In this paper, we present a new signature scheme based on factoring and discrete logarithm problems.
Derived from a variant of ElGamal signature protocol and the RSA alg
Cryptography is the combination of Mathematics and Computer science. Cryptography is used for encryption and decryption of data using mathematics. Cryptography transit the information in an illegible manner such that only intended recipient will be able to decrypt the information
A Primality test is an algorithm for determining whether an input number is Prime. Among other fields of mathematics, it is used for Cryptography. Factorization is thought to be a computationally difficult problem, whereas primality testing is comparatively easy (its running time is polynomial in the size of the input).
Data Structure is a way of collecting and organising data in such a way that we can perform operations on these data in an effective way. Data Structures is about rendering data elements in terms of some relationship, for better organization and storage. For example, we have data player's name "Virat" and age 26. Here "Virat" is of String data type and 26 is of integer data type.
We can organize this data as a record like Player record. Now we can collect and store player's records in a file or database as a data structure. For example: "Dhoni" 30, "Gambhir" 31, "Sehwag" 33
In simple language, Data Structures are structures programmed to store ordered data, so that various operations can be performed on it easily.
International Journal of Research in Engineering and Science is an open access peer-reviewed international forum for scientists involved in research to publish quality and refereed papers. Papers reporting original research or experimentally proved review work are welcome. Papers for publication are selected through peer review to ensure originality, relevance, and readability.
Cryptography is the combination of Mathematics and Computer science. Cryptography is used for encryption and decryption of data using mathematics. Cryptography transit the information in an illegible manner such that only intended recipient will be able to decrypt the information
A Primality test is an algorithm for determining whether an input number is Prime. Among other fields of mathematics, it is used for Cryptography. Factorization is thought to be a computationally difficult problem, whereas primality testing is comparatively easy (its running time is polynomial in the size of the input).
Data Structure is a way of collecting and organising data in such a way that we can perform operations on these data in an effective way. Data Structures is about rendering data elements in terms of some relationship, for better organization and storage. For example, we have data player's name "Virat" and age 26. Here "Virat" is of String data type and 26 is of integer data type.
We can organize this data as a record like Player record. Now we can collect and store player's records in a file or database as a data structure. For example: "Dhoni" 30, "Gambhir" 31, "Sehwag" 33
In simple language, Data Structures are structures programmed to store ordered data, so that various operations can be performed on it easily.
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http://icbda2015.org/
Impact of black hole attack on aodv routing protocolZac Darcy
A
m
obile
a
d
-
hoc
n
etwork (MANET)
is a
collection
of wireless mobile nodes
that dynamically self
-
organize
to form an
arbitrary and temporary network.
The mobile nodes can communicate wit
h each other
without
any fixed infrastructure.
MANET
can be set
up quickly to facilitate communication in a hostile environment
such as battlefield or emergency situation.
The various severe security threats are
increasing
on the
MANET
. One of these secur
ity threats is black hole attack which drops all received data packets intended
for forwarding. In this paper, we are simulating and analyzing the impact of black hole attack on Ad Hoc
On
-
Demand Distance Vector (AODV) protocol. Th
e simulation is carried on
NS
-
2 and t
he simulation
results are analyzed
on
various network performance
metric
s such as packet delivery ratio, normalized
routing overhead
and
average end
-
to
-
end delay
Rejuvenate Pointcut: A Tool for Pointcut Expression Recovery in Evolving Aspe...Raffi Khatchadourian
Invited tool demonstration at the 8th International Conference on Aspect-Oriented Software Development (AOSD '09), Charlottesville, VA, USA, March 2-6, 2009.
Выступление Сергея Кольцова (НИУ ВШЭ) на International Conference on Big Data and its Applications (ICBDA).
ICBDA — конференция для предпринимателей и разработчиков о том, как эффективно решать бизнес-задачи с помощью анализа больших данных.
http://icbda2015.org/
Impact of black hole attack on aodv routing protocolZac Darcy
A
m
obile
a
d
-
hoc
n
etwork (MANET)
is a
collection
of wireless mobile nodes
that dynamically self
-
organize
to form an
arbitrary and temporary network.
The mobile nodes can communicate wit
h each other
without
any fixed infrastructure.
MANET
can be set
up quickly to facilitate communication in a hostile environment
such as battlefield or emergency situation.
