被普遍认可的基于数学的抗量子非对称密码主要有5类？那5类？

Answering about the 5 families of post-quantum asymmetric cryptography

The five recognized families are:

1. 格上加密 (Lattice-based): Solves hard lattice problems, widely used

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Filling in blanks for improving symmetric cipher security

The user seems to be asking how to improve symmetric cipher security, likely in the post-quantum context. Common recommendations include increasing key length, using longer block sizes, adding more rounds, or using a stronger mode. They might be focused on adjusting key length, block size, or rounds—the standard advice for symmetric cryptography.

Improving symmetric cipher security, considering quantum threats

The user seems to want possible ways to improve symmetric cipher security. I suggest filling the blanks with: "Increase key length or algorithm rounds." As a supplement, adding "use larger block sizes or avoid nonce reuse" fits well. For post-quantum contexts, doubling key length (e.g., AES-256) may be necessary.

Suggesting symmetric cipher security improvements

To improve symmetric cipher security, the user might need to fill in: "Increase key length" or "use multiple encryption (e.g., 3DES)." For post

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Explaining the relationship between hashes and symmetric encryption security

In symmetric encryption, hash functions aren't directly improving confidentiality but are vital for things like key derivation, integrity, MACs, and signatures. To increase security, you can expand the hash output length or use longer MAC tags. In a quantum setting, boosting key length parallels increasing hash length since Grover’s algorithm effectively reduces security by sqrt. This means quantum computing cuts down preimage resistance from n-bit to n/2-bit.

Maintaining hash and security strength against quantum attacks

To retain preimage security, use a 256-bit hash like SHA-256, and for stronger security (256-bit), use a 512-bit hash or SHA-3-512. For collision resistance, quantum attacks reduce security, requiring longer outputs like SHA-384 or SHA-512/384. Stronger MACs rely on longer tag lengths—HMAC with longer tags offers better security. For password hashing, use KDFs with a higher work factor, as quantum attacks only provide quadratic speedups.

Linking hash digest length to symmetric cipher security

The user's referring to "杂凑值," which means hash digest. To clarify, increasing the hash output length is like increasing a key length in symmetric ciphers—both increase the difficulty of brute-force attacks. In hashes, length influences collision and preimage security. Lengthening a hash doesn't directly improve symmetric cipher security unless used in key generation or tags.

Clarifying the relationship between hash values and symmetric cipher security

In symmetric encryption, hash values aren't part of the cipher, like AES, but are often used alongside. For example, hashes in key derivation (KDF) affect key strength depending on digest length and preimage resistance. The digest length also impacts HMAC tag security and collision resistance in hash-then-sign protocols. In quantum settings, Grover’s algorithm reduces preimage security by about half.

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Filling in PQC blanks carefully

For the user’s question, I think the first blank could be "范式" (paradigm) or "理念" (concept), and the second blank seems to fit "难题" (hard problem). I’m opting for these terms as they're commonly used in PQC contexts. "范式" for the security paradigm and "难题" for the underlying hard problem makes sense here.

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