Optimizations and Practicality of High-Security CSIDH

Fabio Campos; Jorge Chávez-Saab; Jesús-Javier Chi-Domínguez; Michael Meyer; Krijn Reijnders; Francisco Rodríguez-Henríquez; Peter Schwabe; Thom Wiggers

doi:10.62056/anjbksdja

Optimizations and Practicality of High-Security CSIDH

Authors

Fabio Campos, Jorge Chávez-Saab, Jesús-Javier Chi-Domínguez, Michael Meyer, Krijn Reijnders, Francisco Rodríguez-Henríquez, Peter Schwabe, Thom Wiggers

Fabio Campos

RheinMain University of Applied Sciences, Wiesbaden, Germany
campos at sopmac dot de

Jorge Chávez-Saab

Cryptography Research Center, Technology Innovation Institute, Abu Dhabi, United Arab Emirates
jorge dot saab at tii dot ae

Jesús-Javier Chi-Domínguez

Cryptography Research Center, Technology Innovation Institute, Abu Dhabi, United Arab Emirates
jesus dot dominguez at tii dot ae

Michael Meyer

University of Regensburg, Regensburg, Germany
michael at random-oracles dot org

Krijn Reijnders

Radboud University, Nijmegen, The Netherlands
krijn at cs dot ru dot nl

Francisco Rodríguez-Henríquez

Cryptography Research Center, Technology Innovation Institute, Abu Dhabi, United Arab Emirates
francisco dot rodriguez at tii dot ae

Peter Schwabe

Max Planck Institute for Security and Privacy, Bochum, Germany
Radboud University, Nijmegen, The Netherlands
peter at cryptojedi dot org

Thom Wiggers

PQShield, Nijmegen, The Netherlands
thom at thomwiggers dot nl

Abstract

In this work, we assess the real-world practicality of CSIDH, an isogeny-based non-interactive key exchange. We provide the first thorough assessment of the practicality of CSIDH in higher parameter sizes for conservative estimates of quantum security, and with protection against physical attacks.

This requires a three-fold analysis of CSIDH. First, we describe two approaches to efficient high-security CSIDH implementations, based on SQALE and CTIDH. Second, we optimize such high-security implementations, on a high level by improving several subroutines, and on a low level by improving the finite field arithmetic. Third, we benchmark the performance of high-security CSIDH. As a stand-alone primitive, our implementations outperform previous results by a factor up to 2.53×.

As a real-world use case considering network protocols, we use CSIDH in TLS variants that allow early authentication through a NIKE. Although our instantiations of CSIDH have smaller communication requirements than post-quantum KEM and signature schemes, even our highly-optimized implementations result in too-large handshake latency (tens of seconds), showing that CSIDH is only practical in niche cases.

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DOI: https://doi.org/10.62056/anjbksdja

History

Submitted: 2024-01-09
Accepted: 2024-03-05
Published: 2024-04-09

How to cite

Fabio Campos, Jorge Chávez-Saab, Jesús-Javier Chi-Domínguez, Michael Meyer, Krijn Reijnders, Francisco Rodríguez-Henríquez, Peter Schwabe, and Thom Wiggers, "Optimizations and Practicality of High-Security CSIDH," IACR Communications in Cryptology, vol. 1, no. 1, Apr 09, 2024, doi: 10.62056/anjbksdja.

License

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@article{CiC-1-1-5,
    author = "Campos, Fabio and Chávez-Saab, Jorge and Chi-Domínguez, Jesús-Javier and Meyer, Michael and Reijnders, Krijn and Rodríguez-Henríquez, Francisco and Schwabe, Peter and Wiggers, Thom",
    journal = "{IACR} {C}ommunications in {C}ryptology",
    publisher = "{I}nternational {A}ssociation for {C}ryptologic {R}esearch",
    title = "Optimizations and Practicality of High-Security {CSIDH}",
    volume = "1",
    number = "1",
    date = "2024-04-09",
    year = "2024",
    issn = "3006-5496",
    doi = "10.62056/anjbksdja"
}

TY - JOUR
AU - Campos, Fabio
AU - Chávez-Saab, Jorge
AU - Chi-Domínguez, Jesús-Javier
AU - Meyer, Michael
AU - Reijnders, Krijn
AU - Rodríguez-Henríquez, Francisco
AU - Schwabe, Peter
AU - Wiggers, Thom
PY  - 2024
TI  - Optimizations and Practicality of High-Security CSIDH
JF  - IACR Communications in Cryptology
JA  - CIC
VL  - 1
IS  - 1
DO  - 10.62056/anjbksdja
UR  - https://doi.org/10.62056/anjbksdja
AB  - <p>    In this work, we assess the real-world practicality of CSIDH, an isogeny-based non-interactive key exchange.     We provide the first thorough assessment of the practicality of CSIDH in higher parameter sizes     for conservative estimates of quantum security,     and with protection against physical attacks.</p><p>    This requires a three-fold analysis of CSIDH.     First, we describe two approaches to efficient high-security CSIDH implementations,     based on SQALE and CTIDH.     Second, we optimize such high-security implementations,     on a high level by improving several subroutines,     and on a low level by improving the finite field arithmetic.     Third, we benchmark the performance of high-security CSIDH.     As a stand-alone primitive, our implementations outperform previous     results by a factor up to 2.53×.</p><p>    As a real-world use case considering network protocols,     we use CSIDH in TLS variants that allow early authentication     through a NIKE.     Although our instantiations of CSIDH have smaller communication requirements than     post-quantum KEM and signature schemes, even our highly-optimized implementations result     in too-large handshake latency (tens of seconds), showing that CSIDH is only practical     in niche cases. </p>
ER  -

Fabio Campos, Jorge Chávez-Saab, Jesús-Javier Chi-Domínguez, Michael Meyer, Krijn Reijnders, Francisco Rodríguez-Henríquez, Peter Schwabe, and Thom Wiggers, "Optimizations and Practicality of High-Security CSIDH," IACR Communications in Cryptology, vol. 1, no. 1, Apr 09, 2024, doi: 10.62056/anjbksdja.