2024 • In Joye, Marc (Ed.) Advances in Cryptology – EUROCRYPT 2024 - 43rd Annual International Conference on the Theory and Applications of Cryptographic Techniques, Proceedings
Block ciphers; Feistel ciphers; Generalized feistel; Generalized Feistel structure; In contexts; Lower noise; Non linear; Prime field; Side-channel attacks; Square operations; Theoretical Computer Science; Computer Science (all)
Résumé :
[en] A recent work from Eurocrypt 2023 suggests that prime-field masking has excellent potential to improve the efficiency vs. security tradeoff of masked implementations against side-channel attacks, especially in contexts where physical leakages show low noise. We pick up on the main open challenge that this seed result leads to, namely the design of an optimized prime cipher able to take advantage of this potential. Given the interest of tweakable block ciphers with cheap inverses in many leakage-resistant designs, we start by describing the FPM (Feistel for Prime Masking) family of tweakable block ciphers based on a generalized Feistel structure. We then propose a first instantiation of FPM, which we denote as small-pSquare. It builds on the recent observation that the square operation (which is non-linear in Fp) can lead to masked gadgets that are more efficient than those for multiplication, and is tailored for efficient masked implementations in hardware. We analyze the mathematical security of the FPM family of ciphers and the small-pSquare instance, trying to isolate the parts of our study that can be re-used for other instances. We additionally evaluate the implementation features of small-pSquare by comparing the efficiency vs. security tradeoff of masked FPGA circuits against those of a state-of-the art binary cipher, namely SKINNY, confirming significant gains in relevant contexts.
Disciplines :
Sciences informatiques
Auteur, co-auteur :
Grassi, Lorenzo; Ruhr University Bochum, Bochum, Germany
Masure, Loïc; LIRMM, Univ. Montpellier, CNRS, Montpellier, France
MEAUX, Pierrick ; University of Luxembourg > Interdisciplinary Centre for Security, Reliability and Trust (SNT) > PI Coron
Moos, Thorben; Crypto Group, ICTEAM Institute, UCLouvain, Louvain-la-Neuve, Belgium
Standaert, François-Xavier; Crypto Group, ICTEAM Institute, UCLouvain, Louvain-la-Neuve, Belgium
Co-auteurs externes :
yes
Langue du document :
Anglais
Titre :
Generalized Feistel Ciphers for Efficient Prime Field Masking
Date de publication/diffusion :
2024
Nom de la manifestation :
Eurocrypt
Lieu de la manifestation :
Zurich, Che
Date de la manifestation :
26-05-2024 => 30-05-2024
Titre de l'ouvrage principal :
Advances in Cryptology – EUROCRYPT 2024 - 43rd Annual International Conference on the Theory and Applications of Cryptographic Techniques, Proceedings
Editeur scientifique :
Joye, Marc
Maison d'édition :
Springer Science and Business Media Deutschland GmbH
Lorenzo Grassi was supported by the German Research Foundation (DFG) within the framework of the Excellence Strategy of the Federal Government and the States \u2013 EXC 2092 CaSa \u2013 39078197. Pierrick Méaux was supported by the ERC Advanced Grant 787390. Fran\u00E7ois-Xavier Standaert is a senior research associate of the Belgian Fund for Scientific Research (FNRS-F.R.S.). This work has been funded in parts by the ERC Advanced Grant 101096871. Views and opinions expressed are those of the authors only and do not necessarily reflect those of the European Union or the ERC. Neither the European Union nor the granting authority can be held responsible for them.
