Paper 2023/1745
New PublicKey Cryptosystem Blueprints Using Matrix Products in $\mathbb F_p$
Abstract
Given a set of matrices $\mathbf{A} := \{A_0, \dotsc, A_{k1}\}$, and a matrix $M$ guaranteed to be the product of some ordered subset of $\mathbf{L}\subset\mathbf{A}$, can $\mathbf{L}$ be efficiently recovered? We begin by observing that the answer is positive under some assumptions on $\mathbf{A}$. Noting that appropriate transformations seem to make $\mathbf{L}$'s recovery difficult we provide the blueprint of two new publickey cryptosystems based upon this problem. We term those constructions "blueprints because, given their novelty, we are still uncertain of their exact security. Yet, we daringly conjecture that even if attacks are found on the proposed constructions, these attacks could be thwarted by adjustments in the key generation, key size or the encryption mechanism, thereby resulting on the long run in fullyfledged publickey cryptosystems that do not seem to belong to any of the mainstream publickey encryption paradigms known to date.
Metadata
 Available format(s)
 Category
 Publickey cryptography
 Publication info
 Preprint.
 Keywords
 Publickey cryptosystemMatrix groupNoncommutative cryptography
 Contact author(s)

rgerauds @ qti qualcomm com
david naccache @ ens fr  History
 20231204: last of 5 revisions
 20231111: received
 See all versions
 Short URL
 https://ia.cr/2023/1745
 License

CC BY
BibTeX
@misc{cryptoeprint:2023/1745, author = {Remi GeraudStewart and David Naccache}, title = {New PublicKey Cryptosystem Blueprints Using Matrix Products in $\mathbb F_p$}, howpublished = {Cryptology {ePrint} Archive, Paper 2023/1745}, year = {2023}, url = {https://eprint.iacr.org/2023/1745} }