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Journal articles on the topic 'Extension field cryptosystem'

Author: Grafiati

Published: 25 May 2024

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1

Chakraborty, Olive, Jean-Charles Faugère, and Ludovic Perret. "Cryptanalysis of the extension field cancellation cryptosystem." Designs, Codes and Cryptography 89, no. 6 (2021): 1335–64. http://dx.doi.org/10.1007/s10623-021-00873-9.

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2

Rehman, Hafeez Ur, Mohammad Mazyad Hazzazi, Tariq Shah, Amer Aljaedi, and Zaid Bassfar. "Color image encryption by piecewise function and elliptic curve over the Galois field $ {G}{F}\left({2}^{{n}}\right) $." AIMS Mathematics 9, no. 3 (2024): 5722–45. http://dx.doi.org/10.3934/math.2024278.

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<abstract> <p>Elliptic curve (EC) cryptography supplies an efficient, secure, and lightweight method for executing computer cryptographic protocols. Its widespread use in various applications, including secure communications, digital signatures, and key agreement protocols, highlights its importance in modern computing. Moreover, EC-based image encryption is gaining popularity in cryptography as it offers strong protection with a relatively smaller key size than other famous cryptosystems. Inspired by this, we proposed a novel image encryption scheme that leverages ECs over a binar

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3

El-Kassar, A. N., and Ramzi Haraty. "ElGamal Public-Key cryptosystem in multiplicative groups of quotient rings of polynomials over finite fields." Computer Science and Information Systems 2, no. 1 (2005): 63–77. http://dx.doi.org/10.2298/csis0501063e.

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The ElGamal encryption scheme is described in the setting of any finite cyclic group G. Among the groups of most interest in cryptography are the multiplicative group Zp of the ring of integers modulo a prime p, and the multiplicative groups F2m of finite fields of characteristic two. The later requires finding irreducible polynomials H(x) and constructing the quotient ring Z2[x]/ < h(x)>. El-Kassar et al. modified the ElGamal scheme to the domain of Gaussian integers. El-Kassar and Haraty gave an extension in the multiplicative group of Zp[x]/ < x2 >. Their major finding is that t

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4

George, Kiernan, and Alan J. Michaels. "Designing a Block Cipher in Galois Extension Fields for IoT Security." IoT 2, no. 4 (2021): 669–87. http://dx.doi.org/10.3390/iot2040034.

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This paper focuses on a block cipher adaptation of the Galois Extension Fields (GEF) combination technique for PRNGs and targets application in the Internet of Things (IoT) space, an area where the combination technique was concluded as a quality stream cipher. Electronic Codebook (ECB) and Cipher Feedback (CFB) variations of the cryptographic algorithm are discussed. Both modes offer computationally efficient, scalable cryptographic algorithms for use over a simple combination technique like XOR. The cryptographic algorithm relies on the use of quality PRNGs, but adds an additional layer of s

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5

Saju, M. I., Renjith Varghese, and E. F. Antony John. "A design of public key Cryptosystem in an algebraic extension field over a finite field using the difficulty of solving DLP." Malaya Journal of Matematik 8, no. 2 (2020): 459–63. http://dx.doi.org/10.26637/mjm0802/0022.

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6

Ur Rehman, Hafeez, Mohammad Mazyad Hazzazi, Tariq Shah, Zaid Bassfar, and Dawood Shah. "An Efficient Audio Encryption Scheme Based on Elliptic Curve over Finite Fields." Mathematics 11, no. 18 (2023): 3824. http://dx.doi.org/10.3390/math11183824.

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Elliptic curve (EC) based cryptographic systems are more trustworthy than the currently used cryptographic approaches since they require less computational work while providing good security. This paper shows how to use an EC to make a good cryptosystem for encrypting digital audio. As a preliminary step, the system uses an EC of a particular type over a binary extension field to distort the digital audio pixel position. It reduces the inter-correlation between pixels in the original audio, making the system resistant to statistical attacks. In creating confusion in the data, an EC over a bina

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7

Hammami, Sonia. "Multi-switching combination synchronization of discrete-time hyperchaotic systems for encrypted audio communication." IMA Journal of Mathematical Control and Information 36, no. 2 (2018): 583–602. http://dx.doi.org/10.1093/imamci/dnx058.