The various severe security threats are
increasing
on the
MANET
. One of these secur
ity threats is black hole attack which drops all received data packets intended
for forwarding. In this paper, we are simulating and analyzing the impact of black hole attack on Ad Hoc
On
-
Demand Distance Vector (AODV) protocol. Th
e simulation is carried on
NS
-
2 and t
he simulation
results are analyzed
on
various network performance
metric
s such as packet delivery ratio, normalized
routing overhead
and
average end
-
to
-
end delay
Підзвітність депутатів місцевих рад Волині (8-ми рад)Volyn Media
У рамках проекту "Активна громада - відповідальний депутат" експерти Центру Політичного Аналізу та Виборчого Консалтингу проаналізували рівень відкритості та прозорості роботи рад, що взяли участь у проекті. Про це детально розповів виконавчий директор ЦПАВКу Михайло Шелеп. http://volynmedia.com/articles/2152/
ON MODIFICATION OF PROPERTIES OF P-N-JUNCTIONS DURING OVERGROWTHZac Darcy
In this paper we consider influence of overgrowth of doped by diffusion and ion implantation areas of heterostructures
on distributions of concentrations of dopants. Several conditions to increase sharpness of p-njunctions
(single and framework bipolar transistors), which were manufactured during considered technological
process, have been determined. At the same time we analyzed influence of speed of overgrowth of
doped areas and mechanical stress in the considered heterostructure on distribution of concentrations of
dopants in the structure.
Concepto de La criminología:La criminología es la disciplina que estudia las causas del crimen y preconiza los remedios del comportamiento antisocial del hombre. La criminología es una ciencia interdisciplinaria que basa sus fundamentos en conocimientos propios de la sociología, psicología y la antropología, tomando para ello el marco teórico de la medicina y el derecho penal.
Remote sensing image fusion using contourlet transform with sharp frequency l...Zac Darcy
This paper addresses four different aspects of the remote sensing image fusion: i) image fusion method, ii)
quality analysis of fusion results, iii) effects of image decomposition level, and iv) importance of image
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over the wavelet-based fusion. This fusion method is then utilized withinthe main fusion process to analyze
the final fusion results. Fusion framework, scheme and datasets used in the study are discussed in detail.
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and spectral analyses. Our results indicate that the proposed contourlet-based fusion method performs
better than the conventional wavelet-based fusion methodsin terms of both spatial and spectral analyses.
Third, we conducted an analysis on the effects of the image decomposition level and observed that the
decomposition level of 3 produced better fusion results than both smaller and greater number of levels.
Last, we created four different fusion scenarios to examine the importance of the image registration. As a
result, the feature-based image registration using the edge features of the source images produced better
fusion results than the intensity-based imageregistration.
A New Signature Protocol Based on RSA and Elgamal SchemeZac Darcy
In this paper, we present a new signature scheme based on factoring and discrete logarithm problems.Derived from a variant of ElGamal signature protocol and the RSA algorithm, this method can be seen asan alternative protocol if known systems are broken.
A New Signature Protocol Based on RSA and Elgamal SchemeZac Darcy
In this paper, we present a new signature scheme based on factoring and discrete logarithm problems.
Derived from a variant of ElGamal signature protocol and the RSA algorithm, this method can be seen as
an alternative protocol if known systems are broken.
New Digital Signature Protocol Based on Elliptic Curvesijcisjournal
In this work, a new digital signature based on elliptic curves is presented. We established its efficiency and
security. The method, derived from a variant of ElGamal signature scheme, can be seen as a secure alternative protocol if known systems are completely broken.
A SIGNATURE ALGORITHM BASED ON DLP AND COMPUTING SQUARE ROOTSZac Darcy
n this work, we present a new digital signature protocol based on the discrete logarithm problem and
computing square roots modulo a large composite number. This method can be used as an alternative if
known systems are broken.
A Signature Algorithm Based on DLP and Computing Square RootsZac Darcy
In this work, we present a new digital signature protocol based on the discrete logarithm problem and
computing square roots modulo a large composite number. This method can be used as an alternative if
known systems are broken.
