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Ruma Kareem K. Ajeena

Bio: Ruma Kareem K. Ajeena is an academic researcher from University of Babylon. The author has contributed to research in topics: Scalar multiplication & Elliptic curve. The author has an hindex of 5, co-authored 19 publications receiving 48 citations.

Papers
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Journal ArticleDOI
TL;DR: A new approach called integer sub-decomposition (ISD) based on the GLV idea to compute any multiple kP of a point P of order n lying on an elliptic curve E using two fast endomorphisms ψ1 and ψ2 of E over prime field Fp to calculate kP.
Abstract: In this work, we proposed a new approach called integer sub-decomposition (ISD) based on the GLV idea to compute any multiple kP of a point P of order n lying on an elliptic curve E. This approach uses two fast endomorphisms ψ1 and ψ2 of E over prime field Fp to calculate kP. The basic idea of ISD method is to sub-decompose the returned values k1 and k2 lying outside the range p n from the GLV decomposition of a multiplier k into integers k11, k12, k21 and k22 with − p n < k11, k12, k21, k22 < p n. These integers are computed by solving a closest vector problem in lattice. The new proposed algorithms and implementation results are shown and discussed in this study.

19 citations

Journal ArticleDOI
TL;DR: An integer sub-decomposition (ISD) with explicit constant is proved and the gap in the proof of the bound of kernel K vectors of the reduction map T : (a, b) → a + λb(mod n) on ISD method will be filled through the analysis of the multiplier k.
Abstract: This study proposes a new approach called, integer sub-decomposition (ISD), to compute any multiple kP of a point P of order n lying on an elliptic curve Our method depends, in computations, on fast endomorphisms ψ1 and ψ2 of elliptic curve over prime fields The integer sub-decomposition to multiple kP , when the value of k is decomposed into two values k1 and k2, where both values or one of them is not bounded by ±C √n, is illustrated in the following formula: kP = k11P + k12[λ1]P + k21P + k22[λ2]P = k11P + k12ψ1(P ) + k21P + k22ψ2(P ) where −C√n < k11, k12, k21, k22 < C √ n The integers k11, k12, k21 and k22 are computed by solving a closest vector problem in lattice Consequently, as for this sub-decomposition, we have managed to increase the percentage of a successful computation of kP Moreover, the gap in the proof of the bound of kernel K vectors of the reduction map T : (a, b) → a + λb(mod n) on ISD method will be filled through the analysis of the multiplier k, using two fast endomorphisms with minimal polynomials X2 + rXi + si for i = 1, 2, 3 In particular, we prove an integer sub-decomposition (ISD) with explicit constant

8 citations

Proceedings ArticleDOI
01 Apr 2017
TL;DR: This work proposes improving the EEDSA through computing an elliptic curve scalar multiplication by employing the sub-decomposition of integer which is known by ISD method instead of using doubling and addition points on E over a prime field Fp.
Abstract: The elliptic ElGamal digital signature algorithm (EEDSA) has been created based on the ElGamal public key cryptosystem (EPKC) and the algorithm of the digital signature (DSA), defined on the elliptic curves, which was accepted in several (ANSI, IEEE, NIST and ISO) standards. The processes to generate keys, compute a signature and verify this signature in EEDSA require computing the elliptic curve scalar multiplications kP. This work proposes improving the EEDSA through computing an elliptic curve scalar multiplication by employing the sub-decomposition of integer which is known by ISD method instead of using doubling and addition points on E over a prime field Fp. The proposed method, namely the EEDSA-ISD algorithm, is benefited from the fast computations in the ISD method, which is depended on the sub-decomposition of the scalars in scalar multiplications. The EEDSA-ISD method also depends on speeding the computations of the efficiently computable endomorphisms of elliptic curve E over finite fields in ISD method. On the other hand, the security level of the improved ECDSA-ISD algorithm is determined based on the hardness to solve the elliptic curve discrete logarithm problem (ECDLP) from its sub-decomposition. So, for these reasons, the improved EEDSA-ISD algorithm is considered as more fast and secure to resist the ECDLP attacks. Therefore, it is more efficient in compared to the original EEDSA.

