journal: Journal of Mathematical Cryptology

Open Access Published since January 25, 2007

Journal of Mathematical Cryptology

ISSN: 1862-2984

Editor-in-chief: Nicolas T. Courtois

About this journal

Objective
The Journal of Mathematical Cryptology (JMC) is a forum for original research articles in the area of mathematical cryptology. JMC is a fully peer-reviewed, open access, electronic-only journal publishing works of wide significance, originality and relevance. Works in the theory of cryptology and articles linking mathematics with cryptology (including quantum cryptology) are welcome. Submissions from all areas of mathematics significant for cryptology are invited, including but not limited to, algebra, algebraic geometry, coding theory, combinatorics, number theory, probability and stochastic processes

The scope includes mathematical results of algorithmic or computational nature that are of interest to cryptology. While JMC does not cover information security as a whole, the submission of manuscripts on information security with a strong mathematical emphasis is explicitly encouraged.

Topics

Boolean functions
Elliptic curve cryptography
Mathematical cryptology
Information security
Quantum cryptology
Algebra
Algebraic geometry
Coding theory
Combinatorics and graph theory
Number theory
Probability and stochastic processes
Work linking math to cryptology
Work in the mathematical foundations of crypto
Theoretical aspects of cryptology
Mathematical foundations of cryptology

Article formats
Original research articles

Information on Submission Process

Your Benefits

Authors benefit from critical peer review and promotion of published papers to readers and citers.
The journal uses a continuous publication model - accepted manuscripts are published quickly after acceptance.
Thanks to Open Access, all articles are freely available to the academic community worldwide without any restrictions. Authors also benefit from more liberal policies on copyrights (authors retain copyright) and on self-archiving (no embargo periods).
The journal is archived in Portico.

Publication fees

From June 1, 2022, articles accepted for publication in the Journal of Mathematical Cryptology are subject to Article Processing Charges (APCs). The publication fee amounts to 1000 EUR. Authors who have no funding for the submitted research can request a waiver or a discount during the submission process. For more details please check Article Processing Charges.

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Supplementary Materials

Topics

External Links

Volume 16 Issue 1

January 2022

Regular Articles

Open Access August 5, 2021

On the confusion coefficient of Boolean functions

Yu Zhou, Jianyong Hu, Xudong Miao, Yu Han, Fuzhong Zhang

Page range: 1-13

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Abstract

The notion of the confusion coefficient is a property that attempts to characterize confusion property of cryptographic algorithms against differential power analysis. In this article, we establish a relationship between the confusion coefficient and the autocorrelation function for any Boolean function and give a tight upper bound and a tight lower bound on the confusion coefficient for any (balanced) Boolean function. We also deduce some deep relationships between the sum-of-squares of the confusion coefficient and other cryptographic indicators (the sum-of-squares indicator, hamming weight, algebraic immunity and correlation immunity), respectively. Moreover, we obtain some trade-offs among the sum-of-squares of the confusion coefficient, the signal-to-noise ratio and the redefined transparency order for a Boolean function.

Open Access September 8, 2021

On the supersingular GPST attack

Andrea Basso, Fabien Pazuki

Page range: 14-19

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Abstract

The main attack against static-key supersingular isogeny Diffie–Hellman (SIDH) is the Galbraith–Petit–Shani–Ti (GPST) attack, which also prevents the application of SIDH to other constructions such as non-interactive key-exchange. In this paper, we identify and study a specific assumption on which the GPST attack relies that does not necessarily hold in all circumstances. We show that in some circumstances the attack fails to recover part of the secret key. We also characterize the conditions necessary for the attack to fail and show that it rarely happens in real cases. We give a link with collisions in the Charles-Goren-Lauter (CGL) hash function.

