Paper 2023/1506

IS-CUBE: An isogeny-based compact KEM using a boxed SIDH diagram

Tomoki Moriya, University of Birmingham
Abstract

Isogeny-based cryptography is one of the candidates for post-quantum cryptography. One of the benefits of using isogeny-based cryptography is its compactness. In particular, a key exchange scheme SIDH allowed us to use a 4λ-bit prime for the security parameter λ. Unfortunately, SIDH was broken in 2022 by some studies. After that, some isogeny-based key exchange and public key encryption schemes have been proposed; however, most of these schemes use primes whose sizes are not guaranteed as linearly related to the security parameter λ. As far as we know, the remaining schemes have not been implemented due to the computation of isogenies of high dimensional abelian varieties, or they need to use a ``weak" curve (\textit{i.e.}, a curve whose endomorphism ring is known) as the starting curve. In this study, we propose a novel compact isogeny-based key encapsulation mechanism named IS-CUBE via Kani's theorem and a -dimensional SIDH diagram. A prime used in IS-CUBE is of the size of about bits, and we can use a random supersingular elliptic curve for the starting curve. The public key of IS-CUBE is about times larger than that of SIKE, and the ciphertext of IS-CUBE is about times larger than that of SIKE from theoretical estimation. In practice, compared to FESTA, the public key of IS-CUBE is slightly larger and its ciphertext is slightly smaller. The core idea of IS-CUBE comes from the hardness of some already known computational problems and a novel computational problem (the Long Isogeny with Torsion (LIT) problem), which is the problem to compute a hidden isogeny from two given supersingular elliptic curves and information of torsion points of relatively small order.

Metadata
Available format(s)
PDF
Category
Public-key cryptography
Publication info
Preprint.
Keywords
isogeny-based cryptographyKani's theoremSIDHKEM
Contact author(s)
t moriya @ bham ac uk
History
2024-02-26: last of 2 revisions
2023-10-02: received
See all versions
Short URL
https://ia.cr/2023/1506
License
Creative Commons Attribution
CC BY

BibTeX

@misc{cryptoeprint:2023/1506,
      author = {Tomoki Moriya},
      title = {{IS}-{CUBE}: An isogeny-based compact {KEM} using a boxed {SIDH} diagram},
      howpublished = {Cryptology {ePrint} Archive, Paper 2023/1506},
      year = {2023},
      url = {https://eprint.iacr.org/2023/1506}
}
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