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High-Throughput Elliptic Curve Cryptography Using AVX2 Vector Instructions
Cheng, Hao; Groszschädl, Johann; Tian, Jiaqi et al.
2020In Dunkelman, Orr; Jacobson Jr., Michael J.; O'Flynn, Colin (Eds.) Selected Areas in Cryptography, 27th International Conference, Halifax, NS, Canada (Virtual Event), October 21-23, 2020, Revised Selected Papers
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Keywords :
Throughput-Optimized Cryptography; Elliptic Curve Cryptography; Curve25519; Single Instruction Multiple Data (SIMD); Advanced Vector Extension 2 (AVX2)
Abstract :
[en] Single Instruction Multiple Data (SIMD) execution engines like Intel’s Advanced Vector Extensions 2 (AVX2) offer a great potential to accelerate elliptic curve cryptography compared to implementations using only basic x64 instructions. All existing AVX2 implementations of scalar multiplication on e.g. Curve25519 (and alternative curves) are optimized for low latency. We argue in this paper that many real-world applications, such as server-side SSL/TLS handshake processing, would benefit more from throughput-optimized implementations than latency-optimized ones. To support this argument, we introduce a throughput-optimized AVX2 implementation of variable-base scalar multiplication on Curve25519 and fixed-base scalar multiplication on Ed25519. Both implementations perform four scalar multiplications in parallel, where each uses a 64-bit element of a 256-bit vector. The field arithmetic is based on a radix-2^29 representation of the field elements, which makes it possible to carry out four parallel multiplications modulo a multiple of p=2^255−19 in just 88 cycles on a Skylake CPU. Four variable-base scalar multiplications on Curve25519 require less than 250,000 Skylake cycles, which translates to a throughput of 32,318 scalar multiplications per second at a clock frequency of 2 GHz. For comparison, the to-date best latency-optimized AVX2 implementation has a throughput of some 21,000 scalar multiplications per second on the same Skylake CPU.
Research center :
Interdisciplinary Centre for Security, Reliability and Trust (SnT) > Applied Security and Information Assurance Group (APSIA)
Disciplines :
Computer science
Author, co-author :
Cheng, Hao ;  University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > APSIA
Groszschädl, Johann ;  University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Computer Science (DCS)
Tian, Jiaqi ;  University of Luxembourg > Interdisciplinary Centre for Security, Reliability and Trust (SNT) > APSIA
Roenne, Peter ;  University of Luxembourg > Interdisciplinary Centre for Security, Reliability and Trust (SNT) > APSIA
Ryan, Peter Y A ;  University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Computer Science (DCS)
External co-authors :
no
Language :
English
Title :
High-Throughput Elliptic Curve Cryptography Using AVX2 Vector Instructions
Publication date :
October 2020
Event name :
27th International Conference on Selected Areas in Cryptography (SAC 2020)
Event place :
Halifax, NS, Canada
Event date :
2020-10-19 to 2020-10-23
Audience :
International
Main work title :
Selected Areas in Cryptography, 27th International Conference, Halifax, NS, Canada (Virtual Event), October 21-23, 2020, Revised Selected Papers
Editor :
Dunkelman, Orr
Jacobson Jr., Michael J.
O'Flynn, Colin
Publisher :
Springer Verlag
ISBN/EAN :
978-3-030-81651-3
Collection name :
Lecture Notes in Computer Science, volume 12804
Pages :
698-719
Peer reviewed :
Peer reviewed
Focus Area :
Security, Reliability and Trust
European Projects :
H2020 - 779391 - FutureTPM - Future Proofing the Connected World: A Quantum-Resistant Trusted Platform Module
Funders :
CE - Commission Européenne [BE]
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