Open Access September 17, 2021

Reproducible families of codes and cryptographic applications

Paolo Santini, Edoardo Persichetti, Marco Baldi

Page range: 20-48

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Abstract

Structured linear block codes such as cyclic, quasi-cyclic and quasi-dyadic codes have gained an increasing role in recent years both in the context of error control and in that of code-based cryptography. Some well known families of structured linear block codes have been separately and intensively studied, without searching for possible bridges between them. In this article, we start from well known examples of this type and generalize them into a wider class of codes that we call ℱ-reproducible codes. Some families of ℱ-reproducible codes have the property that they can be entirely generated from a small number of signature vectors, and consequently admit matrices that can be described in a very compact way. We denote these codes as compactly reproducible codes and show that they encompass known families of compactly describable codes such as quasi-cyclic and quasi-dyadic codes. We then consider some cryptographic applications of codes of this type and show that their use can be advantageous for hindering some current attacks against cryptosystems relying on structured codes. This suggests that the general framework we introduce may enable future developments of code-based cryptography.

Open Access October 26, 2021

Evolution of group-theoretic cryptology attacks using hyper-heuristics

Matthew J. Craven, John R. Woodward

Page range: 49-63

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Abstract

In previous work, we developed a single evolutionary algorithm (EA) to solve random instances of the Anshel–Anshel–Goldfeld (AAG) key exchange protocol over polycyclic groups. The EA consisted of six simple heuristics which manipulated strings. The present work extends this by exploring the use of hyper-heuristics in group-theoretic cryptology for the first time. Hyper-heuristics are a way to generate new algorithms from existing algorithm components (in this case, simple heuristics), with EAs being one example of the type of algorithm which can be generated by our hyper-heuristic framework. We take as a starting point the above EA and allow hyper-heuristics to build on it by making small tweaks to it. This adaptation is through a process of taking the EA and injecting chains of heuristics built from the simple heuristics. We demonstrate we can create novel heuristic chains, which when placed in the EA create algorithms that out perform the existing EA. The new algorithms solve a greater number of random AAG instances than the EA. This suggests the approach may be applied to many of the same kinds of problems, providing a framework for the solution of cryptology problems over groups. The contribution of this article is thus a framework to automatically build algorithms to attack cryptology problems given an applicable group.

Open Access January 7, 2022

MAKE: A matrix action key exchange

Nael Rahman, Vladimir Shpilrain

Page range: 64-72

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Abstract

We offer a public key exchange protocol based on a semidirect product of two cyclic (semi)groups of matrices over Z p {{\mathbb{Z}}}_{p} . One of the (semi)groups is additive, and the other one is multiplicative. This allows us to take advantage of both operations on matrices to diffuse information. We note that in our protocol, no power of any matrix or of any element of Z p {{\mathbb{Z}}}_{p} is ever exposed, so standard classical attacks on Diffie–Hellman-like protocols are not applicable.

Open Access January 28, 2022

The mF mode of authenticated encryption with associated data

Bishwajit Chakraborty, Mridul Nandi

Page range: 73-97

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Abstract

In recent years, the demand for lightweight cryptographic protocols has grown immensely. To fulfill this necessity, the National Institute of Standards and Technology (NIST) has initiated a standardization process for lightweight cryptographic encryption. NIST’s call for proposal demands that the scheme should have one primary member that has a key length of 128 bits, and it should be secure up to 2 50 − 1 {2}^{50}-1 byte queries and 2 112 {2}^{112} computations. In this article, we propose a tweakable block cipher (TBC)-based authenticated encryption with associated data (AEAD) scheme, which we call mF {\mathsf{mF}} . We provide authenticated encryption security analysis for mF {\mathsf{mF}} under some weaker security assumptions (stated in the article) on the underlying TBC. We instantiate a TBC using block cipher and show that the TBC achieves these weaker securities, provided the key update function has high periodicity. mixFeed {\mathsf{mixFeed}} is a round 2 candidate in the aforementioned lightweight cryptographic standardization competition. When we replace the key update function with the key scheduling function of Advanced Encryption Standard (AES), the mF {\mathsf{mF}} mode reduces to mixFeed {\mathsf{mixFeed}} . Recently, the low periodicity of AES key schedule is shown. Exploiting this feature, a practical attack on mixFeed {\mathsf{mixFeed}} is reported. We have shown that multiplication by primitive element satisfies the high periodicity property, and we have a secure instantiation of mF {\mathsf{mF}} , a secure variant of mixFeed {\mathsf{mixFeed}} .