Albrecht, M.R., et al.: Feistel structures for MPC, and more. In: Sako, K., Schneider, S., Ryan, P.Y.A. (eds.) ESORICS 2019. LNCS, vol. 11736, pp. 151–171. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-29962-0 8
Albrecht, M., Grassi, L., Rechberger, C., Roy, A., Tiessen, T.: MiMC: efficient encryption and cryptographic hashing with minimal multiplicative complexity. In: Cheon, J.H., Takagi, T. (eds.) ASIACRYPT 2016. LNCS, vol. 10031, pp. 191–219. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-53887-6 7
Aly, A., Ashur, T., Ben-Sasson, E., Dhooghe, S., Szepieniec, A.: Design of symmetric-key primitives for advanced cryptographic protocols. IACR Trans. Symmetric Cryptol. 2020(3), 1–45 (2020)
Balasch, J., Faust, S., Gierlichs, B., Verbauwhede, I.: Theory and practice of a leakage resilient masking scheme. In: Wang, X., Sako, K. (eds.) ASIACRYPT 2012. LNCS, vol. 7658, pp. 758–775. Springer, Heidelberg (2012). https://doi.org/10. 1007/978-3-642-34961-4 45
Battistello, A., Coron, J.-S., Prouff, E., Zeitoun, R.: Horizontal side-channel attacks and countermeasures on the ISW masking scheme. In: Gierlichs, B., Poschmann, A.Y. (eds.) CHES 2016. LNCS, vol. 9813, pp. 23–39. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-53140-2 2
Beierle, C., et al.: The SKINNY family of block ciphers and its low-latency variant MANTIS. In: Robshaw, M., Katz, J. (eds.) CRYPTO 2016. LNCS, vol. 9815, pp. 123–153. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-53008-5 5
Bellizia, D., et al.: Mode-Level vs. implementation-level physical security in symmetric cryptography. In: Micciancio, D., Ristenpart, T. (eds.) CRYPTO 2020. LNCS, vol. 12170, pp. 369–400. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-56784-2 13
Berger, T.P., Minier, M., Thomas, G.: Extended generalized Feistel networks using matrix representation. In: Lange, T., Lauter, K., Lisoněk, P. (eds.) SAC 2013. LNCS, vol. 8282, pp. 289–305. Springer, Heidelberg (2014). https://doi.org/10. 1007/978-3-662-43414-7 15
Berti, F., Guo, C., Pereira, O., Peters, T., Standaert, F.-X.: TEDT, a leakage-resist AEAD mode for high physical security applications. IACR Trans. Cryptogr. Hardw. Embed. Syst. 2020(1), 256–320 (2020)
Berti, F., Guo, C., Peters, T., Standaert, F.-X.: Efficient leakage-resilient MACs without idealized assumptions. In: Tibouchi, M., Wang, H. (eds.) ASIACRYPT 2021. LNCS, vol. 13091, pp. 95–123. Springer, Cham (2021). https://doi.org/10. 1007/978-3-030-92075-3 4
Bertoni, G., Daemen, J., Peeters, M., Van Assche, G.: On the indifferentiability of the sponge construction. In: Smart, N. (ed.) EUROCRYPT 2008. LNCS, vol. 4965, pp. 181–197. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-78967-3 11
Bertoni, G., Daemen, J., Peeters, M., Van Assche, G.: Duplexing the sponge: single-pass authenticated encryption and other applications. In: Miri, A., Vaudenay, S. (eds.) SAC 2011. LNCS, vol. 7118, pp. 320–337. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-28496-0 19
Biham, E.: New types of cryptanalytic attacks using related keys. J. Cryptol. 7(4), 229–246 (1994). https://doi.org/10.1007/BF00203965
Biham, E.: A fast new DES implementation in software. In: Biham, E. (ed.) FSE 1997. LNCS, vol. 1267, pp. 260–272. Springer, Heidelberg (1997). https://doi.org/10.1007/BFb0052352
Biham, E., Biryukov, A., Shamir, A.: Cryptanalysis of skipjack reduced to 31 rounds using impossible differentials. In: Stern, J. (ed.) EUROCRYPT 1999. LNCS, vol. 1592, pp. 12–23. Springer, Heidelberg (1999). https://doi.org/10.1007/3-540-48910-X 2
