Efficient message transmission via twisted Edwards curves

2020 ◽  
Vol 70 (6) ◽  
pp. 1511-1520
Author(s):  
Bariş Bülent Kirlar
Keyword(s):  
Discrete Logarithm ◽  
Encryption Scheme ◽  
Message Transmission ◽  
Edwards Curves ◽  
Diffie Hellman ◽  
Digital Signature Algorithm ◽  
Message Recovery ◽  
Secure Message Transmission ◽  
Chosen Ciphertext Attack ◽  
Twisted Edwards Curves

AbstractIn this paper, we suggest a novel public key scheme by incorporating the twisted Edwards model of elliptic curves. The security of the proposed encryption scheme depends on the hardness of solving elliptic curve version of discrete logarithm problem and Diffie-Hellman problem. It then ensures secure message transmission by having the property of one-wayness, indistinguishability under chosen-plaintext attack (IND-CPA) and indistinguishability under chosen-ciphertext attack (IND-CCA). Moreover, we introduce a variant of Nyberg-Rueppel digital signature algorithm with message recovery using the proposed encryption scheme and give some countermeasures to resist some wellknown forgery attacks.

Signature-Encryption Scheme: A Novel Solution to Mobile Computation

2012 ◽  
Vol 546-547 ◽  
pp. 1415-1420
Author(s):  
Hai Yong Bao ◽  
Man De Xie ◽  
Zhen Fu Cao ◽  
Shan Shan Hong
Keyword(s):  
Mobile Communication ◽  
High Efficiency ◽  
Discrete Logarithm ◽  
Communication Technologies ◽  
Random Oracle ◽  
Security Requirements ◽  
Encryption Scheme ◽  
Daily Lives ◽  
Storage Devices ◽  
Diffie Hellman

Mobile communication technologies have been widely utilized in daily lives, many low-computing-power and weakly-structured-storage devices have emerged, such as PDA, cell phones and smart cards, etc. How to solve the security problems in such devices has become a key problem in secure mobile communication. In this paper, we would like to propose an efficient signature-encryption scheme. The security of the signature part is not loosely related to Discrete Logarithm Problem (DLP) assumption as most of the traditional schemes but tightly related to the Decisional Diffie-Hellman Problem (DDHP) assumption in the Random Oracle Models. Different from the existing solutions, our scheme introduces a trusted agent of the receiver who can filter the “rubbish” messages beforehand. Thus, with high efficiency in computation and storage, it is particularly suitable for the above mobile devices with severely constrained resources and can satisfy the security requirements of mobile computations.

scholarly journals The Order of Edwards and Montgomery Curves

2020 ◽  
Vol 19 ◽  
Keyword(s):  
Finite Field ◽  
Elliptic Curve ◽  
Elliptic Curves ◽  
Digital Signature ◽  
Discrete Logarithm ◽  
Log P ◽  
Edwards Curves ◽  
Digital Signature Algorithm ◽  
Supersingular Curves ◽  
Edwards Curve

The Elliptic Curve Digital Signature Algorithm (ECDSA) is the elliptic curve analogue of the Digital Signature Algorithm (DSA) [2]. It is well known that the problem of discrete logarithm is NP-hard on group on elliptic curve (EC) [5]. The orders of groups of an algebraic affine and projective curves of Edwards [3, 9] over the finite field Fpn is studied by us. We research Edwards algebraic curves over a finite field, which are one of the most promising supports of sets of points which are used for fast group operations [1]. We construct a new method for counting the order of an Edwards curve [F ] d p E over a finite field Fp . It should be noted that this method can be applied to the order of elliptic curves due to the birational equivalence between elliptic curves and Edwards curves. The method we have proposed has much less complexity 22 O p log p at not large values p in comparison with the best Schoof basic algorithm with complexity 8 2 O(log pn ) , as well as a variant of the Schoof algorithm that uses fast arithmetic, which has complexity 42O(log pn ) , but works only for Elkis or Atkin primes. We not only find a specific set of coefficients with corresponding field characteristics for which these curves are supersingular, but we additionally find a general formula by which one can determine whether a curve [F ] d p E is supersingular over this field or not. The symmetric of the Edwards curve form and the parity of all degrees made it possible to represent the shape curves and apply the method of calculating the residual coincidences. A birational isomorphism between the Montgomery curve and the Edwards curve is also constructed. A oneto- one correspondence between the Edwards supersingular curves and Montgomery supersingular curves is established. The criterion of supersingularity for Edwards curves is found over F pn .

scholarly journals A Cryptographic Application of the M-Injectivity of 𝑀𝑛(𝑍𝑝) Over Itself