Open Access February 10, 2022

Cryptanalysis of “MAKE”

Daniel R. L. Brown, Neal Koblitz, Jason T. LeGrow

Page range: 98-102

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Abstract

Rahman and Shpilrain proposed a Diffie–Hellman style key exchange based on a semidirect product of n × n n\times n -matrices over a finite field. We show that, using public information, an adversary can recover the agreed upon secret key by solving a system of n 2 {n}^{2} linear equations.

Volume 13 (2019)

Volume 12 (2018)

Volume 11 (2017)

Volume 10 (2016)

Volume 9 (2015)

Volume 8 (2014)

Volume 7 (2013)

Volume 6 (2012)

Volume 5 (2011)

Volume 4 (2010)

Volume 3 (2009)

Volume 2 (2008)

Volume 1 (2007)

Cite Score	0.9
Journal Citation Indicator	0.15
Mathematical Citation Quotient	0.16
SCImago Journal Rank	0.248
Source Normalized Impact per Paper	0.666

Submit

Submission
Please submit to JMC via ScholarOne Manuscripts　

Your benefits of publishing with us

Authors benefit from critical peer review and promotion of published papers to readers and citers.
The journal uses a continuous publication model - accepted manuscripts are published quickly after acceptance.
Thanks to Open Access, all articles are freely available to the academic community worldwide without any restrictions. Authors also benefit from more liberal policies on copyrights (authors retain copyright) and on self-archiving (no embargo periods).
The journal is archived in Portico.

Submission process

Before submitting an article, please adhere to the Instructions for Authors (Supplementary Information)
Submission of your paper via ScholarOne Manuscripts
Peer review procedure
Decision on your paper
Publishing
You will be guided through the whole process of submission
In case of any problems editorial assistance will be provided

Please note

Before submitting your manuscript, please get familiar with Publication ethics and malpractice statement
Beginning from January 2020, JMC is publishing in the Open Access model
Online publication for all papers accepted after peer review
If you have any general questions please visit our FAQ page for authors

We look forward to receiving your manuscript!

EDITORIAL POLICY

Unpublished material
Submission of a manuscript implies that the work described is not copyrighted, published or submitted elsewhere, except in abstract form. The corresponding author should ensure that all authors approve the manuscript before its submission.

Conflict of interest
When authors submit a manuscript, they are responsible for recognizing and disclosing financial and/or other conflicts of interest that might bias their work and/or could inappropriately influence his/her judgment. If no specified acknowledgement is given, the Editors assume that no conflict of interest exists.

Copyright
All authors retain copyright, unless – due to their local circumstances – their work is not copyrighted. The copyrights are governed by the Creative-Commons Attribution Only license (CC-BY) which is compliant with Plan-S. We may also publish a paper under CC-BY-NC-ND license on author's request. The corresponding author grants the journal license for use of the article, by signing the License To Publish. Scanned copy of license should be sent to the journal, as soon as possible.

Authorship
Authorship should be limited to those who have made a significant contribution to the conception, design, execution, or interpretation of the reported study. All those who have made significant contributions should be listed as coauthors. Where there are others who have participated in certain substantive aspects of the research project, they should be named in an Acknowledgement section.

Peer Review process
The Editors reserve the right to decline the submitted manuscript without review, if the studies reported are not sufficiently novel or important to merit publication in the journal. Manuscripts deemed unsuitable (insufficient originality or of limited interest to the target audience) are returned to the author(s) without review. The Editor seeks advice from experts in the appropriate field. Research articles and communications are refereed by a minimum of two reviewers, review papers by at least three. The journal uses single-blind peer review model. Authors are requested to suggest persons competent to review their manuscript. However, please note that this will be treated only as a suggestion, and the final selection of reviewers is exclusively the Editor’s decision. Suggested reviewers must not include authors’ students, mentors, collaborators, or others who have conflicts of interest. The final decision of acceptance is made by the main Editor of the journal.