Biham, E., Shamir, A.: Differential cryptanalysis of DES-like cryptosystems. J. Cryptol. 4(1), 3–72 (1991). https://doi.org/10.1007/BF00630563
Biham, E., Shamir, A.: Differential Cryptanalysis of the Data Encryption Standard. Springer (1993). https://doi.org/10.1007/978-1-4613-9314-6
Biryukov, A., Wagner, D.: Slide attacks. In: Knudsen, L. (ed.) FSE 1999. LNCS, vol. 1636, pp. 245–259. Springer, Heidelberg (1999). https://doi.org/10.1007/3-540-48519-8 18
Biryukov, A., Wagner, D.: Advanced slide attacks. In: Preneel, B. (ed.) EURO-CRYPT 2000. LNCS, vol. 1807, pp. 589–606. Springer, Heidelberg (2000). https://doi.org/10.1007/3-540-45539-6 41
Borghoff, J., et al.: PRINCE – a low-latency block cipher for pervasive computing applications. In: Wang, X., Sako, K. (eds.) ASIACRYPT 2012. LNCS, vol. 7658, pp. 208–225. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-34961-4 14
Božilov, D., et al.: PRINCEv2. In: Dunkelman, O., Jacobson, Jr., M.J., O’Flynn, C. (eds.) SAC 2020. LNCS, vol. 12804, pp. 483–511. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-81652-0 19
Bronchain, O., Standaert, F.-X.: Breaking masked implementations with many shares on 32-bit software platforms or when the security order does not matter. IACR Trans. Cryptogr. Hardw. Embed. Syst. 2021(3), 202–234 (2021)
Cassiers, G., Bronchain, O.: Scalib: a side-channel analysis library. J. Open Source Softw. 8(86), 5196 (2023)
Cassiers, G., Grégoire, B., Levi, I., Standaert, F.-X.: Hardware private circuits: from trivial composition to full verification. IEEE Trans. Comput. 70(10) (2021)
Cassiers, G., Masure, L., Momin, C., Moos, T., Standaert, F.-X.: Prime-Field masking in hardware and its soundness against low-noise SCA attacks. IACR Trans. Cryptogr. Hardw. Embed. Syst. 2023(2), 482–518 (2023)
Cauchois, V., Gomez, C., Thomas, G.: General diffusion analysis: how to find optimal permutations for generalized Type-II Feistel schemes. IACR Trans. Symmetric Cryptol. 2019(1)
Chari, S., Jutla, C.S., Rao, J.R., Rohatgi, P.: Towards sound approaches to counteract power-analysis attacks. In: Wiener, M. (ed.) CRYPTO 1999. LNCS, vol. 1666, pp. 398–412. Springer, Heidelberg (1999). https://doi.org/10.1007/3-540-48405-1 26
Cho, J., et al.: Transciphering framework for approximate homomorphic encryption. In: Tibouchi, M., Wang, H. (eds.) ASIACRYPT 2021. LNCS, vol. 13092, pp. 640–669. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-92078-4 22
Courtois, N., Klimov, A., Patarin, J., Shamir, A.: Efficient algorithms for solving overdefined systems of multivariate polynomial equations. In: Preneel, B. (ed.) EUROCRYPT 2000. LNCS, vol. 1807, pp. 392–407. Springer, Heidelberg (2000). https://doi.org/10.1007/3-540-45539-6 27
Daemen, J., Peeters, M., Van Assche, G., Rijmen, V.: Nessie Proposal: NOEKEON. In: First Open NESSIE Workshop (2000)
Daemen, J., Rijmen, V.: The wide trail design strategy. In: Honary, B. (ed.) Cryptography and Coding 2001. LNCS, vol. 2260, pp. 222–238. Springer, Heidelberg (2001). https://doi.org/10.1007/3-540-45325-3 20
Daemen, J., Rijmen, V.: Security of a wide trail design. In: Menezes, A., Sarkar, P. (eds.) INDOCRYPT 2002. LNCS, vol. 2551, pp. 1–11. Springer, Heidelberg (2002). https://doi.org/10.1007/3-540-36231-2 1
Dobraunig, C., Eichlseder, M., Mendel, F., Schläffer, M.: Ascon v1.2: lightweight authenticated encryption and hashing. J. Cryptol. 34(3), 1–42 (2021). https://doi. org/10.1007/s00145-021-09398-9
Dobraunig, C., Grassi, L., Guinet, A., Kuijsters, D.: Ciminion: symmetric encryption based on Toffoli-gates over large finite fields. In: Canteaut, A., Standaert, F.-X. (eds.) EUROCRYPT 2021. LNCS, vol. 12697, pp. 3–34. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-77886-6 1
