Paper 2023/1242
Cascading Four Round LRW1 is Beyond Birthday Bound Secure
Abstract
In CRYPTO'02, Liskov et al. have introduced a new symmetric key primitive called tweakable block cipher. They have proposed two constructions of designing a tweakable block cipher from block ciphers. The first proposed construction is called $\mathsf{LRW1}$ and the second proposed construction is called $\mathsf{LRW2}$. Although, $\mathsf{LRW2}$ has been extended in later works to provide beyond birthday bound security (e.g., cascaded $\mathsf{LRW2}$ in CRYPTO'12 by Landecker et al.), but extension of the $\mathsf{LRW1}$ has received no attention until the work of Bao et al. in EUROCRYPT'20, where the authors have shown that one round extension of $\mathsf{LRW1}$, i.e., masking the output of $\mathsf{LRW1}$ with the given tweak and then re-encrypting it with the same block cipher, gives security up to $2^{2n/3}$ queries. Recently, Khairallah has shown a birthday bound distinguishing attack on the construction and hence invalidated the security claim of Bao et al. This has led to the open research question, that {\em how many round are required for cascading $\mathsf{LRW1}$ to achieve beyond birthday bound security ?} In this paper, we have shown that cascading $\mathsf{LRW1}$ up to four rounds is sufficient for ensuring beyond the birthday bound security. In particular, we have shown that $\mathsf{CLRW1}^4$ provides security up to $2^{3n/4}$ queries. Security analysis of our construction is based on the recent development of the mirror theory technique for tweakable random permutations under the framework of the Expectation Method.
Note: The previous version of this work provides $2n/3$-bit security of $\mathsf{CLRW1}^4$. In this version, we have improved the security up to $3n/4$-bit.
Metadata
- Available format(s)
-
PDF
- Category
- Secret-key cryptography
- Publication info
- Preprint.
- Keywords
- Tweakable Block CipherMirror TheoryBlock CipherExpectation Method$\mathsf{TNT}$
- Contact author(s)
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nilanjan datta @ tcgcrest org
exhilarant shreya dey @ gmail com
avirocks dutta13 @ gmail com
sougatamandal2014 @ gmail com - History
- 2023-08-24: revised
- 2023-08-16: received
- See all versions
- Short URL
- https://ia.cr/2023/1242
- License
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CC0
BibTeX
@misc{cryptoeprint:2023/1242, author = {Nilanjan Datta and Shreya Dey and Avijit Dutta and Sougata Mandal}, title = {Cascading Four Round {LRW1} is Beyond Birthday Bound Secure}, howpublished = {Cryptology {ePrint} Archive, Paper 2023/1242}, year = {2023}, url = {https://eprint.iacr.org/2023/1242} }