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In cryptography, the encryption algorithm E and the decryption algorithm D must meet the following conditions to ensure that plaintext P can be securely encrypted and correctly restored!
Network Technology
Section
1) Reversibility Condition
The encryption and decryption must be inverse operations of each other, that is: D(E(P))=PExplanation: Applying the encryption algorithm E to the plaintext results in ciphertext C=E(P), and then applying the decryption algorithm D must restore the original plaintext P.
2) Key Dependency (if a key is used)
If the encryption and decryption processes depend on a key (such as the key K in symmetric encryption or the public key K and private key Ks), the condition must be clearly stated as:DK(EK(P))=P(symmetric encryption) or DKs(EKp(P))=P(asymmetric encryption, public key encryption, private key decryption)Explanation: The keys must match correctly to achieve reversibility. For example, a message encrypted with a public key can only be decrypted with the corresponding private key.
3) Deterministic or Probabilistic
① Deterministic Encryption The same plaintext and key always generate the same ciphertext. In this case, it must satisfy:∀P1,P2 and P1=P2,E(P1)=E(P2)② Probabilistic Encryption (such as encryption using random numbers, like OAEP, AES-GCM): The same plaintext and key may generate different ciphertexts, but it must still satisfy:D(E(P))=P(for all possible ciphertexts)Explanation: Probabilistic encryption can prevent the analysis of plaintext repetition through ciphertext (such as salt values in password hashing).
4) Security Conditions
① Computational Security It should be infeasible to derive the plaintext C from the ciphertext P or the key K in polynomial time.② Semantic Security Given the ciphertext C, it should not be possible to obtain any valuable information about the plaintext P (such as plaintext length, partial content, etc.).
5) Integrity Conditions
The encryption process should not alter the integrity of the plaintext, that is:D(E(P))=P= any other P′=PExplanation: The decryption result must be exactly the same as the original plaintext; otherwise, the encryption system has defects.
Summary
The core conditions for information encryption can be summarized as:D(E(P))=PThis condition ensures the reversibility of encryption and is the basis for the correctness of the cryptographic system. Other security conditions (such as resistance to attacks) must be ensured through specific encryption algorithm designs (such as AES, RSA).
Commonly used encryption algorithms in reality can be divided into
Symmetric Encryption Algorithms,Asymmetric Encryption Algorithms and Hash Algorithms three categories;
1. Symmetric Encryption Algorithms (Single-Key Encryption)
Characteristics: The same key is used for both encryption and decryption, with high encryption efficiency, suitable for large data encryption, but key transmission must be secure.
2. Asymmetric Encryption Algorithms (Public Key Encryption)
Characteristics: Uses public key for encryption and private key for decryption (or vice versa), the key pair consists of a public key and a private key, the public key can be disclosed, while the private key must be kept secret, suitable for key exchange and digital signatures, but with lower encryption efficiency.
3. Hash Algorithms (One-Way Encryption)
Characteristics: Maps input of any length to a fixed-length hash value (digest), irreversible, used for data integrity verification and password storage.
4. Hybrid Encryption Schemes (Combination in Practical Applications)
In practice, the advantages of symmetric and asymmetric encryption are often combined to form a hybrid encryption model,
5. Algorithm Selection Recommendations for Different Scenarios
- For large data encryption, prioritize symmetric algorithms like AES, ChaCha20.
- For key exchange and digital signatures, use RSA, ECC (ECC is recommended due to shorter keys and higher efficiency).
- For password storage, use hashing algorithms with salt and iterations like Bcrypt, Argon2, avoiding direct storage of plaintext or MD5/SHA-1.
- For data integrity verification, use SHA-256, SHA-512, replacing insecure MD5/SHA-1.
- For resistance to quantum computing attacks, focus on post-quantum cryptographic algorithms like ECC, ChaCha20 (currently under research and standardization).
HE ZE LIU CHAO 2024
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