7 citations

Proceedings ArticleDOI
01 Aug 2019
TL;DR: The smaller key sizes and the efficient implementations on the elliptic curve cryptography (ECC) gave the same level of security in comparison with the RSA (Rivest-Shamir- Adleman) and other cryptosystems.
Abstract: Elliptic curves play a major role in cryptography. It used increasingly to form the public key cryptosystems and digital signature schemes. The smaller key sizes and the efficient implementations on the elliptic curve cryptography (ECC) gave the same level of security in comparison with the RSA (Rivest-Shamir- Adleman) and other cryptosystems. The security on the ECC depending on the hardness of the elliptic curve discrete logarithm problem (ECDLP) to solve. The efficiency of the ECC is determined based on the efficient computation of the scalar multiplication on elliptic curves defined over the finite fields. A scalar multiplication is considered as a core operation in the ECC. It is not only the main computational operation but it also forms a central time-consuming process. The efficient performances of scalar multiplication directly determine the ECC performance.

6 citations


Cited by
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Journal ArticleDOI
TL;DR: The aim is to overcome the problem which has not been explained in ECDSA schemes of both Liao and Shen and Chande and Lee by introducing the unknown parameters which are used in the verification of the signature.
Abstract: Elliptic Curve Digital Signature Algorithm (ECDSA) is a public key cryptographic algorithm based on the hardness of the Elliptic Curve Discrete Logarithm Problem (ECDLP), it is used to ensure users...

17 citations

Proceedings ArticleDOI
01 Apr 2017
TL;DR: This work proposes improving the EEDSA through computing an elliptic curve scalar multiplication by employing the sub-decomposition of integer which is known by ISD method instead of using doubling and addition points on E over a prime field Fp.
Abstract: The elliptic ElGamal digital signature algorithm (EEDSA) has been created based on the ElGamal public key cryptosystem (EPKC) and the algorithm of the digital signature (DSA), defined on the elliptic curves, which was accepted in several (ANSI, IEEE, NIST and ISO) standards. The processes to generate keys, compute a signature and verify this signature in EEDSA require computing the elliptic curve scalar multiplications kP. This work proposes improving the EEDSA through computing an elliptic curve scalar multiplication by employing the sub-decomposition of integer which is known by ISD method instead of using doubling and addition points on E over a prime field Fp. The proposed method, namely the EEDSA-ISD algorithm, is benefited from the fast computations in the ISD method, which is depended on the sub-decomposition of the scalars in scalar multiplications. The EEDSA-ISD method also depends on speeding the computations of the efficiently computable endomorphisms of elliptic curve E over finite fields in ISD method. On the other hand, the security level of the improved ECDSA-ISD algorithm is determined based on the hardness to solve the elliptic curve discrete logarithm problem (ECDLP) from its sub-decomposition. So, for these reasons, the improved EEDSA-ISD algorithm is considered as more fast and secure to resist the ECDLP attacks. Therefore, it is more efficient in compared to the original EEDSA.

7 citations

Journal ArticleDOI
TL;DR: In this article, a new graph has been defined as a main point to design a new version of an asymmetric encryption scheme, which is formed based on the scalar multiplication operation on elliptic surfaces.
Abstract: In this work, a new graph has been defined as a main point to design a new version of an asymmetric encryption scheme. This graph is formed based on the scalar multiplication operation on elliptic ...

5 citations

Book ChapterDOI
15 Feb 2020
TL;DR: Different types of IDS are compared and criticized which explores the vulnerability of the system.
Abstract: Intrusion Detection System (IDS) is used to protect a system or a computer network from different kinds of anomaly attacks. Different detection techniques have been discussed on network-based IDS. The study has been done on the operational procedures of network based open source IDS tool Snort based intrusion detection system, which can read every incoming or outgoing packet through a network and alert the admin accordingly. In this paper, Different types of IDS are compared and criticized which explores the vulnerability of the system. To check every packet, Snort uses a central database system of signature. A layered database system has been proposed to upgrade system performance. An analytical operation has been conveyed on the proposed solution and compared with the existing standard system. After applying the proposed solution the number of packets analyzed rate has been increasing remarkably from 86% to 98%.

4 citations