Duc, A., Dziembowski, S., Faust, S.: Unifying leakage models: from probing attacks to noisy leakage. In: Nguyen, P.Q., Oswald, E. (eds.) EUROCRYPT 2014. LNCS, vol. 8441, pp. 423–440. Springer, Heidelberg (2014). https://doi.org/10.1007/978-3-642-55220-5 24
Duc, A., Faust, S., Standaert, F.-X.: Making masking security proofs concrete. In: Oswald, E., Fischlin, M. (eds.) EUROCRYPT 2015. LNCS, vol. 9056, pp. 401–429. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-46800-5 16
Dziembowski, S., Faust, S.: Leakage-resilient cryptography from the inner-product extractor. In: Lee, D.H., Wang, X. (eds.) ASIACRYPT 2011. LNCS, vol. 7073, pp. 702–721. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-25385-0 38
Dziembowski, S., Faust, S., Skórski, M.: Optimal amplification of noisy leakages. In: Kushilevitz, E., Malkin, T. (eds.) TCC 2016. LNCS, vol. 9563, pp. 291–318. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-49099-0 11
Fumaroli, G., Martinelli, A., Prouff, E., Rivain, M.: Affine masking against higher-order side channel analysis. In: Biryukov, A., Gong, G., Stinson, D.R. (eds.) SAC 2010. LNCS, vol. 6544, pp. 262–280. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-19574-7 18
Golić, J.D., Tymen, C.: Multiplicative masking and power analysis of AES. In: Kaliski, B.S., Koç, K., Paar, C. (eds.) CHES 2002. LNCS, vol. 2523, pp. 198–212. Springer, Heidelberg (2003). https://doi.org/10.1007/3-540-36400-5 16
Goudarzi, D., Rivain, M.: How fast can higher-order masking be in software? In: Coron, J.-S., Nielsen, J.B. (eds.) EUROCRYPT 2017. LNCS, vol. 10210, pp. 567– 597. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-56620-7 20
Grassi, L.: On generalizations of the Lai-Massey scheme. Cryptology ePrint Archive, Paper 2022/1245 (2022). https://eprint.iacr.org/2022/1245
Keller, N., Rosemarin, A.: Mind the middle layer: the HADES design strategy revisited. In: Canteaut, A., Standaert, F.-X. (eds.) EUROCRYPT 2021. LNCS, vol. 12697, pp. 35–63. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-77886-6 2
Grassi, L., Masure, L., Méaux, P., Moos, T., Standaert, F.-X.: Generalized feistel ciphers for efficient prime field masking-full version. Cryptology ePrint Archive (2024)
Grassi, L., Rechberger, C., Rønjom, S.: Subspace trail cryptanalysis and its applications to AES. IACR Trans. Symmetric Cryptol. 2016(2)
Gross, H., Mangard, S., Korak, T.: An efficient side-channel protected AES implementation with arbitrary protection order. In: Handschuh, H. (ed.) CT-RSA 2017. LNCS, vol. 10159, pp. 95–112. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-52153-4 6
Guo, J., Peyrin, T., Poschmann, A., Robshaw, M.: The LED block cipher. In: Preneel, B., Takagi, T. (eds.) CHES 2011. LNCS, vol. 6917, pp. 326–341. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-23951-9 22
Hoang, V.T., Rogaway, P.: On generalized Feistel networks. In: Rabin, T. (ed.) CRYPTO 2010. LNCS, vol. 6223, pp. 613–630. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-14623-7 33
Hong, D., et al.: HIGHT: a new block cipher suitable for low-resource device. In: Goubin, L., Matsui, M. (eds.) CHES 2006. LNCS, vol. 4249, pp. 46–59. Springer, Heidelberg (2006). https://doi.org/10.1007/11894063 4
Ishai, Y., Sahai, A., Wagner, D.: Private circuits: securing hardware against probing attacks. In: Boneh, D. (ed.) CRYPTO 2003. LNCS, vol. 2729, pp. 463–481. Springer, Heidelberg (2003). https://doi.org/10.1007/978-3-540-45146-4 27