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Abstract In this paper, encrypted audio communication based on original synchronization form is proposed for a class of discrete-time hyperchaotic systems. The new studied scheme of synchronization presents an extension of the multi-switching one to the combination synchronization, for which, the state variables of two driving systems synchronize with different state variables of the response system, simultaneously. With that in mind, at the outset, a theoretical approach for non-linear control, using aggregation techniques associated to one specific characteristic matrix description, namely,

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8

Li, Jiakun, and Wei Gao. "Hardware Optimization and System Design of Elliptic Curve Encryption Algorithm Based on FPGA." Journal of Sensors 2022 (October 11, 2022): 1–12. http://dx.doi.org/10.1155/2022/9074524.

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Since entering the era of big data, the degree of information sharing is getting higher and higher; the information exchange is becoming more and more convenient, but at the same time, personal information is also easy to be exposed to the network environment, if it is used by criminals to lead to information leakage, and then bring certain risks. Therefore, it is in the information age and do a good job of network information security and confidentiality. At present, the security and secrecy of network information are mainly realized by cryptography. Public key cryptography can encrypt inform

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9

Guang Gong and Lein Harn. "Public-key cryptosystems based on cubic finite field extensions." IEEE Transactions on Information Theory 45, no. 7 (1999): 2601–5. http://dx.doi.org/10.1109/18.796413.

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10

Bessalov, Anatoliy V. "CALCULATION OF PARAMETERS OF CRYPTIC CRIVIAE EDWARDS OVER THE FIELDS OF CHARACTERISTICS 5 AND 7." Cybersecurity: Education, Science, Technique, no. 1 (2018): 94–104. http://dx.doi.org/10.28925/2663-4023.2018.1.94104.

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The method of search of cryptographic strong elliptic curves in the Edwards form (where parameter d is non square in the field) over the extended finite fields of small characteristics p ≠ 2.3 is proposed. For these curves is performed the completeness of the points addition law, so they are called as complete Edwards curve. In the first stage over a small prime fields and we find the parameters d of complete Edwards curves who have minimum orders . For both curves we obtain the same values d = 3, which are non square in the fields and . Next with help recurrent formulae for both curves we cal

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11

ARITA, S. "A Weil Descent Attack against Elliptic Curve Cryptosystems over Quartic Extension Fields." IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences E89-A, no. 5 (2006): 1246–54. http://dx.doi.org/10.1093/ietfec/e89-a.5.1246.

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12

HASHIMOTO, Yasufumi. "Key Recovery Attacks on Multivariate Public Key Cryptosystems Derived from Quadratic Forms over an Extension Field." IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences E100.A, no. 1 (2017): 18–25. http://dx.doi.org/10.1587/transfun.e100.a.18.

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13

Su, Guantong, and Guoqiang Bai. "Towards High-Performance Supersingular Isogeny Cryptographic Hardware Accelerator Design." Electronics 12, no. 5 (2023): 1235. http://dx.doi.org/10.3390/electronics12051235.

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Cryptosystems based on supersingular isogeny are a novel tool in post-quantum cryptography. One compelling characteristic is their concise keys and ciphertexts. However, the performance of supersingular isogeny computation is currently worse than that of other schemes. This is primarily due to the following factors. Firstly, the underlying field is a quadratic extension of the finite field, resulting in higher computational complexity. Secondly, the strategy for large-degree isogeny evaluation is complex and dependent on the elementary arithmetic units employed. Thirdly, adapting the same hard

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14

Al-Hiaja, Qasem Abu, Abdullah AlShuaibi, and Ahmad Al Badawi. "Frequency Analysis of 32-bit Modular Divider Based on Extended GCD Algorithm for Different FPGA chips." INTERNATIONAL JOURNAL OF COMPUTERS & TECHNOLOGY 17, no. 1 (2018): 7133–39. http://dx.doi.org/10.24297/ijct.v17i1.6992.

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Modular inversion with large integers and modulus is a fundamental operation in many public-key cryptosystems. Extended Euclidean algorithm (XGCD) is an extension of Euclidean algorithm (GCD) used to compute the modular multiplicative inverse of two coprime numbers. In this paper, we propose a Frequency Analysis study of 32-bit modular divider based on extended-GCD algorithm targeting different chips of field-programmable gate array (FPGA). The experimental results showed that the design recorded the best performance results when implemented using Kintex7 (xc7k70t-2-fbg676) FPGA kit with a min

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15

Elango, S., and P. Sampath. "Implementation of High Performance Hierarchy-Based Parallel Signed Multiplier for Cryptosystems." Journal of Circuits, Systems and Computers 29, no. 13 (2020): 2050214. http://dx.doi.org/10.1142/s021812662050214x.

