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Concrete quantum cryptanalysis of binary elliptic curves

Gustavo Banegas, Daniel J. Bernstein, Iggy Van Hoof, Tanja Lange
2020 Transactions on Cryptographic Hardware and Embedded Systems  
This paper analyzes and optimizes quantum circuits for computing discrete logarithms on binary elliptic curves, including reversible circuits for fixed-base-point scalar multiplication and the full stack  ...  The number of CNOT gates is also O(n3). Exact gate counts are given for various sizes of elliptic curves currently used for cryptography.  ...  At Asiacrypt 2017, Rötteler, Naehrig, Svore and Lauter [RNSL17] presented concrete quantum cryptanalysis of elliptic curve cryptography over prime fields.  ... 
doi:10.46586/tches.v2021.i1.451-472 fatcat:2chsn37mzba27ktdutfaq7oc2q

Another Concrete Quantum Cryptanalysis of Binary Elliptic Curves [article]

Dedy Septono Catur Putranto, Rini Wisnu Wardhani, Harashta Tatimma Larasati, Howon Kim
2022 IACR Cryptology ePrint Archive  
This paper presents concrete quantum cryptanalysis for binary elliptic curves for a time-efficient implementation perspective (i.e., reducing the circuit depth), complementing the previous research by  ...  Finally, we employ the proposed multiplier and FLT-based inversion for performing quantum cryptanalysis of binary point addition as well as the complete Shor's algorithm for elliptic curve discrete logarithm  ...  Contributions The contributions of this paper can be summarized as follows: 1. This study presents a concrete quantum cryptanalysis for binary elliptic curves.  ... 
dblp:journals/iacr/PutrantoWLK22 fatcat:cnsepnniyvdpredau6kqpxnyxm

Reducing the Depth of Quantum FLT-Based Inversion Circuit [article]

Harashta Tatimma Larasati, Dedy Septono Catur Putranto, Rini Wisnu Wardhani, Howon Kim
2022 arXiv   pre-print
However, there has only been a few studies on finite field inversion despite its essential use in realizing quantum algorithms, such as in Shor's algorithm for Elliptic Curve Discrete Logarith Problem  ...  In this study, we propose to reduce the depth of the existing quantum Fermat's Little Theorem (FLT)-based inversion circuit for binary finite field.  ...  [14] describe the quantum cryptanalysis of binary elliptic curve.  ... 
arXiv:2204.08940v1 fatcat:keuqk7viqrbzjjjcd2jiszj5da

Guest Editors' Introduction to the Special Issue on Cryptographic Engineering in a Post-Quantum World: State of the Art Advances

Zhe Liu, Patrick Longa, Cetin Kaya Koc
2018 IEEE transactions on computers  
T HE vast majority of public-key cryptosystems currently in use is based on integer factorization and (elliptic curve) discrete logarithm problems, which are believed to be intractable with current computing  ...  The concrete goal of this special issue is to highlight new results in the design and analysis of cryptographic hardware and software implementations of post-quantum cryptography (PQC).  ...  His research interests mainly involve elliptic curve and pairing-based cryptography, post-quantum cryptography, efficient algorithmic design, high-performance implementation of cryptographic primitives  ... 
doi:10.1109/tc.2018.2869611 fatcat:aw4i4jifm5ftrgmwn5bgonucje

Quantum-Resistant Security for Software Updates on Low-power Networked Embedded Devices [article]

Gustavo Banegas
2021 arXiv   pre-print
While the performance of SUIT has previously been evaluated in the pre-quantum context, it has not yet been studied in a post-quantum context.  ...  We interpret our benchmark results in the context of SUIT, and estimate the real-world impact of post-quantum alternatives for a range of typical software update categories.  ...  elliptic-curve signatures generated after .  ... 
arXiv:2106.05577v2 fatcat:pcg64enerzgqhe3qw6ime2vksi

A Riddle Wrapped in an Enigma

Neal Koblitz, Alfred Menezes
2016 IEEE Security and Privacy  
However, certain peculiarities in the wording and timing of the statement have puzzled many people and given rise to much speculation concerning the NSA, elliptic curve cryptography (ECC), and quantum-safe  ...  National Security Agency (NSA) released a major policy statement on the need for post-quantum cryptography (PQC).  ...  Of course, none of them is responsible for the judgments and opinions in this article.  ... 
doi:10.1109/msp.2016.120 fatcat:gs3phiptebgydgjmjdkkngl2xa

Quantum Cryptanalysis (Dagstuhl Seminar 15371)

Michele Mosca, Martin Roetteler, Nicolas Sendrier, Rainer Steinwandt, Marc Herbstritt
2016 Dagstuhl Reports  
This report documents the program and the outcomes of Dagstuhl Seminar 15371 "Quantum Cryptanalysis".  ...  the security of proposed quantum-safe cryptosystems against emerging quantum cryptanalytic attacks.  ...  It is known that quantum algorithms exist that jeopardize the security of most of our widely-deployed cryptosystems, including RSA and Elliptic Curve Cryptography.  ... 
doi:10.4230/dagrep.5.9.1 dblp:journals/dagstuhl-reports/MoscaRSS15 fatcat:a3bpfckt3fespm27nxmaqykx6i

