metrics for evaluating the resistance of cryptographic algorithms against attacks are also continuously refined and updated. Future research directions include developing more precise security assessment methods and exploring security assessment metrics for new cryptographic algorithms (such as quantum-resistant cryptographic algorithms).