Abstract: The Elliptic Curve Digital Signature algorithm-based X509v3 certificates are becoming more popular due to their short public and private key sizes. Moreover, these certificates can be stored in Internet of Things (IoT) devices, with limited resources, using less memory and transmitted in network security protocols, such as Internet Key Exchange (IKE), Transport Layer Security (TLS) and Secure Shell (SSH) with less bandwidth. The proposed method gives another advantage, in that it increases the performance of the above-mentioned protocols in terms of key exchange by saving one scalar multiplication operation.
Abstract: Greater common divisor (GCD) attack is an attack that relies on the polynomial structure of the cryptosystem. This attack required two plaintexts differ from a fixed number and encrypted under same modulus. This paper reports a security reaction of Lucas Based El-Gamal Cryptosystem in the Elliptic Curve group over finite field under GCD attack. Lucas Based El-Gamal Cryptosystem in the Elliptic Curve group over finite field was exposed mathematically to the GCD attack using GCD and Dickson polynomial. The result shows that the cryptanalyst is able to get the plaintext without decryption by using GCD attack. Thus, the study concluded that it is highly perilous when two plaintexts have a slight difference from a fixed number in the same Elliptic curve group over finite field.
Abstract: Fingerprints are suitable as long-term markers of human identity since they provide detailed and unique individual features which are difficult to alter and durable over life time. In this paper, we propose an algorithm to encrypt and decrypt fingerprint images by using a specially designed Elliptic Curve Cryptography (ECC) procedure based on block ciphers. In addition, to increase the confusing effect of fingerprint encryption, we also utilize a chaotic-behaved method called Arnold Cat Map (ACM) for a 2D scrambling of pixel locations in our method. Experimental results are carried out with various types of efficiency and security analyses. As a result, we demonstrate that the proposed fingerprint encryption/decryption algorithm is advantageous in several different aspects including efficiency, security and flexibility. In particular, using this algorithm, we achieve a margin of about 0.1% in the test of Number of Pixel Changing Rate (NPCR) values comparing to the-state-of-the-art performances.
Abstract: Internet of Things (IoT) is a powerful industry system, which end-devices are interconnected and automated, allowing the devices to analyze data and execute actions based on the analysis. The IoT technology leverages the technology of Radio-Frequency Identification (RFID) and Wireless Sensor Network (WSN), including mobile and sensor. These technologies contribute to the evolution of IoT. However, due to more devices are connected each other in the Internet, and data from various sources exchanged between things, confidentiality of the data becomes a major concern. This paper focuses on one of the major challenges in IoT; authentication, in order to preserve data integrity and confidentiality are in place. A few solutions are reviewed based on papers from the last few years. One of the proposed solutions is securing the communication between IoT devices and cloud servers with Elliptic Curve Cryptograhpy (ECC) based mutual authentication protocol. This solution focuses on Hyper Text Transfer Protocol (HTTP) cookies as security parameter. Next proposed solution is using keyed-hash scheme protocol to enable IoT devices to authenticate each other without the presence of a central control server. Another proposed solution uses Physical Unclonable Function (PUF) based mutual authentication protocol. It emphasizes on tamper resistant and resource-efficient technology, which equals a 3-way handshake security protocol.
Abstract: This paper begins by describing basic properties of finite field and elliptic curve cryptography over prime field and binary field. Then we discuss the discrete logarithm problem for elliptic curves and its properties. We study the general common attacks on elliptic curve discrete logarithm problem such as the Baby Step, Giant Step method, Pollard’s rho method and Pohlig-Hellman method, and describe in detail experiments of these attacks over prime field and binary field. The paper finishes by describing expected running time of the attacks and suggesting strong elliptic curves that are not susceptible to these attacks.c
Abstract: Elliptic curve discrete logarithm problem(ECDLP) is
one of problems on which the security of pairing-based cryptography
is based. This paper considers Pollard’s rho method to evaluate
the security of ECDLP on Barreto-Naehrig(BN) curve that is an
efficient pairing-friendly curve. Some techniques are proposed to
make the rho method efficient. Especially, the group structure on
BN curve, distinguished point method, and Montgomery trick are
well-known techniques. This paper applies these techniques and
shows its optimization. According to the experimental results for
which a large-scale parallel system with MySQL is applied, 94-bit
ECDLP was solved about 28 hours by parallelizing 71 computers.
Abstract: In this article we will study the elliptic curve defined
over the ring An and we define the mathematical operations of ECC,
which provides a high security and advantage for wireless
applications compared to other asymmetric key cryptosystem.
Abstract: Shifted polynomial basis (SPB) is a variation of
polynomial basis representation. SPB has potential for efficient
bit level and digi -level implementations of multiplication over
binary extension fields with subquadratic space complexity. For
efficient implementation of pairing computation with large finite
fields, this paper presents a new SPB multiplication algorithm based
on Karatsuba schemes, and used that to derive a novel scalable
multiplier architecture. Analytical results show that the proposed
multiplier provides a trade-off between space and time complexities.
Our proposed multiplier is modular, regular, and suitable for very
large scale integration (VLSI) implementations. It involves less
area complexity compared to the multipliers based on traditional
decomposition methods. It is therefore, more suitable for efficient
hardware implementation of pairing based cryptography and elliptic
curve cryptography (ECC) in constraint driven applications.
