Investigation of the k-dimensionality of the LILI-128 cipher Boolean function
DOI:
https://doi.org/10.30837/rt.2018.4.195.14Keywords:
cryptographic properties of boolean functions, -dimensional function, probabilistic algorithm, improved -dimensional test, LILI-128 cipherAbstract
The paper presents results of the experimental study of the k-dimensionality of the LILI-128 cipher Boolean function, which demonstrated the potential for the realization of a statistical attack based on near-proximity of Boolean functions with algebraically degenerate functions.References
Dinur I. Cube attacks on tweakable black box polynomials / I. Dinur, A. Shamir // Advances in Cryptology. – EUROCRYPT’09. Proceedings. Springer-Verlag, 2009. – P. 278–299.
Fischer S. Chosen IV statistical analysis for key recovery attacks on stream ciphers / S. Fischer, S. Khazaei, W. Meier // AFRICACRYPT 2008. Proceedings. Springer-Verlag, 2008. – P. 236–245.
Aumasson J.-Ph. Efficient FPGA implementations of high-dimensional cube testers on the stream cipher Grain-128 / J.-Ph. Aumasson, I. Dinur, L. Hensen, W. Meier, A. Shamir // Cryptology ePrint Archive. – URL: http://eprint.iacr.org/2009/218 (last access: 29.10.18).
Aumasson J.-Ph. Cube testers and key recovery attacks on reduced-raund MD6 and Trivium / J.-Ph. Aumasson, I. Dinur, W. Meier, A. Shamir // Fast Software Encryption – FSE’09. Proceedings. Springer-Verlag. 2009. – P. 1–22.
Aumasson J.-Ph. New features of latin dances: analysis of Salsa, ChaCha, and Rumba / J.-Ph. Aumasson, S. Fischer, S. Khazaei, W. Meier, C. Rechberger // Fast Softvare Encryption – FSE 2008, Proceedings. Springer-Verlag. 2008. – P. 470–488.
Dinur I. An experimentally verified attack on full Grain-128 using dedicated reconfigurable hardware / I. Dinur, T. Gueysu, C. Paar, A. Shamir, R. Zimmermann // Cryptology ePrint Archive. – URL: http://eprint.iacr.org/2011/282 (last access: 29.10.18).
Dinur I. Breaking Grain-128 with dynamic cube attacks / I. Dinur, A. Shamir // Fast Software Encryption – FSE’11. Proceedings. Springer-Verlag. 2011. – P. 167–187.
Faisal Sh. Extended cubes: enhancing cube attacks by low-degree non-linear equations / Sh. Faisal, M. Resa, W. Susilo, J. Seberry // Proc. of the 6-th ACM Symp. on Information, Comput. and Communication Security (AIACCS’11). 2011. – P. 296 – 305.
Алексейчук А.Н. Обобщенная статистическая атака на синхронные поточные шифры / А.Н. Алексейчук, С.Н. Конюшок, А.Ю. Сторожук // Захист інформації. – 2015. – Т. 17. – № 3. – С. 54 – 65.
Алексейчук А.Н. Статистическая атака на генератор гаммы с линейным законом реинициализации начального состояния и функцией усложнения, близкой к алгебраически вырожденной / А.Н. Алексейчук, С.Н. Конюшок, А.Ю. Сторожук // Радиотехника. – 2014. – Вып. 176. – С. 13–21.
Алексейчук А.Н. Алгебраически вырожденные приближения булевых функций / А.Н. Алексейчук, С.Н. Конюшок // Кибернетика и системный анализ. – 2014. – Т. 50. – № 6. – С. 3–14.
Олексійчук А.М. Швидкі алгоритми побудови k-вимірних наближень наближень булевих функцій / А.М. Олексійчук, С.М. Конюшок, А.Ю. Сторожук // Захист інформації. – 2015. – Т. 17. – № 1. – С. 43–52.
Алексейчук А.Н. Усовершенствованный тест k-мерности для булевых функций / А.Н. Алексейчук, С.Н. Конюшок // Кибернетика и системный анализ. – 2013. – Т. 49. – № 2. – С. 27 – 35.
Lechner, R. L. Harmonic analysis of switching functions / R.L. Lechner // Recent Developments in Switching Theory. – New-York. Academic Press, 1971. – P. 122–228.
Dawson E. Construction of correlation immune Boolean functions / E. Dawson, C.K. Wu // Information and Communication Security, Proceedings. Berlin. Springer-Verlag, 1997. – P. 170–180.
Алексеев, Е.К. О некоторых мерах нелинейности булевых функций // Прикладная дискретная математика. – 2011. – № 2(12). – С. 5–16.
Gopalan P. Testing Fourier dimensionality and sparsity / P. Gopalan, R. O’Donnell, A. Servedio, A. Shpilka, K. Wimmer // SIAM J. on Computing. – 2011. – Vol. 40(4). – P. 1075 – 1100.
Golic J., Morgari G. On the resynchronization attack // Fast Software Encryption. – FSE’03, Proceedings. – Springer-Verlag, 2003. – P. 100 – 110.
Алексеев Е.К. О некоторых мерах нелинейности булевых функций // Прикладная дискретная математика. – 2011. – № 2(12). – С. 5 – 16.
Алексеев Е.К. Об атаке на фильтрующий генератор с функцией усложнения, близкой к алгебраически вырожденной // Материалы Шестой междунар. науч. конф. по проблемам безопасности и противодействия терроризму, 11 – 12 ноября 2010 г., Том 2. – Москва : МЦНМО, 2011. – С. 114 – 122.
Логачев О.А. Булевы функции в теории кодирования и криптологии / О.А. Логачев, А.А. Сальников, В.В. Ященко. – Москва : МЦНМО, 2004. – 470 с.
Simpson L.R. LILI Keystream Generator / L.R. Simpson, E. Dawson, J.D. Golić, W.L. Millan // Selected Areas in Cryptography. – SAC 2000. Lecture Notes in Computer Science, vol 2012. – Springer, Berlin, Heidelberg. – P. 248 – 261.
NESSIE New European Schemes for Signatures, Integrity, and Encryption // URL: https://www.cosic.esat.kuleuven.be/nessie/ (last access: 29.10.18).
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