A post-quantum key exchange protocol from the intersection of quadric surfaces

Daniele Di Tullio; Manoj Gyawali

doi:10.1007/s11227-023-05146-x

A post-quantum key exchange protocol from the intersection of quadric surfaces

Daniele Di Tullio
, Manoj Gyawali^*

^*Corresponding author for this work

Roma Tre University

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

Abstract

In this paper, we present a new key exchange protocol in which Alice and Bob have secret keys given by quadric surfaces embedded in a large ambient space by means of the Veronese embedding and public keys given by hyperplanes containing the embedded quadrics. Both of them reconstruct the isomorphism class of the intersection which is a curve of genus 1, and is uniquely determined by the j-invariant. An eavesdropper, to find this j-invariant, has to solve problems which are conjecturally quantum-resistant.

Original language	English
Pages (from-to)	16529-16558
Number of pages	30
Journal	Journal of Supercomputing
Volume	79
Issue number	15
DOIs	https://doi.org/10.1007/s11227-023-05146-x
Publication status	Published - Oct 2023

Keywords

Post-quantum cryptography
Quadric surfaces
Segre embedding
Veronese embedding

Access to Document

10.1007/s11227-023-05146-x

Cite this

@article{0a2e05fbf8c9435ea58cb899ad5e35c2,

title = "A post-quantum key exchange protocol from the intersection of quadric surfaces",

abstract = "In this paper, we present a new key exchange protocol in which Alice and Bob have secret keys given by quadric surfaces embedded in a large ambient space by means of the Veronese embedding and public keys given by hyperplanes containing the embedded quadrics. Both of them reconstruct the isomorphism class of the intersection which is a curve of genus 1, and is uniquely determined by the j-invariant. An eavesdropper, to find this j-invariant, has to solve problems which are conjecturally quantum-resistant.",

keywords = "Post-quantum cryptography, Quadric surfaces, Segre embedding, Veronese embedding",

author = "Tullio, \{Daniele Di\} and Manoj Gyawali",

note = "Publisher Copyright: {\textcopyright} 2023, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.",

year = "2023",

month = oct,

doi = "10.1007/s11227-023-05146-x",

language = "English",

volume = "79",

pages = "16529--16558",

journal = "Journal of Supercomputing",

issn = "0920-8542",

number = "15",

}

TY - JOUR

T1 - A post-quantum key exchange protocol from the intersection of quadric surfaces

AU - Tullio, Daniele Di

AU - Gyawali, Manoj

PY - 2023/10

Y1 - 2023/10

N2 - In this paper, we present a new key exchange protocol in which Alice and Bob have secret keys given by quadric surfaces embedded in a large ambient space by means of the Veronese embedding and public keys given by hyperplanes containing the embedded quadrics. Both of them reconstruct the isomorphism class of the intersection which is a curve of genus 1, and is uniquely determined by the j-invariant. An eavesdropper, to find this j-invariant, has to solve problems which are conjecturally quantum-resistant.

AB - In this paper, we present a new key exchange protocol in which Alice and Bob have secret keys given by quadric surfaces embedded in a large ambient space by means of the Veronese embedding and public keys given by hyperplanes containing the embedded quadrics. Both of them reconstruct the isomorphism class of the intersection which is a curve of genus 1, and is uniquely determined by the j-invariant. An eavesdropper, to find this j-invariant, has to solve problems which are conjecturally quantum-resistant.

KW - Post-quantum cryptography

KW - Quadric surfaces

KW - Segre embedding

KW - Veronese embedding

UR - https://www.scopus.com/pages/publications/85153719410

U2 - 10.1007/s11227-023-05146-x

DO - 10.1007/s11227-023-05146-x

M3 - Article

AN - SCOPUS:85153719410

SN - 0920-8542

VL - 79

SP - 16529

EP - 16558

JO - Journal of Supercomputing

JF - Journal of Supercomputing

IS - 15

ER -

A post-quantum key exchange protocol from the intersection of quadric surfaces

Abstract

Keywords

Access to Document

Other files and links

Cite this