The Legendre Pseudorandom Function as a Multivariate Quadratic Cryptosystem: Security and Applications [article]

István András Seres, Máté Horváth, Péter Burcsi
2021 IACR Cryptology ePrint Archive  
This new perspective sheds some light on the complexity of key-recovery attacks against the Legendre PRF. We conduct algebraic cryptanalysis on the resulting MQ instance.  ...  The security of these PRFs is not known to be reducible to standard cryptographic assumptions.  ...  of an elliptic curve over F p .  ... 
dblp:journals/iacr/SeresHB21 fatcat:cz2shencbbb3hit7u3lwjwg3v4

Pre- and post-quantum Diffie-Hellman from groups, actions, and isogenies [article]

Benjamin Smith
2019 arXiv   pre-print
number-theoretic structures formed by isogenies of elliptic curves.  ...  Diffie-Hellman key exchange is at the foundations of public-key cryptography, but conventional group-based Diffie-Hellman is vulnerable to Shor's quantum algorithm.  ...  Our focus is mostly constructive, and our discussion of quantum cryptanalysis will be purely asymptotic, for reasons discussed in §6. Limiting scope.  ... 
arXiv:1809.04803v3 fatcat:feyexp5afbdurg5rbtbp75rvgq

Pre- and Post-quantum Diffie–Hellman from Groups, Actions, and Isogenies [chapter]

Benjamin Smith
2018 Lecture Notes in Computer Science  
number-theoretic structures formed by isogenies of elliptic curves.  ...  Diffie-Hellman key exchange is at the foundations of publickey cryptography, but conventional group-based Diffie-Hellman is vulnerable to Shor's quantum algorithm.  ...  Our focus is mostly constructive, and our discussion of quantum cryptanalysis will be purely asymptotic, for reasons discussed in §6. Limiting scope.  ... 
doi:10.1007/978-3-030-05153-2_1 fatcat:hrtt6eon7fhnlpfkwxmzwtgd4a

Page 6574 of Mathematical Reviews Vol. , Issue 99i [page]

1999 Mathematical Reviews  
Sundaram, An efficient discrete log pseudo- random generator (304-317); Tsuyoshi Takagi, Fast RSA-type cryptosystem modulo p*q (318-326); Neal Koblitz, An elliptic curve implementation of the finite field  ...  Louis Salvail, Quantum bit commitment from a physical as- sumption (338-353); Kazuo Ohta and Tatsuaki Okamoto, On concrete security treatment of signatures derived from identifica- tion (354-369); Chris  ... 

SÉTA: Supersingular Encryption from Torsion Attacks [article]

Cyprien Delpech de Saint Guilhem, Péter Kutas, Christophe Petit, Javier Silva
2019 IACR Cryptology ePrint Archive  
We present Séta, 11 a new family of public-key encryption schemes with post-quantum security based on isogenies of supersingular elliptic curves.  ...  given an endomorphism of the starting curve and images of torsion points.  ...  He computes the shared secret E → E/ A, B and hashes the j-invariant of E/ A, B to a binary string s.  ... 
dblp:journals/iacr/GuilhemKPS19 fatcat:mfjxxjuzpvcdrerviwb5tmlq6y

Side-channel attacks on the McEliece and Niederreiter public-key cryptosystems

Roberto Avanzi, Simon Hoerder, Dan Page, Michael Tunstall
2011 Journal of Cryptographic Engineering  
Research within "post-quantum" cryptography has focused on development of schemes that resist quantum cryptanalysis.  ...  However, if such schemes are to be deployed, practical questions of efficiency and physical security should also be addressed; this is particularly important for embedded systems.  ...  Concrete examples of quantum cryptanalysis include Shor's algorithms for factoring and discrete logarithms [16] which, given a suitable quantum computer, could threaten the security of RSA and elliptic  ... 
doi:10.1007/s13389-011-0024-9 fatcat:2d4isnzqfzfmbcr7a4naxylzru

Another code-based adaptation of Lyubashevsky's signature cryptanalysed [article]

Nicolas Aragon, Jean-Christophe Deneuville, Philippe Gaborit
2020 IACR Cryptology ePrint Archive  
As an example, it requires 32 signatures and 2 hours to recover the secret key of the parameter set targeting 80 bits of security.  ...  We show that it is possible to fully recover the secret key from a very limited number of signatures.  ...  group of points on an elliptic curve.  ... 
dblp:journals/iacr/AragonDG20 fatcat:o54brqt4o5f5dawsjplzt2ktw4

Collisions in Supersingular Isogeny Graphs and the SIDH-based Identification Protocol [article]

Wissam Ghantous, Federico Pintore, Mattia Veroni
2021 IACR Cryptology ePrint Archive  
The security of the resulting schemes is therefore deduced from that of the base identification protocol.  ...  The existence of these special cycles not only enjoys a theoretical interest, but is generally relevant for the Isogeny-based Cryptography.  ...  cryptanalysis.  ... 
dblp:journals/iacr/GhantousPV21 fatcat:ydsk63bfcjamrpc5ufy3c2vjuu
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