Data sharing policy
Effective January 2021, the journal requires authors to follow data sharing policy. Research data should be made widely available to the research community in order to demonstrate the robustness and validity of the research presented in the journal, to encourage replication of the results, and to provide the community with opportunities to learn. By publishing in the journal authors are required to provide a data availability statement (DAS) in their articles. Authors are encouraged to share their data but not required to. The decision to publish will not be affected by whether or not authors share their research data.

Scientific Misconduct
This journal publishes only original manuscripts that are not also published or going to be published elsewhere. Multiple submissions/publications, or redundant publications (re-packaging in different words of data already published by the same authors) will be rejected. If they are detected only after publication, the journal reserves the right to publish a Retraction Note. In each particular case Editors will follow COPE’s Code of Conduct and implement its advice.

Editorial

Editor-in-Chief
Nicolas Courtois, University College London, UK

Editorial Advisory Board
Timothy J. Hodges, University of Cincinnati, USA
Wasim Alhamdani, School of Computer and Information Sciences, University of the Cumberlands, KY, USA
Lejla Batina, Institute for Computing and Information Sciences, Radboud University, The Netherlands
Joseph J. Boutros, Texas A&M University at Qatar, Doha, Qatar
Ray CC Cheung, City University of Hong Kong, Hong Kong
Bernardo David, IT-Universitetet i København, Copenhagen, Denmark
Roberto De Prisco, Università di Salerno, Salerno, Italy
Vipul Goyal, Carnegie Mellon University, Pittsburgh, USA
Shay Gueron, University of Haifa and Intel Corporation, Israel
Chunlei Li, Department of Informatics, University of Bergen, Norway
Carlos Aguilar Melchor, ISAE-SUPAERO, Toulouse University, France
Dominique Schröder, Department of Computer Science, Friedrich-Alexander-Universität Erlangen-Nürnberg, Germany
Gil Segev, School of Computer Science and Engineering, Hebrew University of Jerusalem
Susanne Wetzel, Stevens Institute of Technology, Department of Computer Science, Castle Point on Hudson, USA
Øyvind Ytrehus, Simula UiB AS, Norway
Chao Zhang, School of Mathematics, Harbin Institute of Technology, China

Editorial Board
Arkadii Slinko, Department of Mathematics, The University of Auckland, New Zealand
Barbara Masucci, Dipartimento di Informatica, Università di Salerno, Italy
Dmytro Savchuk, Department of Mathematics and Statistics, University of South Florida, USA
Andrej Dujella, University of Zagreb, Croatia
Wai Ho Mow, Department of Electronic and Computer Engineering, Hong Kong University of Science and Technology, Hong Kong
Huaxiong Wang, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore
Jacques Patarin, University of Versailles, France
Jean-Jacques Quisquater, Université Catholique de Louvain (UCL), Belgium
Juha Partala, University of Oulu, Finland
Liqun Chen, Department of Computer Science, University of Surrey, United Kingdom
Massimiliano Sala, Department of Mathematics, University of Trento, Italy
Chris Mitchell, Royal Holloway University of London, Egham, United Kingdom
Paolo D'Arco, Università di Salerno, Salerno, Italy
Peter Schwabe, Digital Security Group, Radboud University, The Netherlands
Vladimir Shpilrain, University of New York, USA
Tamir Tassa, Department of Mathematics and Computer Science, The Open University of Israel, Israel
David Naccache, École Normale Supérieure, France
Antoine Joux, Sorbonne Université, France
Nikola Batina, Universidad Autónoma Metropolitana-Iztapalapa, Mexico
Pavol Zajac, Slovenska Technicka Univerzita, Slovakia

Editorial Contact
Monika Maleszka
jmc_editorial@degruyter.com

(Deutsch)

Type: Journal
Language: English
Publisher: De Gruyter
First published: January 25, 2007
Publication Frequency: 1 Issue per Year
Audience: All those interested in selected areas lying at the crossroads of mathematics and cryptology.