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Merkle Tree Ladder Mode: Reducing the Size Impact of NIST PQC Signature Algorithms in Practice

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Topics in Cryptology – CT-RSA 2023 (CT-RSA 2023)

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Abstract

We introduce the Merkle Tree Ladder (MTL) mode of operation for signature schemes. MTL mode signs messages using an underlying signature scheme in such a way that the resulting signatures are condensable: a set of MTL mode signatures can be conveyed from a signer to a verifier in fewer bits than if the MTL mode signatures were sent individually. In MTL mode, the signer sends a shorter condensed signature for each message of interest and occasionally provides a longer reference value that helps the verifier process the condensed signatures. We show that in a practical scenario involving random access to an initial series of \(10{,}000\) signatures that expands gradually over time, MTL mode can reduce the size impact of the NIST PQC signature algorithms, which have signature sizes of \(666\) to \(\mathrm{49,856}\) bytes with example parameters at various security levels, to a condensed signature size of 248 to 472 bytes depending on the selected security level. Even adding the overhead of the reference values, MTL mode signatures still reduce the overall signature size impact under a range of operational assumptions. Because MTL mode itself is quantum-safe, the mode can support long-term cryptographic resiliency in applications where signature size impact is a concern without limiting cryptographic diversity only to algorithms whose signatures are naturally short.

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Acknowledgments

We thank our Verisign colleagues for reviewing drafts of this paper and discussing its concepts, with particular appreciation to Duane Wessels for guidance on the selection of data sources for Section 7.3 and assistance with the data analysis. Thanks also to DNS-OARC for providing access to their data sets and servers. Finally, the paper would not have reached its final form without the improvements encouraged by the anonymous CT-RSA reviewers. We thank them for their generous commitment to the peer review process.

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  1. Verisign Labs, Reston, VA, 20190, USA

    Andrew Fregly, Joseph Harvey, Burton S. Kaliski Jr. & Swapneel Sheth

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Correspondence to Burton S. Kaliski Jr. .

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    Mike Rosulek

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Fregly, A., Harvey, J., Kaliski Jr., B.S., Sheth, S. (2023). Merkle Tree Ladder Mode: Reducing the Size Impact of NIST PQC Signature Algorithms in Practice. In: Rosulek, M. (eds) Topics in Cryptology – CT-RSA 2023. CT-RSA 2023. Lecture Notes in Computer Science, vol 13871. Springer, Cham. https://doi.org/10.1007/978-3-031-30872-7_16

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