Abstract: Lenstra’s attack uses Chinese remainder theorem as a tool and requires a faulty signature to be successful. This paper reports on the security responses of fourth and sixth order Lucas based (LUC4,6) cryptosystem under the Lenstra’s attack as compared to the other two Lucas based cryptosystems such as LUC and LUC3 cryptosystems. All the Lucas based cryptosystems were exposed mathematically to the Lenstra’s attack using Chinese Remainder Theorem and Dickson polynomial. Result shows that the possibility for successful Lenstra’s attack is less against LUC4,6 cryptosystem than LUC3 and LUC cryptosystems. Current study concludes that LUC4,6 cryptosystem is more secure than LUC and LUC3 cryptosystems in sustaining against Lenstra’s attack.
Abstract: Inter-agent communication manager facilitates communication among mobile agents via message passing mechanism. Until now, all Foundation for Intelligent Physical Agents (FIPA) compliant agent systems are capable of exchanging messages following the standard format of sending and receiving messages. Previous works tend to secure messages to be exchanged among a community of collaborative agents commissioned to perform specific tasks using cryptosystems. However, the approach is characterized by computational complexity due to the encryption and decryption processes required at the two ends. The proposed approach to secure agent communication allows only agents that are created by the host agent server to communicate via the agent communication channel provided by the host agent platform. These agents are assumed to be harmless. Therefore, to secure communication of legitimate agents from intrusion by external agents, a 2-phase policy enforcement system was developed. The first phase constrains the external agent to run only on the network server while the second phase confines the activities of the external agent to its execution environment. To implement the proposed policy, a controller agent was charged with the task of screening any external agent entering the local area network and preventing it from migrating to the agent execution host where the legitimate agents are running. On arrival of the external agent at the host network server, an introspector agent was charged to monitor and restrain its activities. This approach secures legitimate agent communication from Man-in-the Middle and Replay attacks.
Abstract: The arithmetic operations over GF(2m) have been
extensively used in error correcting codes and public-key
cryptography schemes. Finite field arithmetic includes addition,
multiplication, division and inversion operations. Addition is very
simple and can be implemented with an extremely simple circuit.
The other operations are much more complex. The multiplication
is the most important for cryptosystems, such as the elliptic
curve cryptosystem, since computing exponentiation, division, and
computing multiplicative inverse can be performed by computing
multiplication iteratively. In this paper, we present a parallel
computation algorithm that operates Montgomery multiplication over
finite field using redundant basis. Also, based on the multiplication
algorithm, we present an efficient semi-systolic multiplier over finite
field. The multiplier has less space and time complexities compared
to related multipliers. As compared to the corresponding existing
structures, the multiplier saves at least 5% area, 50% time, and 53%
area-time (AT) complexity. Accordingly, it is well suited for VLSI
implementation and can be easily applied as a basic component for
computing complex operations over finite field, such as inversion and
division operation.
Abstract: One of the crucial parameters of digital cryptographic
systems is the selection of the keys used and their distribution. The
randomness of the keys has a strong impact on the system’s security
strength being difficult to be predicted, guessed, reproduced, or
discovered by a cryptanalyst. Therefore, adequate key randomness
generation is still sought for the benefit of stronger cryptosystems.
This paper suggests an algorithm designed to generate and test
pseudo random number sequences intended for cryptographic
applications. This algorithm is based on mathematically manipulating
a publically agreed upon information between sender and receiver
over a public channel. This information is used as a seed for
performing some mathematical functions in order to generate a
sequence of pseudorandom numbers that will be used for
encryption/decryption purposes. This manipulation involves
permutations and substitutions that fulfill Shannon’s principle of
“confusion and diffusion”. ASCII code characters were utilized in the
generation process instead of using bit strings initially, which adds
more flexibility in testing different seed values. Finally, the obtained
results would indicate sound difficulty of guessing keys by attackers.
Abstract: Although there is no theoretical weakness in a cryptographic algorithm, Side Channel Analysis can find out some secret data from the physical implementation of a cryptosystem. The analysis is based on extra information such as timing information, power consumption, electromagnetic leaks or even sound which can be exploited to break the system. Differential Power Analysis is one of the most popular analyses, as computing the statistical correlations of the secret keys and power consumptions. It is usually necessary to calculate huge data and takes a long time. It may take several weeks for some devices with countermeasures. We suggest and evaluate the methods to shorten the time to analyze cryptosystems. Our methods include distributed computing and parallelized processing.
