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On the lower bound of cost of MDS matrices
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Venkateswarlu, Ayineedi, Kesarwani, Abhishek and Sarkar, Sumanta (2022) On the lower bound of cost of MDS matrices. IACR Transactions on Symmetric Cryptology, 2022 (4). pp. 266-290. doi:10.46586/tosc.v2022.i4.266-290 ISSN 2519-173X.
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Official URL: http://dx.doi.org/10.46586/tosc.v2022.i4.266-290
Abstract
Ever since lightweight cryptography emerged as one of the trending topics in symmetric key cryptography, optimizing the implementation cost of MDS matrices has been in the center of attention. In this direction, various metrics like d-XOR, s-XOR and g-XOR have been proposed to mimic the hardware cost. Consequently, efforts also have been made to search for the optimal MDS matrices for dimensions relevant to cryptographic applications according to these metrics. However, finding the optimal MDS matrix in terms of hardware cost still remains an unsolved problem. In this paper, we settle the question of the optimal 4 x 4 MDS matrices over GL(n, F2) under the recently proposed metric sequential XOR count based on words (sw-XOR). We prove that the sw-XOR of such matrices is at least 8n + 3, and the bound is tight as matrices with sw-XOR cost 35 and 67 for the values of n = 4 and 8, respectively, were already known. Moreover, the lower bound for these values of n matches with the known lower bounds according to s-XOR and g-XOR metrics.
Item Type: | Journal Article | ||||||
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Subjects: | Q Science > QA Mathematics > QA76 Electronic computers. Computer science. Computer software | ||||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Computer Science | ||||||
Library of Congress Subject Headings (LCSH): | Data encryption (Computer science) , Cryptography, Computer security -- Mathematics, Computer algorithms | ||||||
Journal or Publication Title: | IACR Transactions on Symmetric Cryptology | ||||||
Publisher: | Ruhr-Universitaet Bochum | ||||||
ISSN: | 2519-173X | ||||||
Official Date: | 7 December 2022 | ||||||
Dates: |
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Volume: | 2022 | ||||||
Number: | 4 | ||||||
Page Range: | pp. 266-290 | ||||||
DOI: | 10.46586/tosc.v2022.i4.266-290 | ||||||
Status: | Peer Reviewed | ||||||
Publication Status: | Published | ||||||
Access rights to Published version: | Open Access (Creative Commons) | ||||||
Date of first compliant deposit: | 3 January 2023 | ||||||
Date of first compliant Open Access: | 4 January 2023 |
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