Efficient arithmetic for embedded cryptography and cryptanalysis

180 Pages·2012·2.69 MB·English

by  Junfeng Fan

ArenbergDoctoralSchoolofScience,Engineering&Technology
FacultyofEngineering
DepartmentofElectricalEngineering
Efficient arithmetic for embedded
cryptography and cryptanalysis
Junfeng FAN
Dissertationpresentedinpartial
fulfillmentoftherequirementsfor
thedegreeofDoctor
inEngineering
January2012

Efficient arithmetic for embedded cryptography and
cryptanalysis
Junfeng FAN
Jury: Dissertation presented in partial
Prof. dr. ir. Hugo Hens, chair fulfillment of the requirements for
Prof. dr. ir. Ingrid Verbauwhede, promotor the degree of Doctor
Prof. dr. ir. Bart Preneel, co-promotor of Engineering
Prof. dr. ir. Wim Dehaene
Prof. dr. ir. Joos Vandewalle
Dr. ir. Fré Vercauteren
Dr. ir. Marc Joye
(Technicolor, France)
Prof. dr. ir. Patrick Schaumont
(Virginia Tech, USA)
January 2012
© Katholieke Universiteit Leuven – Faculty of Engineering
Kasteelpark Arenberg 10, B-3001 Heverlee(Belgium)
Allerechtenvoorbehouden. Nietsuitdezeuitgavemagwordenvermenigvuldigd
en/of openbaar gemaakt worden door middel van druk, fotocopie, microfilm,
elektronisch of op welke andere wijze ook zonder voorafgaande schriftelijke
toestemming van de uitgever.
All rights reserved. No part of the publication may be reproduced in any form
byprint, photoprint, microfilmoranyothermeanswithoutwrittenpermission
from the publisher.
D/2012/7515/13
ISBN 978-94-6018-474-1
Acknowledgements
It would not have beenpossible to write this dissertation without the help and
supportofmanypeoplearoundme, toonlysomeofwhomitispossibletogive
particular mention here.
First, I would like to express my deepest gratitude to my supervisor, Prof.
Ingrid Verbauwhede for offering me the opportunity to conduct PhD research
atCOSIC,forgrantingthefreedomandflexibilityinmyresearchwork,andfor
the guidance and support in the last 5 years. I would like to thank Prof. Bart
Preneelfortheinspiringdiscussionsandexcellentcommentsonmydissertation.
I would also like to thank Prof. Wim Dehaene and Prof. Joos Vandewalle, my
assessors during my PhD study, for many valuable advices. I am honored to
have Prof. Hugo Hens to be the chair and Prof. Patrick Schaumont and Dr.
Marc Joye to be the members of my jury.
Special thanks go to Dr. Fré Vercauteren, who is a great colleague, co-author,
and friend. I am especially grateful for his patience with my questions in
mathematics, inspiring talk we had on new ideas, and careful review of my
dissertation.
I am very grateful to our COSIC members who make up such a nice mixture
of culture, wisdom and personalities. I thank them for their generosity and
encouragement, and for making my life in Leuven a lot more colorful. I would
especially like to thank Péla for being so nice and helpful all the time.
Duringthelast5years,Iwasluckyenoughtomeetandcollaboratewithmany
talented researchers. I would like to thank Kazuo Sakiyama, Lejla Batina
and Nele Mentens for guiding me after I joined COSIC. I also enjoyed the
collaboration with Miroslav Knežević, Duško Karaklajić, Yong Ki Lee, Roel
Maes,VladimirRožić,BenediktGierlichs,ÖzgülKüç¨ck,JensHermans,Markus
Ullrich and Elke De Mulder. I am also grateful to many people that I have
remotely collaborated with: Xu Guo, Tanja Lange, Daniel J. Bernstein, Peter
i
ii ACKNOWLEDGEMENTS
Schwabe, Xiaoxu Yao and Tim Güneysu. Their passion and diligence have
encouraged me to push my research forward.
Theseacknowledgmentswouldcertainlyremainincompletewithoutmentioning
manyofmyfriendsinLeuven. IwouldliketothankElenaAndreevaforsharing
with me many delicious dinners, countless quick jokes and an enthusiastic
attitude towards life. I am grateful to many Chinese friends in Leuven. I
wouldespeciallyliketothankNinaFan,LinZhou,ChangChen,YunanCheng,
Hang Gao, Yangyin Chen, Tingyao Wu, Min Li, Li Weng, Junfeng Zhou, Feng
Qi, Lianggong Wen, Hongjun Wu, Beier Li, Min Liu, Enze Chen, Yuemei Ji,
YannanDing,Fu-ChiaoHuang,Yu-YuanHungandKaiZhoufortheirgenerous
help and support, for interesting chats at Alma, and for celebrating with me
many Chinese festivals. Thanks to them, I have never felt that home was far
away.
Finally, I would like to thank my parents and my sisters for the unconditional
support and love. I would like to thank Di Mo for being supportive and
understanding during all these years.
Junfeng Fan
January 2012
Abstract
PublicKeyCryptography(PKC)isacriticalcomponentoftoday’sinformation
infrastructure. TheuseofPKCcoversawidespectrumofdevicesrangingfrom
web servers to mobile handsets, from contact smart cards to passive RFID
tags. Therefore, PKC implementations tailored to different environments need
specific optimizations to meet the requirements for performance, power and
security against physical attacks.
This thesis focuses on arithmetic and architecture design for PKC. In the
first part, we analyze the computation structures of RSA, Elliptic Curve
Cryptography(ECC),HyperellipticCurveCryptography(HECC),Torus-based
cryptographyandPairings,andexplorevariousrepresentations,algorithmsand
architecturesfordifferentdesigntargets. Inparticular,weproposeamulti-core
Montgomerymultiplier,alow-complexitymodularmultiplicationalgorithmfor
pairings, and two novel architectures for low-area implementations of HECC.
In the second part, we use efficient arithmetic as the basis for hardware-based
cryptanalysis. The security margin of a cryptosystem erodes continuously due
to Moore’s law. We study the power of FPGA clusters to break ECC using
the parallelized Pollard rho method and implement this attack on an FPGA
wherewetrytomaximizethenumberofPollardrhoiterationspersecond. We
also give an estimation of the effort to break ECC2-131 and ECC2k-160 with
state-of-the-art FPGAs.
Inthethirdandfinalpart,weprovideasystematicoverviewofimplementation
attacks and countermeasures for ECC. By monitoring the timing, power
consumption, electromagnetic emission of the device or by inserting faults,
adversaries can gain information about internal data or operations and
extract the secret key without mathematically breaking the primitives. We
provide implementers of ECC with ready-to-use recommendations of which
combinations of countermeasures result in a secure implementation.
iii