Abstract: Finding suitable non-supersingular elliptic curves for
pairing-based cryptosystems becomes an important issue for the
modern public-key cryptography after the proposition of id-based
encryption scheme and short signature scheme. In previous work
different algorithms have been proposed for finding such elliptic
curves when embedding degree k ∈ {3, 4, 6} and cofactor h ∈ {1, 2, 3,
4, 5}. In this paper a new method is presented to find more
non-supersingular elliptic curves for pairing-based cryptosystems with
general embedding degree k and large values of cofactor h. In
addition, some effective parameters of these non-supersingular elliptic
curves are provided in this paper.
Abstract: Cellular automata have been used for design of cryptosystems. Recently some secret sharing schemes based on linear memory cellular automata have been introduced which are used for both text and image. In this paper, we illustrate that these secret sharing schemes are vulnerable to dishonest participants- collusion. We propose a cheating model for the secret sharing schemes based on linear memory cellular automata. For this purpose we present a novel uniform model for representation of all secret sharing schemes based on cellular automata. Participants can cheat by means of sending bogus shares or bogus transition rules. Cheaters can cooperate to corrupt a shared secret and compute a cheating value added to it. Honest participants are not aware of cheating and suppose the incorrect secret as the valid one. We prove that cheaters can recover valid secret by removing the cheating value form the corrupted secret. We provide methods of calculating the cheating value.
Abstract: S-boxes (Substitution boxes) are keystones of modern
symmetric cryptosystems (block ciphers, as well as stream ciphers).
S-boxes bring nonlinearity to cryptosystems and strengthen their
cryptographic security. They are used for confusion in data security
An S-box satisfies the strict avalanche criterion (SAC), if and only if
for any single input bit of the S-box, the inversion of it changes each
output bit with probability one half. If a function (cryptographic
transformation) is complete, then each output bit depends on all of
the input bits. Thus, if it were possible to find the simplest Boolean
expression for each output bit in terms of the input bits, each of these
expressions would have to contain all of the input bits if the function
is complete. From some important properties of S-box, the most
interesting property SAC (Strict Avalanche Criterion) is presented
and to analyze this property three analysis methods are proposed.
Abstract: Long number multiplications (n ≥ 128-bit) are a
primitive in most cryptosystems. They can be performed better by
using Karatsuba-Ofman technique. This algorithm is easy to
parallelize on workstation network and on distributed memory, and
it-s known as the practical method of choice. Multiplying long
numbers using Karatsuba-Ofman algorithm is fast but is highly
recursive. In this paper, we propose different designs of
implementing Karatsuba-Ofman multiplier. A mixture of sequential
and combinational system design techniques involving pipelining is
applied to our proposed designs. Multiplying large numbers can be
adapted flexibly to time, area and power criteria. Computationally
and occupation constrained in embedded systems such as: smart
cards, mobile phones..., multiplication of finite field elements can be
achieved more efficiently. The proposed designs are compared to
other existing techniques. Mathematical models (Area (n), Delay (n))
of our proposed designs are also elaborated and evaluated on
different FPGAs devices.
Abstract: Recently, wireless sensor networks have been paid
more interest, are widely used in a lot of commercial and military
applications, and may be deployed in critical scenarios (e.g. when a
malfunctioning network results in danger to human life or great
financial loss). Such networks must be protected against human
intrusion by using the secret keys to encrypt the exchange messages
between communicating nodes. Both the symmetric and asymmetric
methods have their own drawbacks for use in key management. Thus,
we avoid the weakness of these two cryptosystems and make use of
their advantages to establish a secure environment by developing the
new method for encryption depending on the idea of code
conversion. The code conversion-s equations are used as the key for
designing the proposed system based on the basics of logic gate-s
principals. Using our security architecture, we show how to reduce
significant attacks on wireless sensor networks.
Abstract: Key management represents a major and the most
sensitive part of cryptographic systems. It includes key generation,
key distribution, key storage, and key deletion. It is also considered
the hardest part of cryptography. Designing secure cryptographic
algorithms is hard, and keeping the keys secret is much harder.
Cryptanalysts usually attack both symmetric and public key
cryptosystems through their key management. We introduce a
protocol to exchange cipher keys over insecure communication
channel. This protocol is based on public key cryptosystem,
especially elliptic curve cryptosystem. Meanwhile, it tests the cipher
keys and selects only the good keys and rejects the weak one.
