Provable security of substitution-permutation encryption networks against linear cryptanalysis
Bibliographic record
Abstract
Block ciphers are an important class of cryptographic algorithms, often used for the efficient encryption of large volumes of information. They can serve as cryptographic primitives in larger security frameworks, for example, the systems used to conduct secure e-commerce over the Internet. A block cipher is a objective mapping from N bits to N bits (N is called the block size) parameterized by a bitstring called a key, denoted k. Typically k is secret, known only to the communicating parties. Common block sizes are 64 and 128 bits. The input to a block cipher is called a plaintext, and the output is called a ciphertext. We consider a fundamental block cipher architecture known as a substitution-permutation network (SPN). Specifically, we investigate the resistance of SPNs to linear cryptanalysis, one of the most powerful attacks on block ciphers. Previous work on linear cryptanalysis of SPNs has been based on approximations known as linear characteristics, and has made use of two assumptions which do not hold in general. In order to demonstrate provable security of a block cipher against linear cryptanalysis, it is necessary to remove these two assumptions. This requires considering linear cryptanalysis based on families of approximations known as approximate linear hulls. The main contribution of this work is the derivation of the expected resistance of SPNs to linear cryptanalysis based on approximate linear hulls. Values computed from our result show that an SPN with a practical block size is expected to be secure against this attack after a reasonably small number of rounds.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.003 | 0.017 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.002 | 0.005 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.003 |
| Insufficient payload (model declined to judge) | 0.002 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".