RSA ALGORITHM WITH A NEW APPROACH ENCRYPTION AND DECRYPTION MESSAGE TEXT BY A...ijcisjournal
In many research works, there has been an orientation to studying and developing many of the applications of public-key cryptography to secure the data while transmitting in the systems, In this paper we present an approach to encrypt and decrypt the message text according to the ASCII(American Standard Code for Information Interchange) and RSA algorithm by converting the message text into binary representation and dividing this representation to bytes(8s of 0s and 1s) and applying a bijective function between the group of those bytes and the group of characters of ASCII and then using this mechanism to be compatible with using RSA algorithm, finally, Java application was built to apply this approach directly.
Cryptography is the practice and study of techniques for conveying information security.
The goal of Cryptography is to allow the intended recipients of the message to receive the message securely.
The most famous algorithm used today is RSA algorithm
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
Novel Methods of Generating Self-Invertible Matrix for Hill Cipher Algorithm.CSCJournals
In this paper, methods of generating self-invertible matrix for Hill Cipher algorithm have been proposed. The inverse of the matrix used for encrypting the plaintext does not always exist. So, if the matrix is not invertible, the encrypted text cannot be decrypted. In the self-invertible matrix generation method, the matrix used for the encryption is itself self-invertible. So, at the time of decryption, we need not to find inverse of the matrix. Moreover, this method eliminates the computational complexity involved in finding inverse of the matrix while decryption.
This paper provides an overview of the RSA algorithm, exploring the foundations and mathematics in detail. It then uses this base information to explore issues with the RSA algorithm that detract from the algorithms security.
Securing your Kubernetes cluster_ a step-by-step guide to success !KatiaHIMEUR1
Today, after several years of existence, an extremely active community and an ultra-dynamic ecosystem, Kubernetes has established itself as the de facto standard in container orchestration. Thanks to a wide range of managed services, it has never been so easy to set up a ready-to-use Kubernetes cluster.
However, this ease of use means that the subject of security in Kubernetes is often left for later, or even neglected. This exposes companies to significant risks.
In this talk, I'll show you step-by-step how to secure your Kubernetes cluster for greater peace of mind and reliability.
Transcript: Selling digital books in 2024: Insights from industry leaders - T...BookNet Canada
The publishing industry has been selling digital audiobooks and ebooks for over a decade and has found its groove. What’s changed? What has stayed the same? Where do we go from here? Join a group of leading sales peers from across the industry for a conversation about the lessons learned since the popularization of digital books, best practices, digital book supply chain management, and more.
Link to video recording: https://bnctechforum.ca/sessions/selling-digital-books-in-2024-insights-from-industry-leaders/
Presented by BookNet Canada on May 28, 2024, with support from the Department of Canadian Heritage.
Elevating Tactical DDD Patterns Through Object CalisthenicsDorra BARTAGUIZ
After immersing yourself in the blue book and its red counterpart, attending DDD-focused conferences, and applying tactical patterns, you're left with a crucial question: How do I ensure my design is effective? Tactical patterns within Domain-Driven Design (DDD) serve as guiding principles for creating clear and manageable domain models. However, achieving success with these patterns requires additional guidance. Interestingly, we've observed that a set of constraints initially designed for training purposes remarkably aligns with effective pattern implementation, offering a more ‘mechanical’ approach. Let's explore together how Object Calisthenics can elevate the design of your tactical DDD patterns, offering concrete help for those venturing into DDD for the first time!
Accelerate your Kubernetes clusters with Varnish CachingThijs Feryn
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Epistemic Interaction - tuning interfaces to provide information for AI supportAlan Dix
Paper presented at SYNERGY workshop at AVI 2024, Genoa, Italy. 3rd June 2024
https://alandix.com/academic/papers/synergy2024-epistemic/
As machine learning integrates deeper into human-computer interactions, the concept of epistemic interaction emerges, aiming to refine these interactions to enhance system adaptability. This approach encourages minor, intentional adjustments in user behaviour to enrich the data available for system learning. This paper introduces epistemic interaction within the context of human-system communication, illustrating how deliberate interaction design can improve system understanding and adaptation. Through concrete examples, we demonstrate the potential of epistemic interaction to significantly advance human-computer interaction by leveraging intuitive human communication strategies to inform system design and functionality, offering a novel pathway for enriching user-system engagements.
The Art of the Pitch: WordPress Relationships and SalesLaura Byrne
Clients don’t know what they don’t know. What web solutions are right for them? How does WordPress come into the picture? How do you make sure you understand scope and timeline? What do you do if sometime changes?
