Security estimates of the NTRUCipher and NTRUCipher+ encryption schemes against BKW-attack

Fìz.-mat. model. ìnf. tehnol. 2021, 33:28-32

Abstract

Due to the need of creation a symmetric encryption scheme for practical usage, the security of which (similarly to asymmetric cryptosystems) is based on the difficulty of solving only one computational problem, in 2017 the NTRUCipher encryption scheme was proposed. Preliminary researches of this encryption scheme have been conducted, but the question of NTRUCipher’s security to certain specific attacks is open. This article provides estimates of the complexity of chosen-plaintext attack on the NTRUCipher encryption scheme and even on its natural improvement NTRUCipher+. The given analytical estimates allow to compare the security of these encryption schemes and to make a conclusion about inexpediency of usage the NTRUCipher+ encryption scheme for its increase.

References

1. Valluri, M. R. (2017). “NTRUCipher-lattice based secret key encryption”, in World Congress on Internet Security, UK, 2017. [Online]. Available: arXiv:1710.01928V2. 6/10/2017.
2. Hoffstein, J., Pipher, J., Silverman, J. H. (1998). “NTRU: a new high speed public key cryptosystem“, Algorithmic Number Theory (ANTS III). LNCS, 1423, 267–288.
   DOI https://doi.org/10.1007/bfb0054868
3. Matiyko, A. A. (2019). “The comparative analysis of NTRUCipher and NTRUEncrypt encryption schemes”, Mathimatical and computer modelling. Series: Technical science, 19, 81–87. (in Ukrainian).
   DOI https://doi.org/10.32626/2308-5916.2019-19.81-87
4. Stehle, D., Steinfeld, R. (2011). “Making NTRU as secure as worst-case problems over ideal lattices”, in Advances in Cryptology – EUROCRYPT 2011, Tallin, Estonia.
   DOI https://doi.org/10.1007/978-3-642-20465-4_4
5. Blum, A., Kalai, A., Wasserman, H. (2003). “Noise-tolerant learning, the parity problem, and the statistical query model”, Journal of the ACM, 50(3), 506–519.
   DOI https://doi.org/10.1145/792538.792543
6. Alekseychuk, A. N., Ignatenko, S. M., Poremskyi, M. V. (2017). “Systems of linear equations corrupted by noise over arbitrary finite rings” Mathematical and Computer Modelling, ser. Technical Sciences, 15, 150–155. (in Ukrainian).