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Digital Cryptosystems play an inevitable part in modern-day communication. Due to the complexity involved in the execution of crypto algorithms, it is realized as modular arithmetic modules. Generally, multipliers are the most time-consuming data path elements which influence the performance of modular arithmetic implementations. In this paper, the design of a hierarchy-based parallel signed multiplier without sign extension is presented. A mathematical model of the algorithm, two VLSI architectures, namely, Carry Save Adder (CSA)-based design and Parallel Prefix-based architecture are propose

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16

Shaukat Jamal, Sajjad, Dawood Shah, Abdulaziz Deajim, and Tariq Shah. "The Effect of the Primitive Irreducible Polynomial on the Quality of Cryptographic Properties of Block Ciphers." Security and Communication Networks 2020 (September 24, 2020): 1–14. http://dx.doi.org/10.1155/2020/8883884.

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Substitution boxes are the only nonlinear component of the symmetric key cryptography and play a key role in the cryptosystem. In block ciphers, the S-boxes create confusion and add valuable strength. The majority of the substitution boxes algorithms focus on bijective Boolean functions and primitive irreducible polynomial that generates the Galois field. For binary field F2, there are exactly 16 primitive irreducible polynomials of degree 8 and it prompts us to construct 16 Galois field extensions of order 256. Conventionally, construction of affine power affine S-box is based on Galois field

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17

Cheng, Hao, Georgios Fotiadis, Johann Großschädl, and Peter Y. A. Ryan. "Highly Vectorized SIKE for AVX-512." IACR Transactions on Cryptographic Hardware and Embedded Systems, February 15, 2022, 41–68. http://dx.doi.org/10.46586/tches.v2022.i2.41-68.

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It is generally accepted that a large-scale quantum computer would be capable to break any public-key cryptosystem used today, thereby posing a serious threat to the security of the Internet’s public-key infrastructure. The US National Institute of Standards and Technology (NIST) addresses this threat with an open process for the standardization of quantum-safe key establishment and signature schemes, which is now in the final phase of the evaluation of candidates. SIKE (an abbreviation of Supersingular Isogeny Key Encapsulation) is one of the alternate candidates under evaluation and distingu

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18

Cheng, Hao, Georgios Fotiadis, Johann Großschädl, Peter Y. A. Ryan, and Peter B. Rønne. "Batching CSIDH Group Actions using AVX-512." IACR Transactions on Cryptographic Hardware and Embedded Systems, August 11, 2021, 618–49. http://dx.doi.org/10.46586/tches.v2021.i4.618-649.

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Commutative Supersingular Isogeny Diffie-Hellman (or CSIDH for short) is a recently-proposed post-quantum key establishment scheme that belongs to the family of isogeny-based cryptosystems. The CSIDH protocol is based on the action of an ideal class group on a set of supersingular elliptic curves and comes with some very attractive features, e.g. the ability to serve as a “drop-in” replacement for the standard elliptic curve Diffie-Hellman protocol. Unfortunately, the execution time of CSIDH is prohibitively high for many real-world applications, mainly due to the enormous computational cost o

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19

Cramer, Ronald, and Serge Fehr. "Optimal Black-Box Secret Sharing over Arbitrary Abelian Groups." BRICS Report Series 9, no. 8 (2002). http://dx.doi.org/10.7146/brics.v9i8.21726.

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A black-box secret sharing scheme for the threshold access structure T_t,n is one which works over any finite Abelian group G. Briefly, such a scheme differs from an ordinary linear secret sharing scheme (over, say, a given finite field) in that distribution matrix and reconstruction vectors are defined over Z and are designed independently of the group G from which the secret and the shares are sampled. This means that perfect completeness and perfect privacy are guaranteed regardless of which group G is chosen. We define the black-box secret sharing problem as the problem of devising, for an

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20

Abukari, Zakaria, Edward Yellakuor Baagyere, and Mohammed Muniru Iddrisu. "Efficient Elliptic Curve Arithmetic for Lightweight Cryptographic Schemes for IoT Applications." Asian Journal of Research in Computer Science, December 23, 2022, 228–37. http://dx.doi.org/10.9734/ajrcos/2022/v14i4307.

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The Internet of Things’ (IoT) market is expected to grow exponentially at the global level in the coming years, due to the proliferation of more reliable and faster networks resulting from the extensive rollout of 5 to 10 G mobile networks. By 2025, it is expected that worldwide projection of IoT connected devices will be pegged at 30.9 billion units. Despite the potential benefits of the new technology, security in IoT is a major threat. According to HP, 70% of IoT devices are vulnerable to sniffing attacks and reliable solution is yet to be found. The standard cryptographic algorithms such a

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