Jakobsen, T., Knudsen, L.R.: The interpolation attack on block ciphers. In: Biham, E. (ed.) FSE 1997. LNCS, vol. 1267, pp. 28–40. Springer, Heidelberg (1997). https://doi.org/10.1007/BFb0052332
Jean, J., Nikolić, I., Peyrin, T.: Tweaks and keys for block ciphers: the TWEAKEY framework. In: Sarkar, P., Iwata, T. (eds.) ASIACRYPT 2014. LNCS, vol. 8874, pp. 274–288. Springer, Heidelberg (2014). https://doi.org/10.1007/978-3-662-45608-8 15
Kerckhof, S., Durvaux, F., Hocquet, C., Bol, D., Standaert, F.-X.: Towards green cryptography: a comparison of lightweight ciphers from the energy viewpoint. In: Prouff, E., Schaumont, P. (eds.) CHES 2012. LNCS, vol. 7428, pp. 390–407. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-33027-8 23
Knichel, D., Moradi, A., Müller, N., Sasdrich, P.: Automated generation of masked hardware. IACR Trans. Cryptogr. Hardw. Embed. Syst. 2022(1)
Knudsen, L.R.: Truncated and higher order differentials. In: Preneel, B. (ed.) FSE 1994. LNCS, vol. 1008, pp. 196–211. Springer, Heidelberg (1995). https://doi.org/10.1007/3-540-60590-8 16
Kranz, T., Leander, G., Stoffelen, K., Wiemer, F.: Shorter Linear Straight-Line Programs for MDS Matrices. IACR Trans. Symmetric Cryptol. 2017(4), 188–211 (2017)
Lai, X.: Higher Order Derivatives and Differential Cryptanalysis. In: Blahut, R.E., Costello, D.J., Maurer, U., Mittelholzer, T. (eds.) Two Sides of One Tapestry, Communications and Cryptography, vol. 276. Springer, Boston, (1994). https://doi.org/10.1007/978-1-4615-2694-0 23
Lai, X., Massey, J.L.: A proposal for a new block encryption standard. In: Damgård, I.B. (ed.) EUROCRYPT 1990. LNCS, vol. 473, pp. 389–404. Springer, Heidelberg (1991). https://doi.org/10.1007/3-540-46877-3 35
Leander, G., Abdelraheem, M.A., AlKhzaimi, H., Zenner, E.: A cryptanalysis of PRINTcipher: the invariant subspace attack. In: Rogaway, P. (ed.) CRYPTO 2011. LNCS, vol. 6841, pp. 206–221. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-22792-9 12
Leander, G., Minaud, B., Rønjom, S.: A generic approach to invariant subspace attacks: cryptanalysis of robin, iSCREAM and Zorro. In: Oswald, E., Fischlin, M. (eds.) EUROCRYPT 2015. LNCS, vol. 9056, pp. 254–283. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-46800-5 11
Li, C., Wang, Q.: Design of lightweight linear diffusion layers from near-MDS matrices. IACR Trans. Symmetric Cryptol. 2017(1)
Liu, M., Sim, S.M.: Lightweight MDS generalized circulant matrices. In: Peyrin, T. (ed.) FSE 2016. LNCS, vol. 9783, pp. 101–120. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-52993-5 6
Masure, L., Méaux, P., Moos, T., Standaert, F.-X.: Effective and efficient masking with low noise using small-mersenne-prime ciphers. In: Hazay, C., Stam, M. (eds.) EUROCRYPT,vol. 14007. Springer, Cham (2023). https://doi.org/10.1007/978-3-031-30634-1 20
Matsui, M.: Linear cryptanalysis method for DES cipher. In: Helleseth, T. (ed.) EUROCRYPT 1993. LNCS, vol. 765, pp. 386–397. Springer, Heidelberg (1994). https://doi.org/10.1007/3-540-48285-7 33
Moos, T., Moradi, A., Richter, B.: Static power side-channel analysis of a threshold implementation prototype chip. In: Design, Automation & Test in Europe Conference & Exhibition (DATE), 2017 (2017)
Nagpal, R., Gigerl, B., Primas, R., Mangard, S.: Riding the waves towards generic single-cycle masking in hardware. IACR Trans. Cryptogr. Hardw. Embed. Syst. 4(2022)
Nyberg, K.: Generalized feistel networks. In: Kim, K., Matsumoto, T. (eds.) ASI-ACRYPT 1996. LNCS, vol. 1163, pp. 91–104. Springer, Heidelberg (1996). https://doi.org/10.1007/BFb0034838