Abstract: This paper is introduced a modification to Diffie-
Hellman protocol to be applicable on the decimal numbers, which
they are the numbers between zero and one. For this purpose we
extend the theory of the congruence. The new congruence is over
the set of the real numbers and it is called the “real congruence"
or the “real modulus". We will refer to the existing congruence by
the “integer congruence" or the “integer modulus". This extension
will define new terms and redefine the existing terms. As the
properties and the theorems of the integer modulus are extended as
well. Modified Diffie-Hellman key exchange protocol is produced a
sharing, secure and decimal secret key for the the cryptosystems that
depend on decimal numbers.
Abstract: Polynomial bases and normal bases are both used for
elliptic curve cryptosystems, but field arithmetic operations such as
multiplication, inversion and doubling for each basis are implemented
by different methods. In general, it is said that normal bases, especially
optimal normal bases (ONB) which are special cases on normal bases,
are efficient for the implementation in hardware in comparison with
polynomial bases. However there seems to be more examined by
implementing and analyzing these systems under similar condition. In
this paper, we designed field arithmetic operators for each basis over
GF(2233), which field has a polynomial basis recommended by SEC2
and a type-II ONB both, and analyzed these implementation results.
And, in addition, we predicted the efficiency of two elliptic curve
cryptosystems using these field arithmetic operators.
Abstract: The major building block of most elliptic curve cryptosystems
are computation of multi-scalar multiplication. This paper
proposes a novel algorithm for simultaneous multi-scalar multiplication,
that is by employing addition chains. The previously known
methods utilizes double-and-add algorithm with binary representations.
In order to accomplish our purpose, an efficient empirical
method for finding addition chains for multi-exponents has been
proposed.
Abstract: Modular multiplication is the basic operation
in most public key cryptosystems, such as RSA, DSA, ECC,
and DH key exchange. Unfortunately, very large operands
(in order of 1024 or 2048 bits) must be used to provide
sufficient security strength. The use of such big numbers
dramatically slows down the whole cipher system, especially
when running on embedded processors.
So far, customized hardware accelerators - developed on
FPGAs or ASICs - were the best choice for accelerating
modular multiplication in embedded environments. On the
other hand, many algorithms have been developed to speed
up such operations. Examples are the Montgomery modular
multiplication and the interleaved modular multiplication
algorithms. Combining both customized hardware with
an efficient algorithm is expected to provide a much faster
cipher system.
This paper introduces an enhanced architecture for computing
the modular multiplication of two large numbers X
and Y modulo a given modulus M. The proposed design is
compared with three previous architectures depending on
carry save adders and look up tables. Look up tables should
be loaded with a set of pre-computed values. Our proposed
architecture uses the same carry save addition, but replaces
both look up tables and pre-computations with an enhanced
version of sign detection techniques. The proposed architecture
supports higher frequencies than other architectures.
It also has a better overall absolute time for a single operation.
Abstract: This paper examines the implementation of RC5 block cipher for digital images along with its detailed security analysis. A complete specification for the method of application of the RC5 block cipher to digital images is given. The security analysis of RC5 block cipher for digital images against entropy attack, bruteforce, statistical, and differential attacks is explored from strict cryptographic viewpoint. Experiments and results verify and prove that RC5 block cipher is highly secure for real-time image encryption from cryptographic viewpoint. Thorough experimental tests are carried out with detailed analysis, demonstrating the high security of RC5 block cipher algorithm.
Abstract: Groups where the discrete logarithm problem (DLP) is believed to be intractable have proved to be inestimable building blocks for cryptographic applications. They are at the heart of numerous protocols such as key agreements, public-key cryptosystems, digital signatures, identification schemes, publicly verifiable secret sharings, hash functions and bit commitments. The search for new groups with intractable DLP is therefore of great importance.The goal of this article is to study elliptic curves over the ring Fq[], with Fq a finite field of order q and with the relation n = 0, n ≥ 3. The motivation for this work came from the observation that several practical discrete logarithm-based cryptosystems, such as ElGamal, the Elliptic Curve Cryptosystems . In a first time, we describe these curves defined over a ring. Then, we study the algorithmic properties by proposing effective implementations for representing the elements and the group law. In anther article we study their cryptographic properties, an attack of the elliptic discrete logarithm problem, a new cryptosystem over these curves.