Abstract
ARX-based crypto-designs are gaining popularity nowadays because of their simplicity and efficiency. Rotation-based diffusion functions are used as building blocks in such designs. Invertibility or bijectivity of a diffusion function is a foremost requirement for the crypto-designs. In this paper, we analyse this aspect of diffusion functions. We consider a class of rotation-based linear diffusion functions and derive a necessary condition under which a diffusion function of this class is invertible. Further, we find a particular case where this necessary condition is sufficient also.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
C.E. Shannon, Communication theory of secrecy systems. Bell Syst. Tech. J. 28(4), 656–715 (1949)
R.P. Weinmann, AXR—crypto made from modular additions, XORs and word rotations, in Dagstuhl Seminar 09031 (2009). http://www.dagstuhl.de/Materials/AbstractListing/index.en.phtml?09031
D. Khovratovich, I. Nikolic, I., Rotational cryptanalysis of ARX. Fast software encryption, in LNCS, 6147, pp. 333–346 (2010). https://doi.org/10.1007/978-3-642-13858-4-19.
A. himizu, S. Miyaguchi, Fast data encipherment algorithm FEAL, in EUROCRYPT, ed. by D. Chaum, W.L. Price. Lecture Notes in Computer Science, vol. 304, pp. 267–278. Springer (1987)
M. Matsui, A. Yamagishi, A new method for known plaintext attack of FEAL Cipher, in EUROCRYPT, pp. 81–91 (1992)
L.C. Guillou, J.-J. Quisquater, Advances in Cryptology EUROCRYPT 95: International Conference
D.J. Bernstein, Salsa20 specification. http://cr.yp.to/snuffle/spec.pdf (April 2005)
D.J. Bernstein, Salsa20/8 and Salsa20/12. http://cr.yp.to/snuffle/812.pdf (February 2006)
Babbage et al., The eSTREAM Portfolio. [Online]. Available http://ecrypt.eu.org/stvl/ (April, 2008)
J.P. Aumasson, S. Fischer, S. Khazaei, W. Meier, C. Rechberger, New Features of Latin Dances: Analysis of Salsa, ChaCha, and Rumba, ed. by Nyberg, pp. 470–488
“Chacha, a variant of salsa20”, (2008). [Online]. Available http://cr.yp.to/papers.html#chacha
H. Wu, The stream cipher HC-128, in New Stream Cipher Designs, Lecture Notes in Computer Science, vol. 4986 (Springer, Berlin, 2008), pp. 39–47
A. Kumar, S.K. Pal, O. Ojella, A heuristic approach towards variability of HC-128. J. Discrete Math. Sci. Crypt. ISSN 2169-0065 (Online) (April, 2019). https://doi.org/10.1080/09720529.2019.1569834.
R.L. Rivest, The MD6 hash function—a proposal to NIST for SHA-3. Submission to the NIST SHA-3 Competition (Round 1) (2008)
A. Biryukov, I. Nikolic, A. Roy, Boomerang attacks on BLAKE-32, in FSE, ed. by A. Joux, Lecture Notes in Computer Science, vol. 6733 (Springer, Berlin, 2011), pp. 218–237
J.P. Aumasson, C. Calik, W. Meier, O. Ozen, C. Raphael, W. Phan, K. Varici, Improved cryptanalysis of skein, in ASIACRYPT, ed. by M. Matsui, Lecture Notes in Computer Science, vol. 5912 (Springer, Berlin, 2009), pp. 542–559
D.J. Bernstein, Cubehash. Submission to NIST, Round 2 (2009)
M. Kumar, D. Dey, S.K. Pal, A. Panigrahi, HeW: a Hash Function based on lightweight Block cipher FeW. Defence Sci. J. 67(6), 636–644 (2017). https://doi.org/10.14429/dsj.67.10791
D. Gligoroski, H. Mihajloska, S. Samardjiska, J. Jacobsen, M. El-Hadedy, R.E. Jensen, \(\pi \)- cipher v2, Cryptographic competitions: CAESAR (2014). http://competitions.cr.yp.to/round1/picipherv2.pdf
C. Chaigneau, T. Fuhr, H. Gilbert, J. Jean, J.R. Reinhard, Cryptanalysis of NORX v2. IACR Trans. Symmetric Cryptology, pp. 156–174 (2017). https://doi.org/10.13154/tosc.v2017.i1.156-174
Cryptanalysis of MORUS—Cryptology ePrint Archive—IACR (2018). https://eprint.iacr.org/2018/464.pdf
P.J. Davis, Circulant matrices (Wiley, New York, 1970). ISBN 0471057711
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2020 Springer Nature Singapore Pte Ltd.
About this paper
Cite this paper
Kumar, A., Mishra, P.R., Ojjela, O. (2020). Analysis of Rotation-Based Diffusion Functions. In: Nagar, A., Deep, K., Bansal, J., Das, K. (eds) Soft Computing for Problem Solving 2019 . Advances in Intelligent Systems and Computing, vol 1138. Springer, Singapore. https://doi.org/10.1007/978-981-15-3290-0_17
Download citation
DOI: https://doi.org/10.1007/978-981-15-3290-0_17
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-15-3289-4
Online ISBN: 978-981-15-3290-0
eBook Packages: Intelligent Technologies and RoboticsIntelligent Technologies and Robotics (R0)