Beknopte samenvatting
Publieke-sleutel cryptografie (PSC) speelt een essentiële rol in de huidige
informatiemaatschappij. Het gebruik van PSC vindt men terug in allerhande
toepassingen, van webservers tot mobiele telefoons, van smartcards tot
passieve RFID tags. Deze uiteenlopende toepassingen maken specifieke
optimalisatiesvoordeverscheideneomgevingennoodzakelijkzowelophetvlak
van performantie, en energieverbruik als op het valk van en veiligheid tegen
nevenkanaalaanvallen.
Deze thesis handelt over aritmetica en architectuurontwerp voor PSC. In een
eerste deel analyseren we de algoritmische structuren van RSA, Elliptische
kromme cryptografie (ECC), Hyperelliptische kromme cryptografie (HECC),
Torus-gebaseerde cryptografie en Paringen, waarbij we verscheidene voorstel-
lingswijzen, algoritmes en architecturen voor verschillende ontwerpdoeleinden
verkennen. Meer specifiek stellen we een multi-core Montgomery vermenigvul-
diger voor, een modulair vermenigvuldigingsalgoritme voor paringen van lage
complexiteitentenslottetweenieuwearchitecturenvoorHECCimplementaties
met kleine oppervlakte.
In het tweede deel gebruiken we efficiënte aritmetica als basis voor hardware-
gebaseerde cryptanalyse. De niet-aflatende verbetering van chiptechnologieën
zorgt ervoor dat de veiligheidsmarge van een cryptosysteem continu afneemt.
We bestuderen het gebruik van FPGA clusters om ECC aan te vallen via
de parallelle Pollard rho methode en implementeren deze aanval op een
FPGA waarbij we het aantal iteraties per seconde proberen te maximaliseren.
Bovendien geven we ook een schatting van de praktische veiligheidsmarge van
ECC2-131 en ECC2k-160 wanneer we state-of-the-art FPGA’s gebruiken.
In het derde en laatste deel, geven we een systematisch overzicht van
implementatieaanvallen en tegenmaatregelen voor ECC. Door de looptijd,
energieverbruikenelectromagnetischestralingvaneenimplementatietemeten
of door fouten te induceren, kan een aanvaller informatie te weten komen over
v
vi BEKNOPTESAMENVATTING
internedataenopdezemanierdegeheimesleutelberekenen. Onssystematisch
overzicht kan door programmeurs van ECC gebruikt worden om combinaties
van tegenmaatregelen te selecteren die in een veilige implementatie resulteren.