scholarly journals Cryptanalysis and improvement of an encryption scheme that uses elliptic curves over finite fields

2021 ◽  
Vol 49 (1) ◽  
Author(s):  
Malik Zia Ullah Bashir ◽  
◽  
Rashid Ali ◽  
Keyword(s):  
Elliptic Curves ◽  
Discrete Logarithm ◽  
Security Requirements ◽  
Encryption Scheme ◽  
Secret Key ◽  
Public Keys ◽  
Secret Keys ◽  
Curves Over Finite Fields ◽  
Original Message ◽  
Global Parameters

In this paper, we cryptanalyzed a recently proposed encryption scheme that uses elliptic curves over a finite field. The security of the proposed scheme depends upon the elliptic curve discrete logarithm problem. Two secret keys are used to increase the security strength of the scheme as compared to traditionally used schemes that are based on one secret key. In this scheme, if an adversary gets one secret key then he is unable to get the contents of the original message without the second secret key. Our analysis shows that the proposed scheme is not secure and unable to provide the basic security requirements of the encryption scheme. Due to our successful cryptanalysis, an adversary can get the contents of the original message without the knowledge of the secret keys of the receiver. To mount the attack, Mallory first gets the transmitted ciphertext and then uses public keys of the receiver and global parameters of the scheme to recover the associated plaintext message. To overcome the security flaws, we introduced an improved version of the scheme.

Hiding Data in Plain Sight: Towards Provably Unbreakable Encryption with Short Secret Keys and One-Way Functions

2021 ◽  
Author(s):  
Mircea-Adrian Digulescu
Keyword(s):  
Encryption Scheme ◽  
Secret Key ◽  
Small Probability ◽  
Random Data ◽  
Computing Power ◽  
Plain Text ◽  
Secret Keys ◽  
The One ◽  
One Way Function ◽  
The Cost

It has long been known that cryptographic schemes offering provably unbreakable security exist, namely the One Time Pad (OTP). The OTP, however, comes at the cost of a very long secret key - as long as the plain-text itself. In this paper we propose an encryption scheme which we (boldly) claim offers the same level of security as the OTP, while allowing for much shorter keys, of size polylogarithmic in the computing power available to the adversary. The Scheme requires a large sequence of truly random words, of length polynomial in the both plain-text size and the logarithm of the computing power the adversary has. We claim that it ensures such an attacker cannot discern the cipher output from random data, except with small probability. We also show how it can be adapted to allow for several plain-texts to be encrypted in the same cipher output, with almost independent keys. Also, we describe how it can be used in lieu of a One Way Function.

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 Public key cryptosystem based on multiple chaotic maps for image encryption

2021 ◽  
Vol 22 (3) ◽  
pp. 1457
Author(s):  
Yousif S. Najaf ◽  
Maher K. Mahmood Al-Azawi
Keyword(s):  
Chaotic Maps ◽  
Third Party ◽  
Public Key ◽  
Secret Key ◽  
Chebyshev Map ◽  
Key Space ◽  
Public Keys ◽  
Secret Keys ◽  
Shared Secret ◽  
Multiple Chaotic Maps

Image is one of the most important forms of information. In this paper, two public key encryption systems are proposed to protect images from various attacks. Both systems depend on generating a chaotic matrix (<em>I</em>) using multiple chaotic maps. The parameters for these maps are taken from the shared secret keys generated from Chebyshev map using public keys for Alice and secret key for Bob or vice versa. The second system has the feature of deceiving the third party for searching for fake keys. Analysis and tests showed that the two proposed systems resist various attacks and have very large key space. The results are compared with other chaos based systems to show the superiority of these two proposed systems.

scholarly journals Efficient and Provable Secure Pairing-Free Security-Mediated Identity-Based Identification Schemes

2014 ◽  
Vol 2014 ◽  
pp. 1-14
Author(s):  
Ji-Jian Chin ◽  
Syh-Yuan Tan ◽  
Swee-Huay Heng ◽  
Raphael C.-W. Phan
Keyword(s):  
Discrete Logarithm ◽  
Bilinear Pairings ◽  
Public Key ◽  
Encryption Scheme ◽  
Secret Key ◽  
Cryptographic Primitives ◽  
Main Motivation ◽  
Identification Scheme ◽  
Identification Schemes ◽  
Identity Based

