Differential Cryptanalysis of Two Joint Encryption and Error Correction Schemes
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Bibliographic record
Abstract
In GLOBECOM'10, Adamo et. al. proposed an interesting encryption scheme, called Error Correction-Based Cipher (ECBC), working at the physical layer. This scheme, together with its ancestor, Secret Error Correcting Code (SECC), belongs to the family of Joint Encryption and Error Correction (JEEC), which combines error correction and data encryption as one process to enable efficient implementations. In this paper, we provide rigorous investigation on the security of ECBC and SECC to unveil their cryptographic strengths under chosen-plaintext attacks. For ECBC, we found a 3-stage differential-style attack, which breaks the scheme with O(k × 2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">deg(f)</sup> + 2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</sup> ) effort, where deg(f) is the degree of the core cryptographic function f. For SECC, we found a similar attack of complexity O(k × 2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k+1</sup> ). Both of the attacks are significantly improved from exhaustive search, e.g., O(2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2k+kn+n × 2k</sup> ) for ECBC and O(2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">kn+ (k+n) × 2k</sup> ) for SECC. In addition, we exhibit that f used in ECBC's implementation is particularly vulnerable to our attack, which allows the attacker to recover the secret generator matrix in O(1). To mitigate this vulnerability, we propose a secure yet lightweight construction of f achieving the maximum degree. Finally, the core part of our attack against ECBC has been implemented utilizing GPU acceleration and demonstrated on a cluster GPU instance provided by Amazon EC2. Experimental results confirm that the original implementation of ECBC scheme can be broken in (almost) constant time (<;0.4 second) regardless of k, whereas the ECBC scheme enhanced by our proposed f can withstand this attack to the maximum extent.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 0.000 |
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 it