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Learning with Errors (LWE) is a hard math problem underlying recently standardized post-quantum cryptography (PQC) systems for key exchange and digital signatures.
Factoring polynomials with rational coefficients
Lenstra, H., Lenstra, A., and Lovász, L · 1982
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A hierarchy of polynomial time lattice basis reduction algorithms
Schnorr, C.-P · 1987
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Optimal depth neural networks for multiplication and related problems
Siu, K.-Y. and Roychowdhury, V · 1992
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Generating hard instances of lattice problems
Ajtai, M · 1996
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On Lattices, Learning with Errors, Random Linear Codes, and Cryptography
Regev, O · 2005
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Faster exponential time algorithms for the shortest vector problem
Micciancio, D. and Voulgaris, P · 2010
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BKZ 2.0: Better Lattice Security Estimates
Chen, Y. and Nguyen, P. Q · 2011
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Can homomorphic encryption be practical?
Lauter, K., Naehrig, M., and Vaikuntanathan, V · 2011
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Neuro-cryptanalysis of DES and triple-DES
Alani, M. M · 2012
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On the concrete hardness of learning with errors
Albrecht, M. R., Player, R., and Scott, S · 2015
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Kaiser, Ł. and Sutskever, I · 2015
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Kalchbrenner, N., Danihelka, I., and Graves, A · 2015
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Learning simple algorithms from examples
Zaremba, W., Mikolov, T., Joulin, A., and Fergus, R · 2015
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On dual lattice attacks against small-secret LWE and parameter choices in HElib and SEAL
Albrecht, M. R · 2017
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Revisiting the expected cost of solving usvp and applications to lwe
Albrecht, M. R., Göpfert, F., Virdia, F., and Wunderer, T · 2017
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Learning the enigma with recurrent neural networks
Greydanus, S · 2017
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Investigating the ability of neural networks to learn simple modular arithmetic
Palamas, T · 2017
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Attention is all you need
Vaswani, A., Shazeer, N., Parmar, N., et al · 2017
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On the Learning Capabilities of Recurrent Neural Networks: A Cryptographic Perspective
Srivastava, S. and Bhatia, A · 2018
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Homomorphic encryption standard
Albrecht, M., Chase, M., Chen, H., et al · 2019
Cited alongside, same era.
On the feasibility and impact of standardising sparse-secret LWE parameter sets for homomorphic encryption
Curtis, B. R. and Player, R · 2019
Cited alongside, same era.
Universal transformers
Dehghani, M., Gouws, S., Vinyals, O., Uszkoreit, J., and Kaiser, Ł · 2019
Cited alongside, same era.
BERT: Pre-training of deep bidirectional transformers for language understanding
Devlin, J., Chang, M.-W., Lee, K., and Toutanova, K · 2019
Cited alongside, same era.
Improving attacks on round-reduced speck32/64 using deep learning
Gohr, A · 2019
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Bridging Machine Learning and Cryptanalysis via EDLCT
Chen, Y. and Yu, H · 2021
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Solving Arithmetic Word Problems with Transformers and Preprocessing of Problem Text
Griffith, K. and Kalita, J · 2021
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Output Prediction Attacks on SPN Block Ciphers using Deep Learning
Kimura, H., Emura, K., Isobe, T., Ito, R., Ogawa, K., and Ohigashi, T · 2021
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Jurassic-1: Technical details and evaluation
Lieber, O., Sharir, O., Lenz, B., and Shoham, Y · 2021
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Investigating the limitations of transformers with simple arithmetic tasks
Nogueira, R., Jiang, Z., and Lin, J · 2021
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Goncharov, S. V · 2019
Cited alongside, same era.
Solving math word problems with double-decoder transformer
Meng, Y. and Rumshisky, A · 2019
Cited alongside, same era.
Can sequence-to-sequence models crack substitution ciphers?
Aldarrab, N. and May, J · 2020
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Recent advances of neural attacks against block ciphers
Baek, S. and Kim, K · 2020
Cited alongside, same era.
Language models are few-shot learners
Brown, T., Mann, B., Ryder, N., Subbiah, M., Kaplan, J. D., Dhariwal, P., Neelakantan, A., Shyam, P., Sastry, G., Askell, A., et al · 2020
Cited alongside, same era.
On the Concrete Security of LWE with Small Secret
Chen, H., Chua, L., Lauter, K., and Song, Y · 2020
Cited alongside, same era.
Deberta: Decoding-enhanced bert with disentangled attention
He, P., Liu, X., Gao, J., and Chen, W · 2020
Cited alongside, same era.
Charton, F · 2022
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PQC Standardization Process: Announcing Four Candidates to be Standardized, Plus Fourth Round Candidates
Chen, L., Moody, D., Liu, Y.-K., et al · 2022
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Breaking a fifth-order masked implementation of crystals-kyber by copy-paste
Dubrova, E., Ngo, K., and Gärtner, J · 2022
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Towards understanding grokking: An effective theory of representation learning
Liu, Z., Kitouni, O., Nolte, N. S., Michaud, E., Tegmark, M., and Williams, M · 2022
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Grokking: Generalization Beyond Overfitting on Small Algorithmic Datasets
Power, A., Burda, Y., Edwards, H., Babuschkin, I., and Misra, V · 2022
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Salsa: Attacking lattice cryptography with transformers
Wenger, E., Chen, M., Charton, F., and Lauter, K · 2022
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Faith and fate: Limits of transformers on compositionality
Dziri, N., Lu, X., Sclar, M., Li, X. L., et al · 2023
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Gromov, A · 2023
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Teaching arithmetic to small transformers
Lee, N., Sreenivasan, K., Lee, J. D., Lee, K., and Papailiopoulos, D · 2023
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Fast practical lattice reduction through iterated compression
Ryan, K. and Heninger, N · 2023
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fplll, a lattice reduction library, Version: 5.4.4
The FPLLL development team · 2023
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Llama 2: Open foundation and fine-tuned chat models
Touvron, H., Martin, L., Stone, K., Albert, P., Almahairi, A., Babaei, Y., et al · 2023
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Can transformers learn the greatest common divisor?
Charton, F · 2024
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An efficient algorithm for integer lattice reduction
Charton, F., Lauter, K., Li, C., and Tygert, M · 2024
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