Paper 2023/1506
ISCUBE: An isogenybased compact KEM using a boxed SIDH diagram
Abstract
Isogenybased cryptography is one of the candidates for postquantum cryptography. One of the benefits of using isogenybased cryptography is its compactness. In particular, a key exchange scheme SIDH allowed us to use a $4\lambda$bit prime for the security parameter $\lambda$. Unfortunately, SIDH was broken in 2022 by some studies. After that, some isogenybased 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 $\lambda$. 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 isogenybased key encapsulation mechanism named ISCUBE via Kani's theorem and a $3$dimensional SIDH diagram. A prime used in ISCUBE is of the size of about $8\lambda$ bits, and we can use a random supersingular elliptic curve for the starting curve. The public key of ISCUBE is about $3$ times larger than that of SIKE, and the ciphertext of ISCUBE is about $4$ times larger than that of SIKE from theoretical estimation. In practice, compared to FESTA, the public key of ISCUBE is slightly larger and its ciphertext is slightly smaller. The core idea of ISCUBE 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)
 Category
 Publickey cryptography
 Publication info
 Preprint.
 Keywords
 isogenybased cryptographyKani's theoremSIDHKEM
 Contact author(s)
 t moriya @ bham ac uk
 History
 20240226: last of 2 revisions
 20231002: received
 See all versions
 Short URL
 https://ia.cr/2023/1506
 License

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