2021 ◽  
Vol 10 (4) ◽  
pp. 7-14
Author(s):  
Wannarisuk Nongbsap ◽  
◽  
Dr. Madan Mohan Singh ◽  
Keyword(s):  
Discrete Logarithm ◽  
Matrix Ring ◽  
Discrete Logarithm Problem ◽  
Public Key ◽  
Encryption Scheme ◽  
Diffie Hellman ◽  
Hill Cipher ◽  
The Matrix ◽  
Elgamal Encryption

In this paper, we present a public key scheme using Discrete Logarithm problem, proposed by Diffie and Hellman (DLP)[1], particularly known as the Computational Diffie-Hellman Problem (CDH)[12]. This paper uses the Elgamal encryption scheme [6] and extends it so that more than one message can be sent. The combination of Hill Cipher[14 ] and the property of the matrix ring 𝑴𝒏(𝒁𝒑), of being left m-injective over itself, where 𝒑 is a very large prime, are major contributions towards the proposal of this scheme.

scholarly journals A Pairing-Free Identity-Based Identification Scheme with Tight Security Using Modified-Schnorr Signatures

Symmetry ◽  
2021 ◽  
Vol 13 (8) ◽  
pp. 1330
Author(s):  
Jason Chia ◽  
Ji-Jian Chin ◽  
Sook-Chin Yip
Keyword(s):  
Key Management ◽  
Discrete Logarithm ◽  
Probability Bounds ◽  
Diffie Hellman ◽  
Identity Based ◽  
Symmetric Key ◽  
Security Guarantees ◽  
Lightweight Authentication ◽  
Tight Security ◽  
Schnorr Signatures

The security of cryptographic schemes is proven secure by reducing an attacker which breaks the scheme to an algorithm that could be used to solve the underlying hard assumption (e.g., Discrete Logarithm, Decisional Diffie–Hellman). The reduction is considered tight if it results in approximately similar probability bounds to that of solving the underlying hard assumption. Tight security is desirable as it improves security guarantees and allows the use of shorter parameters without the risk of compromising security. In this work, we propose an identity-based identification (IBI) scheme with tight security based on a variant of the Schnorr signature scheme known as TNC signatures. The proposed IBI scheme enjoys shorter parameters and key sizes as compared to existing IBI schemes without increasing the number of operations required for its identification protocol. Our scheme is suitable to be used for lightweight authentication in resource-constrained Wireless Sensor Networks (WSNs) as it utilizes the lowest amount of bandwidth when compared to other state-of-the-art symmetric key lightweight authentication schemes. Although it is costlier than its symmetric key counterparts in terms of operational costs due to its asymmetric key nature, it enjoys other benefits such as decentralized authentication and scalable key management. As a proof of concept to substantiate our claims, we perform an implementation of our scheme to demonstrate its speed and memory usage when it runs on both high and low-end devices.

scholarly journals BESTIE: Broadcast Encryption Scheme for Tiny IoT Equipment

Electronics ◽  
2020 ◽  
Vol 9 (9) ◽  
pp. 1389
Author(s):  
Jiwon Lee ◽  
Jihye Kim ◽  
Hyunok Oh
Keyword(s):  
The Other ◽  
Public Key ◽  
Broadcast Encryption ◽  
Encryption Scheme ◽  
The Public ◽  
Private Key ◽  
Diffie Hellman ◽  
The Standard Model ◽  
Encryption Decryption ◽  
Subset Difference

In public key broadcast encryption, anyone can securely transmit a message to a group of receivers such that privileged users can decrypt it. The three important parameters of the broadcast encryption scheme are the length of the ciphertext, the size of private/public key, and the performance of encryption/decryption. It is suggested to decrease them as much as possible; however, it turns out that decreasing one increases the other in most schemes. This paper proposes a new broadcast encryption scheme for tiny Internet of Things (IoT) equipment (BESTIE), minimizing the private key size in each user. In the proposed scheme, the private key size is O(logn), the public key size is O(logn), the encryption time per subset is O(logn), the decryption time is O(logn), and the ciphertext text size is O(r), where n denotes the maximum number of users, and r indicates the number of revoked users. The proposed scheme is the first subset difference-based broadcast encryption scheme to reduce the private key size O(logn) without sacrificing the other parameters. We prove that our proposed scheme is secure under q-Simplified Multi-Exponent Bilinear Diffie-Hellman (q-SMEBDH) in the standard model.

scholarly journals Improved cryptanalysis of a ElGamal Cryptosystem Based on Matrices Over Group Rings

