Geodesic
Diffusion properties of generalized quasi-Hadamard transformations on finite Abelian groups
Prikladnaya Diskretnaya Matematika. Supplement, no. 15 (2022), pp. 14-17.

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In this paper, we introduce a generalization of quasi-Hadamard transformations on a finite abelian group $X$. For $X = \mathbb{Z}_{2^m}$, it includes the pseudo-Hadamard transformation employed in block ciphers Safer and Twofish, and the quasi-Hadamard transformations proposed by H. Lipmaa. For bijective generalized quasi-Hadamard transformations, we describe diffusion properties of imprimitivity systems of regular permutation representations of additive groups $\mathbb{Z}_{2^m}^2$ and $\mathbb{Z}_{2^{2m}}$. We describe a set of generalized quasi-Hadamard transformations having the best diffusion properties of the imprimitivity systems. We also give conditions such that some generalized quasi-Hadamard transformations have bad diffusion properties.
Keywords: Safer block cipher family, Twofish block cipher, imprimitivity system, regular permutation representation, primitive group.
Mots-clés : pseudo-Hadamard transformation, quasi-Hadamard transformation 
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B. A. Pogorelov; M. A. Pudovkina. Diffusion properties of generalized quasi-Hadamard transformations on finite Abelian groups. Prikladnaya Diskretnaya Matematika. Supplement, no. 15 (2022), pp. 14-17. http://geodesic.mathdoc.fr/item/PDMA_2022_15_a3/

[1] Massey J. L., “SAFER K-64: a byte-oriented block-ciphering algorithm”, FSE 1994, LNCS, 1267, 1994, 1–17

[2] Hong D., Sung J., Hong S., et al., “A new block cipher suitable for low-resource device”, CHES 2006, LNCS, 4249, 2006, 46–59 | Zbl

[3] Stern J. and Vaudenay S., “CS-Cipher”, FSE 1998, LNCS, 1372, 1998, 189–204 | Zbl

[4] Zheng Y., “The SPEED cipher”, Financial Cryptography, LNCS, 1318, 1997, 71–89

[5] Lipmaa H., “On differential properties of pseudo-Hadamard transform and related mappings”, INDOCRYPT 2002, LNCS, 2551, 2002, 48–61 | Zbl

[6] St Denis T., Fast Pseudo-Hadamard Transforms, Cryptology Archive, Report 2004/010, , 2004 https://eprint.iacr.org/2004/010.pdf

[7] Schnorr C.-P., “FFT-Hash II, efficient cryptographic hashing”, EUROCRYPT'92, LNCS, 658, 1992, 45–54 | MR

[8] Massey J., Khachatrian G., and Kuregian M., Nomination of SAFER+ as Candidate Algorithm for the Advanced Encryption Standard (AES), NIST AES Proposal, 1998 http://www.princeton.edu/r̃blee/safer+/

[9] Massey J., Khachatrian G., and Kuregian M., Nomination of SAFER++ as Candidate Algorithm for NESSIE, 2003 https://www.cosic.esat.kuleuven.be/nessie/workshop/submissions/safer++.zip

[10] Schneier B., Kelsey J., Whiting D., et al., The Twofish Encryption Algorithm: A 128-Bit Block Cipher, John Wiley Sons, N.Y., 1999

[11] Pogorelov B. A., Pudovkina M. A., “O rasstoyaniyakh ot podstanovok do imprimitivnykh grupp pri fiksirovannoi sisteme imprimitivnosti”, Diskretnaya matematika, 25:3 (2013), 78–95