Security-mediated cryptography was first introduced by Boneh et al. in 2001. The main motivation behind security-mediated cryptography was the capability to allow instant revocation of a user’s secret key by necessitating the cooperation of a security mediator in any given transaction. Subsequently in 2003, Boneh et al. showed how to convert a RSA-based security-mediated encryption scheme from a traditional public key setting to an identity-based one, where certificates would no longer be required. Following these two pioneering papers, other cryptographic primitives that utilize a security-mediated approach began to surface. However, the security-mediated identity-based identification scheme (SM-IBI) was not introduced until Chin et al. in 2013 with a scheme built on bilinear pairings. In this paper, we improve on the efficiency results for SM-IBI schemes by proposing two schemes that are pairing-free and are based on well-studied complexity assumptions: the RSA and discrete logarithm assumptions.

scholarly journals Efficient functional encryption for inner product with simulation-based security

Cybersecurity ◽  
2021 ◽  
Vol 4 (1) ◽  
Author(s):  
Wenbo Liu ◽  
Qiong Huang ◽  
Xinjian Chen ◽  
Hongbo Li
Keyword(s):  
Inner Product ◽  
Encryption Scheme ◽  
Secret Key ◽  
Functional Encryption ◽  
Private Key ◽  
Simulation Based ◽  
Encryption And Decryption ◽  
The Standard Model ◽  
Secret Keys ◽  
Decisional Linear Assumption

AbstractFunctional encryption (FE) is a novel paradigm for encryption scheme which allows tremendous flexibility in accessing encrypted information. In FE, a user can learn specific function of encrypted messages by restricted functional key and reveal nothing else about the messages. Inner product encryption (IPE) is a special type of functional encryption where the decryption algorithm, given a ciphertext related to a vector x and a secret key related to a vector y, computes the inner product x·y. In this paper, we construct an efficient private-key functional encryption (FE) for inner product with simulation-based security, which is much stronger than indistinguishability-based security, under the External Decisional Linear assumption in the standard model. Compared with the existing schemes, our construction is faster in encryption and decryption, and the master secret key, secret keys and ciphertexts are shorter.

scholarly journals Contemporary Physical Clone-Resistant Identity for IoTs and Emerging Technologies

Cryptography ◽  
2021 ◽  
Vol 5 (4) ◽  
pp. 32
Author(s):  
Emad Hamadaqa ◽  
Saleh Mulhem ◽  
Wael Adi ◽  
Mladen Berekovic
Keyword(s):  
Communication Networks ◽  
Public Key Cryptography ◽  
Security Requirements ◽  
Secret Key ◽  
Open Communication ◽  
Secret Keys ◽  
Iot Devices ◽  
Classical Means ◽  
Future Technologies ◽  
Identification Techniques

Internet of things (IoT) technologies have recently gained much interest from numerous industries, where devices, machines, sensors, or simply things are linked with each other over open communication networks. However, such an operation environment brings new security threats and technology challenges in securing and stabilizing such large systems in the IoT world. Device identity in such an environment is an essential security requirement as a secure anchor for most applications towards clone-resistant resilient operational security. This paper analyzes different contemporary authenticated identification techniques and discusses possible future technologies for physically clone-resistant IoT units. Two categories of identification techniques to counteract cloning IoT units are discussed. The first category is inherently cloneable and includes the classical identification mechanisms based on secret and public key cryptography. Such techniques deploy mainly secret keys stored permanently somewhere in the IoT devices as classical means to make units clone-resistant. However, such techniques are inherently cloneable as the manufacturer or device personalizers can clone them by re-using the same secret key (which must be known to somebody) or reveal keys to third parties to create cloned entities. In contrast, the second, more resilient category is inherently unclonable because it deploys unknown and hard to predict born analog modules such as physical unclonable functions (PUFs) or mutated digital modules and so-called secret unknown ciphers (SUCs). Both techniques are DNA-like identities and hard to predict and clone even by the manufacturer itself. Born PUFs were introduced two decades ago; however, PUFs as analog functions failed to serve as practically usable unclonable electronic identities due to being costly, unstable/inconsistent, and non-practical for mass application. To overcome the drawbacks of analog PUFs, SUCs techniques were introduced a decade ago. SUCs, as mutated modules, are highly consistent, being digital modules. However, as self-mutated digital modules, they offer only clone-resistant identities. Therefore, the SUC technique is proposed as a promising clone-resistant technology embedded in emerging IoT units in non-volatile self-reconfiguring devices. The main threats and expected security requirements in the emerging IoT applications are postulated. Finally, the presented techniques are analyzed, classified, and compared considering security, performance, and complexity given future expected IoT security features and requirements.

scholarly journals Cryptanalysis of a Proposal Based on the Discrete Logarithm Problem Inside Sn