All these questions and more will be explored as we talk about matching clients’ needs with what your agency offers without pulling teeth or pulling your hair out. Practical tips, and strategies for successful relationship building that leads to closing the deal.
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The latest edition of the OT/ICS and IoT security Threat Landscape Report 2024 also covers:
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Sectoral targets and attacks as well as the cost of ransom
Global APT activity, AI usage, actor and tactic profiles, and implications
Rise in volumes of AI-powered cyberattacks
Major cyber events in 2024
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In-depth analysis of the cyber threat landscape across North America, South America, Europe, APAC, and the Middle East
Why are attacks on smart factories rising?
Cyber risk predictions
Axis of attacks – Europe
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Download the full report from here:
https://sectrio.com/resources/ot-threat-landscape-reports/sectrio-releases-ot-ics-and-iot-security-threat-landscape-report-2024/
Builder.ai Founder Sachin Dev Duggal's Strategic Approach to Create an Innova...Ramesh Iyer
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LF Energy Webinar: Electrical Grid Modelling and Simulation Through PowSyBl -...DanBrown980551
Do you want to learn how to model and simulate an electrical network from scratch in under an hour?
Then welcome to this PowSyBl workshop, hosted by Rte, the French Transmission System Operator (TSO)!
During the webinar, you will discover the PowSyBl ecosystem as well as handle and study an electrical network through an interactive Python notebook.
PowSyBl is an open source project hosted by LF Energy, which offers a comprehensive set of features for electrical grid modelling and simulation. Among other advanced features, PowSyBl provides:
- A fully editable and extendable library for grid component modelling;
- Visualization tools to display your network;
- Grid simulation tools, such as power flows, security analyses (with or without remedial actions) and sensitivity analyses;
The framework is mostly written in Java, with a Python binding so that Python developers can access PowSyBl functionalities as well.
What you will learn during the webinar:
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Welcome to UiPath Test Automation using UiPath Test Suite series part 4. In this session, we will cover Test Manager overview along with SAP heatmap.
The UiPath Test Manager overview with SAP heatmap webinar offers a concise yet comprehensive exploration of the role of a Test Manager within SAP environments, coupled with the utilization of heatmaps for effective testing strategies.
Participants will gain insights into the responsibilities, challenges, and best practices associated with test management in SAP projects. Additionally, the webinar delves into the significance of heatmaps as a visual aid for identifying testing priorities, areas of risk, and resource allocation within SAP landscapes. Through this session, attendees can expect to enhance their understanding of test management principles while learning practical approaches to optimize testing processes in SAP environments using heatmap visualization techniques
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1. Insights into SAP testing best practices
2. Heatmap utilization for testing
3. Optimization of testing processes
4. Demo
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Execution from the test manager
Orchestrator execution result
Defect reporting
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A New Signature Protocol Based on RSA and Elgamal Scheme
1. International Journal of Information Technology, Modeling and Computing (IJITMC) Vol. 4, No.3, August 2016
DOI: 10.5121/ijitmc.2016.4302 11
A NEW SIGNATURE PROTOCOL BASED ON RSA
AND ELGAMAL SCHEME
J. Ettanfouhi and O. Khadir
Laboratory of Mathematics, Cryptography and Mechanics, Fstm,
University Hassan II of Casablanca, Morocco
ABSTRACT
In this paper, we present a new signature scheme based on factoring and discrete logarithm problems.
Derived from a variant of ElGamal signature protocol and the RSA algorithm, this method can be seen as
an alternative protocol if known systems are broken.
KEYWORDS
Factoring, DLP, PKC, ElGamal signature scheme, RSA.
MSC: 6094A
1. INTRODUCTION
In 1977, Rivest, Shamir, and Adleman[6 ] described the famous RSA algorithm which is based
on the presumed difficulty of factoring large integers. In 1985, ElGamal [2] proposed a signature
digital protocol that uses the hardness of the discrete logarithm problem[5 p.116, 7 p. 213, 8
p. 228 ]. Since then, many similar schemes were elaborated and published[1,3].
Among them, a new variant was conceived in 2010 by the second author[ 4 ].In this work, we
apply a combination of the new variant of Elgamal and RSA algorithm to build a secure digital
signature. The efficiency of the method is discussed and its security analyzed.