Del Pozo, S.M., Standaert, F.-X., Kamel, D., Moradi, A.: Side-channel attacks from static power: when should we care?. In: DATE (2015)
Prouff, E., Rivain, M.: Masking against side-channel attacks: a formal security proof. In: Johansson, T., Nguyen, P.Q. (eds.) EUROCRYPT 2013. LNCS, vol. 7881, pp. 142–159. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-38348-9 9
Roche, T., Prouff, E.: Higher-order glitch free implementation of the AES using secure multi-party computation protocols-extended version. J. Cryptogr. Eng. 2(2), 111–127 (2012). https://doi.org/10.1007/s13389-012-0033-3
Sasdrich, P., Bilgin, B., Hutter, M., Marson, M.E.: Low-latency hardware masking with application to AES. IACR Trans. Cryptogr. Hardw. Embed. Syst. 2020(2), 300–326 (2020)
Schindler, W., Lemke, K., Paar, C.: A stochastic model for differential side channel cryptanalysis. In: Rao, J.R., Sunar, B. (eds.) CHES 2005. LNCS, vol. 3659, pp. 30–46. Springer, Heidelberg (2005). https://doi.org/10.1007/11545262 3
Shen, Y., Peters, T., Standaert, F.-X., Cassiers, G., Verhamme, C.: Triplex: an efficient and one-pass leakage-resistant mode of operation. IACR Trans. Cryptogr. Hardw. Embed. Syst. 2022(4), 135–162 (2022)
Shirai, T., Shibutani, K., Akishita, T., Moriai, S., Iwata, T.: The 128-Bit Block-cipher CLEFIA (extended abstract). In: Biryukov, A. (ed.) FSE 2007. LNCS, vol. 4593, pp. 181–195. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-74619-5 12
Standaert, F.-X.: How (not) to use Welch’s T-Test in side-channel security evaluations. In: Bilgin, B., Fischer, J.-B. (eds.) CARDIS 2018. LNCS, vol. 11389, pp. 65–79. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-15462-2 5
Standaert, F.-X., Archambeau, C.: Using subspace-based template attacks to compare and combine power and electromagnetic information leakages. In: Oswald, E., Rohatgi, P. (eds.) CHES 2008. LNCS, vol. 5154, pp. 411–425. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-85053-3 26
Standaert, F.-X., Piret, G., Rouvroy, G., Quisquater, J.-J.: FPGA implementations of the ICEBERG block cipher. Integration 40(1), 20–27 (2007)
Suzaki, T., Minematsu, K.: Improving the generalized feistel. In: Hong, S., Iwata, T. (eds.) FSE 2010. LNCS, vol. 6147, pp. 19–39. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-13858-4 2
Vaudenay, S.: On the Lai-Massey scheme. In: Lam, K.-Y., Okamoto, E., Xing, C. (eds.) ASIACRYPT 1999. LNCS, vol. 1716, pp. 8–19. Springer, Heidelberg (1999). https://doi.org/10.1007/978-3-540-48000-6 2
Verhamme, C., Cassiers, G., Standaert, F.X.: In: Buhan, I., Schneider, T. (eds.) Analyzing the Leakage Resistance of the NIST’s Lightweight Crypto Competition’s Finalists. CARDIS,vol. 13820. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-25319-5 15
Wagner, D.: The boomerang attack. In: Knudsen, L. (ed.) FSE 1999. LNCS, vol. 1636, pp. 156–170. Springer, Heidelberg (1999). https://doi.org/10.1007/3-540-48519-8 12
Wang, L., Guo, J., Zhang, G., Zhao, J., Gu, D.: How to build fully secure tweakable Blockciphers from classical Blockciphers. In: Cheon, J.H., Takagi, T. (eds.) ASIACRYPT 2016. LNCS, vol. 10031, pp. 455–483. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-53887-6 17
Wang, W., Méaux, P., Cassiers, G., Standaert, F.-X.: Efficient and private computations with code-based masking. IACR Trans. Cryptogr. Hardw. Embed. Syst. 2020(2), 128–171 (2020)
Zheng, Y., Matsumoto, T., Imai, H.: On the construction of block ciphers provably secure and not relying on any unproved hypotheses. In: Brassard, G. (ed.) CRYPTO 1989. LNCS, vol. 435, pp. 461–480. Springer, New York (1990). https://doi.org/10.1007/0-387-34805-0 42