Cryptography ◽  
2018 ◽  
Vol 2 (3) ◽  
pp. 16
Author(s):  
María González Vasco ◽  
Angela Robinson ◽  
Rainer Steinwandt
Keyword(s):  
Symmetric Group ◽  
Efficient Method ◽  
Chinese Remainder Theorem ◽  
Discrete Logarithm ◽  
Discrete Logarithm Problem ◽  
Encryption Scheme ◽  
Secret Key ◽  
Natural Representation ◽  
Key Recovery ◽  
Key Recovery Attack

In 2008, Doliskani et al. proposed an ElGamal-style encryption scheme using the symmetric group Sn as mathematical platform. In 2012, an improvement of the cryptosystem’s memory requirements was suggested by Othman. The proposal by Doliskani et al. in particular requires the discrete logarithm problem in Sn, using its natural representation, to be hard. Making use of the Chinese Remainder Theorem, we describe an efficient method to solve this discrete logarithm problem, yielding a polynomial time secret key recovery attack against Doliskani et al.’s proposal.

scholarly journals CRYPTOGRAPHIC AUTHENTICATION PROTOCOL ZERO-KNOWLEDGE SECRET ON ELLIPTIC CURVES USING PUBLIC KEYS AND RANDOM MESSAGES

2019 ◽  
Vol 26 ◽  
pp. 22-28
Author(s):  
A.V. ONATSKIY ◽  
Keyword(s):  
Elliptic Curve ◽  
Elliptic Curves ◽  
Information Exchange ◽  
Discrete Logarithm ◽  
Security Protocol ◽  
Discrete Logarithm Problem ◽  
Cryptographic Protocol ◽  
Zero Knowledge ◽  
Public Keys ◽  
Zero Knowledge Proof

We propose a cryptographic protocol with zero-knowledge proof (ZKP) on elliptic curves (EC) using public keys and random messages, allowing to establish the truth of a statement not conveying any additional information about the statement itself. The cryptographic protocols based on zero-knowledge proof allow identification, key exchange and other cryptographic operations to be performed without leakage of sensitive information during the information exchange. The implementation of the cryptographic protocol of the zero-knowledge proof on the basis of the mathematical apparatus of elliptic curves allows to significantly reduce the size of the protocol parameters and increase its cryptographic strength (computational complexity of the breaking). The security of cryptosystems involving elliptic curves is based on the difficulty of solving the elliptic curve discrete logarithm problem. We determine the completeness and correctness of the protocol and give an example of the calculation is given. The cryptographic protocol was modeled in the High-Level Protocol Specification Language, the model validation and verification of the protocol were also performed. The software verification of the cryptographic protocol was performed using the software modules On the Fly Model Checker and Constraint Logic based Attack Searcher. In order to validate the cryptographic protocol resistance to intruder attacks, we used the Security Protocol Animator package for Automated Validation of Internet Security Protocols and Applications. The security of the proposed cryptographic protocol ZKP EC is based on the difficulty of solving the elliptic curve discrete logarithm problem). The recommended elliptical curves according to DSTU 4145-2002 may be used to implement such cryptographic protocol.

PERSPECTIVES OF ELLIPTICAL CRYPTOGRAPHY TO ENSURE THE INTEGRITY AND CONFIDENTIALITY OF INFORMATION

2019 ◽  
Author(s):  
Anna ILYENKO ◽  
Sergii ILYENKO ◽  
Yana MASUR
Keyword(s):  
Information Systems ◽  
Elliptic Curve ◽  
Elliptic Curves ◽  
Finite Fields ◽  
Computational Efficiency ◽  
Digital Signature ◽  
Discrete Logarithm ◽  
Algebraic Groups ◽  
Schnorr Signature ◽  
Stability Of Algorithms

In this article, the main problems underlying the current asymmetric crypto algorithms for the formation and verification of electronic-digital signature are considered: problems of factorization of large integers and problems of discrete logarithm. It is noted that for the second problem, it is possible to use algebraic groups of points other than finite fields. The group of points of the elliptical curve, which satisfies all set requirements, looked attractive on this side. Aspects of the application of elliptic curves in cryptography and the possibilities offered by these algebraic groups in terms of computational efficiency and crypto-stability of algorithms were also considered. Information systems using elliptic curves, the keys have a shorter length than the algorithms above the finite fields. Theoretical directions of improvement of procedure of formation and verification of electronic-digital signature with the possibility of ensuring the integrity and confidentiality of information were considered. The proposed method is based on the Schnorr signature algorithm, which allows data to be recovered directly from the signature itself, similarly to RSA-like signature systems, and the amount of recoverable information is variable depending on the information message. As a result, the length of the signature itself, which is equal to the sum of the length of the end field over which the elliptic curve is determined, and the artificial excess redundancy provided to the hidden message was achieved.

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