The paper is organised as follows: In section 2, we describe the basic ElGamal digital signature
algorithm and its variant. Section 3 is devoted to our new digital signature method. We end with
the conclusion in section 4.
In the paper, we will respect ElGamal work notations [3]. N, Z are respectively the sets of
integers and non-negative integers. For every positive integer n , we denote by ZZ n/ the finite
ring of modular integers and by *
)/( ZZ n the multiplicative group of its invertible elements. Let
a ,b , c be three integers. The GCD of a and b is written as ),( bagcd . We write
][0.1 ccmba ≡ if c divides ba − , and cba mod= if a is the rest in the division of b by
c . The bit length of n is the number of bits in its binary model, with n an integer .We start by
presenting the basic ElGamal digital signature algorithm and its variant:
2. International Journal of Information Technology, Modeling and Computing (IJITMC) Vol. 4, No.3, August 2016
12
2. ELGAMAL SIGNATURE SCHEME
In this section we recall ElGamal signature scheme[2] and its variant[4].
1. Alice chooses three numbers:
- p , a large prime integer.
- α , a primitive root of the finite multiplicative group *
)/( ZZ p
- x , a random element of {1,2,..., 1−p }
2. She computes x
y α= mod p . Alice’s public key is ),,( yp α , and x is her private key.
3. To sign the document m , Alice must solve the problem:
(1)
where sr, are the unknown variables.
Alice fixes arbitrary r to be k
r α= mod p , where k is chosen randomly and invertible
modulo 1−p . Equation (1) is then equivalent to:
(2)
Since Alice has the secret key x , and as the number k is invertible modulo 1−p , she calculates
the other unknown variable s by
(3)
4. Bob can verify the signature by checking if congruence (1) is valid for the variables r and s
given by Alice.
3. VARIANT OF ELGAMAL SIGNATURE SCHEME
We present a variant of ElGamal digital signature system.
This variant Error! Reference source not found. is based on the equation:
(4)
tsr ,, are the unknown parameters, and ),,( yp α are Alice public keys. p is an integer (a large
prime). α is a primitive root of *
pZ . y is calculated by x
y α= mod p . x is a random
element of {1,2,...,p-1}.
3. International Journal of Information Technology, Modeling and Computing (IJITMC) Vol. 4, No.3, August 2016
13
Let )(= Mhm , where h is a hash function, and M the message to be signed by Alice.
To give the solution (3), she fixes randomly r as pmodr k
α≡ , and s to be pmods l
α≡ ,
where lk, are selected arbitrary in {1,2,...,p-1}.
Equation (3) is then equivalent to:
(5)
as Alice recognize the values of xmlksr ,,,,, , she is able to calculate the last unknown variable
t .
Bob verify the signature by verifying the congruence (4).
this system does not use the extended Euclidean algorithm for calculating 1)(1
−−
pmodk .
We clarify the scheme by the example given by the creator of this alternative[4].
3.1 EXAMPLE
Let ),,( yp α be Alice public keys where: 509=p , 2=α and 482=y . We assert that we are
not confident if using a small value of α does not abate the protocol. The private key is
281=x . Suppose that Alice wants to generate a signature for the document M for which
432[508])( ≡≡ Mhm with the exponents 208=k and 386=l are randomly taken. She
computes ]332[2208
pr k
≡≡≡ α , ]39[2386
ps l
≡≡≡ α and 1]440[ −≡++≡ plmksrxt .
Bob or anyone can verify the relation ][psry msrt
≡α . Indeed, we find that ]436[p≡α and
]436[psry msr
≡ .
4. OUR PROTOCOL
4.1 DESCRIPTION
In this section, we describe our new digital signature. The protocol is based simultaneously on
two hard problems.
We assume first that h is a public secure hash function like SHA1[5 p.348, 7 p. 242 , 8
p.133].
We suppose that Alice public keys are ),,,( eyP α where:
- 12= +pqP , p , q are three primes.
- α , a primitive root of the multiplicative group *
)/( ZZ p .
- x
y α= mod P , where x is the private key of Alice, which is randomly taken in
1}{1,2,..., −P .
4. International Journal of Information Technology, Modeling and Computing (IJITMC) Vol. 4, No.3, August 2016
14
- Element e is the public exponent in the RSA cryptosystem.
We propose the following protocol:
If Alice wants to sign the message M , she must give a solution for the modular equation:
(6)
where )(= Mhm mod p , and r , s , t are unknown.