2020 ◽  
Vol 15 (1) ◽  
pp. 266-279
Author(s):  
Atul Pandey ◽  
Indivar Gupta ◽  
Dhiraj Kumar Singh
Keyword(s):  
Discrete Logarithm ◽  
Public Key Cryptography ◽  
Public Key ◽  
Quantum Computers ◽  
Group Rings ◽  
Diffie Hellman ◽  
Algebra Approach ◽  
Elgamal Cryptosystem ◽  
Diffie Hellman Key Exchange ◽  
Equivalent Keys

AbstractElGamal cryptosystem has emerged as one of the most important construction in Public Key Cryptography (PKC) since Diffie-Hellman key exchange protocol was proposed. However, public key schemes which are based on number theoretic problems such as discrete logarithm problem (DLP) are at risk because of the evolution of quantum computers. As a result, other non-number theoretic alternatives are a dire need of entire cryptographic community.In 2016, Saba Inam and Rashid Ali proposed a ElGamal-like cryptosystem based on matrices over group rings in ‘Neural Computing & Applications’. Using linear algebra approach, Jia et al. provided a cryptanalysis for the cryptosystem in 2019 and claimed that their attack could recover all the equivalent keys. However, this is not the case and we have improved their cryptanalysis approach and derived all equivalent key pairs that can be used to totally break the ElGamal-like cryptosystem proposed by Saba and Rashid. Using the decomposition of matrices over group rings to larger size matrices over rings, we have made the cryptanalysing algorithm more practical and efficient. We have also proved that the ElGamal cryptosystem proposed by Saba and Rashid does not achieve the security of IND-CPA and IND-CCA.

scholarly journals The Pairing Computation on Edwards Curves

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Hongfeng Wu ◽  
Liangze Li ◽  
Fan Zhang
Keyword(s):  
Geometric Interpretation ◽  
Tate Pairing ◽  
Quadric Surfaces ◽  
Edwards Curves ◽  
Explicit Formulae ◽  
Pairing Computation ◽  
Twisted Edwards Curves ◽  
Group Law

We propose an elaborate geometry approach to explain the group law on twisted Edwards curves which are seen as the intersection of quadric surfaces in place. Using the geometric interpretation of the group law, we obtain the Miller function for Tate pairing computation on twisted Edwards curves. Then we present the explicit formulae for pairing computation on twisted Edwards curves. Our formulae for the doubling step are a little faster than that proposed by Arène et al. Finally, to improve the efficiency of pairing computation, we present twists of degrees 4 and 6 on twisted Edwards curves.

Digital signature with message recovery based on factoring and discrete logarithm

2015 ◽  
Vol 62 (3) ◽  
pp. 415-423 ◽  
Author(s):  
Min-Shiang Hwang ◽  
Shih-Ming Chen ◽  
Chi-Yu Liu
Keyword(s):  
Digital Signature ◽  
Discrete Logarithm ◽  
Message Recovery

scholarly journals Time-constrained strong multi-designated verifier signature suitable for Internet of things–based collaborative fog computing systems

2021 ◽  
Vol 17 (3) ◽  
pp. 155014772110017
Author(s):  
Han-Yu Lin
Keyword(s):  
Internet Of Things ◽  
Fog Computing ◽  
Discrete Logarithm ◽  
Signature Scheme ◽  
Computing Systems ◽  
Extended Technique ◽  
Diffie Hellman ◽  
Designated Verifier ◽  
Designated Verifier Signature ◽  
Cloud Servers

Fog computing is viewed as an extended technique of cloud computing. In Internet of things–based collaborative fog computing systems, a fog node aggregating lots of data from Internet of things devices has to transmit the information to distributed cloud servers that will collaboratively verify it based on some predefined auditing policy. However, compromised fog nodes controlled by an adversary might inject bogus data to cheat or confuse remote servers. It also causes the waste of communication and computation resources. To further control the lifetime of signing capability for fog nodes, an appropriate mechanism is crucial. In this article, the author proposes a time-constrained strong multi-designated verifier signature scheme to meet the above requirement. In particular, a conventional non-delegatable strong multi-designated verifier signature scheme with low computation is first given. Based on its constructions, we show how to transform it into a time-constrained variant. The unforgeability of the proposed schemes is formally proved based on the famous elliptic curve discrete logarithm assumption. The security requirement of strong signer ambiguity for our substantial constructions is also analyzed by utilizing the intractable assumption of decisional Diffie–Hellman. Moreover, some comparisons in terms of the signature size and computational costs for involved entities among related mechanisms are made.

Utilization of Corner Filters, AES and LSB Steganography for Secure Message Transmission

2021 ◽  
Author(s):  
Wassim Alexan ◽  
Abdelrahman Elkhateeb ◽  
Eyad Mamdouh ◽  
Fahd Al-Seba'Ey ◽  
Ziad Amr ◽  
...  
Keyword(s):  
Message Transmission ◽  
Secure Message Transmission
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