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: In this work, we consider the rational points on elliptic curves over finite fields Fp where p ≡ 5 (mod 6). We obtain results on the number of points on an elliptic curve y2 ≡ x3 + a3(mod p), where p ≡ 5 (mod 6) is prime. We give some results concerning the sum of the abscissae of these points. A similar case where p ≡ 1 (mod 6) is considered in [5]. The main difference between two cases is that when p ≡ 5 (mod 6), all elements of Fp are cubic residues.
Abstract: Recently, Jia et al. proposed a remote user authentication scheme using bilinear pairings and an Elliptic Curve Cryptosystem (ECC). However, the scheme is vulnerable to privileged insider attack at their proposed registration phase and to forgery attack at their proposed authentication phase. In addition, the scheme can be vulnerable to server spoofing attack because it does not provide mutual authentication between the user and the remote server. Therefore, this paper points out that the Jia et al. scheme is vulnerable to the above three attacks.
Abstract: In this work, we study elliptic divisibility sequences
over finite fields. Morgan Ward in [14], [15] gave arithmetic theory
of elliptic divisibility sequences and formulas for elliptic divisibility
sequences with rank two over finite field Fp. We study elliptic
divisibility sequences with rank three, four and five over a finite field
Fp, where p > 3 is a prime and give general terms of these sequences
and then we determine elliptic and singular curves associated with
these sequences.
Abstract: In elliptic curve theory, number of rational points on
elliptic curves and determination of these points is a fairly important
problem. Let p be a prime and Fp be a finite field and k ∈ Fp. It
is well known that which points the curve y2 = x3 + kx has and
the number of rational points of on Fp. Consider the circle family
x2 + y2 = r2. It can be interesting to determine common points of
these two curve families and to find the number of these common
points. In this work we study this problem.
Abstract: SIP (Session Initiation Protocol), using HTML based
call control messaging which is quite simple and efficient, is being
replaced for VoIP networks recently. As for authentication and
authorization purposes there are many approaches and considerations
for securing SIP to eliminate forgery on the integrity of SIP
messages. On the other hand Elliptic Curve Cryptography has
significant advantages like smaller key sizes, faster computations on
behalf of other Public Key Cryptography (PKC) systems that obtain
data transmission more secure and efficient. In this work a new
approach is proposed for secure SIP authentication by using a public
key exchange mechanism using ECC. Total execution times and
memory requirements of proposed scheme have been improved in
comparison with non-elliptic approaches by adopting elliptic-based
key exchange mechanism.
Abstract: In this work, we first give in what fields Fp, the cubic
root of unity lies in F*p, in Qp and in K*p where Qp and K*p denote
the sets of quadratic and non-zero cubic residues modulo p. Then we
use these to obtain some results on the classification of the Bachet
elliptic curves y2 ≡ x3 +a3 modulo p, for p ≡ 1 (mod 6) is prime.
Abstract: With the rapid development of wireless mobile communication, applications for mobile devices must focus on network security. In 2008, Chang-Chang proposed security improvements on the Lu et al.-s elliptic curve authentication key agreement protocol for wireless mobile networks. However, this paper shows that Chang- Chang-s improved protocol is still vulnerable to off-line password guessing attacks unlike their claims.
Abstract: In this paper the authors propose a protocol, which uses Elliptic Curve Cryptography (ECC) based on the ElGamal-s algorithm, for sending small amounts of data via an authentication server. The innovation of this approach is that there is no need for a symmetric algorithm or a safe communication channel such as SSL. The reason that ECC has been chosen instead of RSA is that it provides a methodology for obtaining high-speed implementations of authentication protocols and encrypted mail techniques while using fewer bits for the keys. This means that ECC systems require smaller chip size and less power consumption. The proposed protocol has been implemented in Java to analyse its features and vulnerabilities in the real world.
Abstract: Let F(x, y) = ax2 + bxy + cy2 be a positive definite
binary quadratic form with discriminant Δ whose base points lie on
the line x = -1/m for an integer m ≥ 2, let p be a prime number
and let Fp be a finite field. Let EF : y2 = ax3 + bx2 + cx be an
elliptic curve over Fp and let CF : ax3 + bx2 + cx ≡ 0(mod p) be
the cubic congruence corresponding to F. In this work we consider
some properties of positive definite quadratic forms, elliptic curves
and cubic congruences.
Abstract: Blind signatures enable users to obtain valid signatures for a message without revealing its content to the signer. This paper presents a new blind signature scheme, i.e. identity-based blind signature scheme with message recovery. Due to the message recovery property, the new scheme requires less bandwidth than the identitybased blind signatures with similar constructions. The scheme is based on modified Weil/Tate pairings over elliptic curves, and thus requires smaller key sizes for the same level of security compared to previous approaches not utilizing bilinear pairings. Security and efficiency analysis for the scheme is provided in this paper.
Abstract: Deniable authentication is a new protocol which not only enables a receiver to identify the source of a received message but also prevents a third party from identifying the source of the message. The proposed protocol in this paper makes use of bilinear pairings over elliptic curves, as well as the Diffie-Hellman key exchange protocol. Besides the security properties shared with previous authentication protocols, the proposed protocol provides the same level of security with smaller public key sizes.