To solve equation (5) , Alice starts by putting:
(7)
(8)
Equation (5) becomes:
(9)
Alice uses the new variant of Elgamal algorithm[4] to solve equation (9) and to get the values of
r′ , s′ and t .
Then with her RSA private key she solves equations (7) and (8) . The cupel r and s is her
signature for the message M .
Bob or anybody can check that the signature is valid by replacing r , s and t in relation (5) .
4.2 EXAMPLE
Let us illustrate the method by the following example.
Suppose that Alice’s public key is: 104543=1313*167*2= +P , 5=α , 23292=y , 7=e .
The private keys for RSA and ElGamal systems are respectively: 9502=x , 7399=d .
Assume that 12345=)(= Mhm is the hashed message that she likes to sign.
If she takes Randomly 845=k and 2561=l .
She will find from equation 8 that 17744=r′ , 31839=s′ .
Relation 4 implies 57764=t .
Alice uses (6) and (7) to obtain:
5. International Journal of Information Technology, Modeling and Computing (IJITMC) Vol. 4, No.3, August 2016
15
r ≡ 1][ −′ Pr d
≡ 75282
s ≡ 1][ −′ Ps d
≡ 19005.
To verify Bob puts 62833=mod= PA t
α , 79849=mod= 1mod
PyB Per −
,
83421=mod1)mod(= 1)mod(
PPrC Pese −
− and 212997=mod1)mod(= PPsD me
− , and
checks if PDCBA mod**= .
4.3 SECURITY ANALYSIS
Now that we have presented the protocol, we will discuss some possible attacks. Assume that
Oscar is Alice’s opponent.
ATTACK 1: If the attacker try to imitate the computation made by Alice, he can find r and s ,
but to find t he needs the value of the private key x to solve equation 4 .
ATTACK 2: Suppose Oscar is capable to solve the discrete logarithm problem [2]. He cannot
calculate r and s from equation (7) and (8) he will be confronted to the factorisation of a
large composite modulus [5,8].
ATTACK 3: Suppose Oscar is capable to solve RSA equations (7) and (8) . Oscar cannot get t
from equation (9) since x is Alice’s secret key. If he tries to get t from equation (4) , he will be
stopped by the discrete logarithm problem.
4.4 COMPLEXITY OF OUR ALGORITHM
As in [1], let expT , multT and hT be appropriately the time to calculate an exponentiation, a
multiplication and hash function of a document M . We neglect the time needed for modular
substraction, additions, comparisons and apply the conversion multexp TT 240= .
4.4.1 SIGNATURE COMPLEXITY
To sign the message M , Alice must compute the six parameters:
)(= Mhm mod P , k
r α≡′ ][P , l
s α≡′ ][P , d
rr ′≡ 1][ −P , d
ss ′≡ 1][ −P ,
lmskrxt +′+′≡ 1][ −P .
Alice needs to perform four modular exponentiations, three modular multiplications and one hash
function computation. So the global required time is :
hmulthmultexp TTTTTT +++ 963=34=1
4.4.2 VERIFICATION COMPLEXITY
Bob should calculate 4 exponentiations, 2 multiplications and one hash function. So the global
required time is :
hmulthmultexp TTTTTT +++ 962=24=2
6. International Journal of Information Technology, Modeling and Computing (IJITMC) Vol. 4, No.3, August 2016
16
5. CONCLUSION
In this work, we proposed a new signature protocol that can be an alternative if old systems are
broken. Our method is based simultanyously on RSA cryptosystem and DLP.
ACKNOWLEDGEMENTS
This work is supported by the MMS e-orientation project.
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Authors
Jaouad Ettanfouhi holds an engineer degree in Computer Science from the University of
Hassan II of Casablanca (2011). Member of the laboratory of Mathematics, Cryptography
and Mechanics, he is preparing a thesis in public key cryptography.
Dr Omar Khadir received his Ph.D. degree in Computer Science from the University
of Rouen, France (1994). Co-founder of the Laboratory of Mathematics, Cryptography
and Mechanics at the University of Hassan II Casablanca, Morocco, where he is a
professor in the Department of Mathematics. He teaches cryptography for graduate
students preparing a degree in computer science. His current research interests include
public key cryptography, digital signature, primality, factorisation of large integers and
more generally, all subjects connected to the information technology.