Generation and Implementation of Cryptographically Strong Elliptic Curves

Dąbrowski, P.; Gliwa, Rafał; Szmidt, Janusz; Wicik, Robert

doi:10.1007/978-3-319-76620-1_2

Cited by 4 publications

(3 citation statements)

References 6 publications

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“…RSA) or discrete logarithm (e.g. DH, MQV, DSA, ECDH, ECMQV, ECDSA) [6], in the model of attack using a quantum computer, they no longer provide security [1]. This is due to the fact that there are algorithms that can be performed on a quantum computer, which significantly reduce the computational complexity of cryptosystems based on these problems.…”

Section: Security Degradation Of Session Key Agreement Protocols Basementioning

confidence: 99%

Cryptographic protection of classified information in military radio communication faced with threats from quantum computers

Wicik

Borowski

2020

Radioelectronic Systems Conference 2019

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Section: Security Degradation Of Session Key Agreement Protocols Basementioning

confidence: 99%

Cryptographic protection of classified information in military radio communication faced with threats from quantum computers

Wicik

Borowski

2020

Radioelectronic Systems Conference 2019

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“…RSA) or discrete logarithm (e.g. DH, MQV, DSA, ECDH, ECMQV, ECDSA) [11], in the model of attack using a quantum computer, they no longer provide security [12]. This is due to the fact that there are algorithms that can be performed on a quantum computer, which significantly reduce the computational complexity of cryptosystems based on these problems.…”

Section: A Security Degradation Of Key Agreement Protocolsmentioning

confidence: 99%

International Journal of Electronics and Telecommunications

Białas¹,

Grzonkowski²,

Wicik³

2020

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Protecting the confidentiality, integrity and availability of information is very important in any telecommunications system. Information protection requires use of necessary physical, personal, information and communication technologies and above allelectromagnetic and cryptographic security measures. Equipment and tools for cryptographic protection should be examined and assessed in terms of resistance to known threats. Additional requirements are put on information protection for radio communication, especially military, where radio transmission is characterized by uncertainty of establishing and maintaining connections, bit rates are relatively low, often without full duplex. All this has an impact on the methods of cryptographic synchronization and implementation of cryptographic functions. A different approach to information protection is required by classic narrowband radio communications, a different one in time-division multi-access modes, and another one in broadband packet data transmission. Systems designed for information protection in radio communications implement appropriate operating modes of operation for cryptographic algorithms and protocols. Latest threats from quantum computers pose new challenges, especially in systems using public-key cryptography, because there are algorithms that can be used to attack these schemes with polynomial complexity.

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“…The elliptic curves with prime order have advantage over nonprime case since each non-neutral element of the curve is a generator of the group of points on the curve. The arithmetic on elliptic curves is presented in papers [5], [12] and over the field F 2 521 −1 in [13]. We check the class number criterion and the twist security for our examples of curves.…”

Section: Introductionmentioning

confidence: 99%

International Journal of Electronics and Telecommunications

Szmidt

Gliwa

Barański

2020

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The purpose of this paper is to generate cryptographically strong elliptic curves over prime fields Fp, where p is a Mersenne prime, one of the special primes or a random prime. We search for elliptic curves which orders are also prime numbers. The cryptographically strong elliptic curves are those for which the discrete logarithm problem is computationally hard. The required mathematical conditions are formulated in terms of parameters characterizing the elliptic curves. We present an algorithm to generate such curves. Examples of elliptic curves of prime order are generated with Magma.

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Generation and Implementation of Cryptographically Strong Elliptic Curves

Cited by 4 publications

References 6 publications

Cryptographic protection of classified information in military radio communication faced with threats from quantum computers

Cryptographic protection of classified information in military radio communication faced with threats from quantum computers

International Journal of Electronics and Telecommunications

International Journal of Electronics and Telecommunications

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