Explicit constructions of extremal graphs and new multivariate cryptosystems

2015 ◽  
Vol 52 (2) ◽  
pp. 185-204 ◽  
Author(s):  
Vasyl Ustimenko
Keyword(s):  
Discrete Logarithm ◽  
Public Key Infrastructure ◽  
Public Key ◽  
Polynomial Degree ◽  
Affine Spaces ◽  
Private Key ◽  
Explicit Constructions ◽  
Diffie Hellman ◽  
Polynomial Transformations ◽  
Finite Commutative Ring

New multivariate cryptosystems are introduced. Sequences f(n) of bijective polynomial transformations of bijective multivariate transformations of affine spaces Kn, n = 2, 3, ... , where K is a finite commutative ring with special properties, are used for the constructions of cryptosystems. On axiomatic level, the concept of a family of multivariate maps with invertible decomposition is proposed. Such decomposition is used as private key in a public key infrastructure. Requirements of polynomiality of degree and density allow to estimate the complexity of encryption procedure for a public user. The concepts of stable family and family of increasing order are motivated by studies of discrete logarithm problem in Cremona group. Statement on the existence of families of multivariate maps of polynomial degree and polynomial density with the invertible decomposition is formulated. We observe known explicit constructions of special families of multivariate maps. They correspond to explicit constructions of families of nonlinear algebraic graphs of increasing girth which appeared in Extremal Graph Theory. The families are generated by pseudorandom walks on graphs. This fact ensures the existence of invertible decomposition; a certain girth property guarantees the increase of order for the family of multivariate maps, good expansion properties of families of graphs lead to good mixing properties of graph based private key algorithms. We describe the general schemes of cryptographic applications of such families (public key infrastructure, symbolic Diffie—Hellman protocol, functional versions of El Gamal algorithm).

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 Survey on Asymmetric Key Cryptographic Algorithms

2020 ◽  
pp. 404-408
Author(s):  
Sabitha S ◽  
Binitha V Nair
Keyword(s):  
Public Key Cryptography ◽  
Public Key ◽  
The Public ◽  
Private Key ◽  
Design And Implementation ◽  
Diffie Hellman ◽  
Encryption And Decryption ◽  
Cryptographic Algorithms ◽  
Symmetric Key ◽  
Symmetric Key Cryptography

Cryptography is an essential and effective method for securing information’s and data. Several symmetric and asymmetric key cryptographic algorithms are used for securing the data. Symmetric key cryptography uses the same key for both encryption and decryption. Asymmetric Key Cryptography also known as public key cryptography uses two different keys – a public key and a private key. The public key is used for encryption and the private key is used for decryption. In this paper, certain asymmetric key algorithms such as RSA, Rabin, Diffie-Hellman, ElGamal and Elliptical curve cryptosystem, their security aspects and the processes involved in design and implementation of these algorithms are examined.

scholarly journals Dynamic Public Key Certificates with Forward Secrecy

Electronics ◽  
2021 ◽  
Vol 10 (16) ◽  
pp. 2009
Author(s):  
Hung-Yu Chien
Keyword(s):  
Public Key Infrastructure ◽  
Public Key ◽  
Practical Reasons ◽  
Forward Secrecy ◽  
The Public ◽  
Private Key ◽  
Security Properties ◽  
The Subject ◽  
Key Exposure ◽  
Chameleon Hash

Conventionally, public key certificates bind one subject with one static public key so that the subject can facilitate the services of the public key infrastructure (PKI). In PKI, certificates need to be renewed (or revoked) for several practical reasons, including certificate expiration, private key breaches, condition changes, and possible risk reduction. The certificate renewal process is very costly, especially for those environments where online authorities are not available or the connection is not reliable. A dynamic public key certificate (DPKC) facilitates the dynamic changeover of the current public–private key pairs without renewing the certificate authority (CA). This paper extends the previous study in several aspects: (1) we formally define the DPKC; (2) we formally define the security properties; (3) we propose another implementation of the Krawczyk–Rabin chameleon-hash-based DPKC; (4) we propose two variants of DPKC, using the Ateniese–Medeiros key-exposure-free chameleon hash; (5) we detail two application scenarios.

A new public key cryptosystem over ℤn2*

2017 ◽  
Vol 09 (06) ◽  
pp. 1750080
Author(s):  
Pinkimani Goswami ◽  
Madan Mohan Singh ◽  
Bubu Bhuyan
Keyword(s):  
Multiplicative Group ◽  
Discrete Logarithm ◽  
Public Key ◽  
Public Key Cryptosystem ◽  
Quadratic Residues ◽  
Diffie Hellman ◽  
New Public ◽  
Intractable Problems ◽  
The One ◽  
Safe Primes

At Eurocrypt ’99, Paillier showed a cryptographic application of the group [Formula: see text], the multiplicative group modulo [Formula: see text] where [Formula: see text] is some RSA modulus. In this paper, we have present a new public key cryptosystem over [Formula: see text] where [Formula: see text] is a product of two safe primes, which is based on two intractable problems namely, integer factorization and partial discrete logarithm problem over [Formula: see text], the group of quadratic residues modulo [Formula: see text]. This scheme is a combination of BCP (Bresson–Catalano–Pointcheval) cryptosystem, proposed by Bresson et al. at Asiacrypt ’03 and the Rabin–Paillier scheme proposed by Galindo et al. at PKC 2003. We will show that the one-wayness of this new scheme equally depends on the Computational Diffie–Hellman assumption and factoring assumption. We will also prove that the proposed scheme is more secure than the BCP cryptosystem and the Rabin–Paillier cryptosystem.

scholarly journals IMPLEMENTATION OF THE DIFFIE-HELLMAN PROTOCOL IN A CHANNEL UNLESS PROTECTED FROM INTERCEPT

2020 ◽  
pp. 24-28
Author(s):  
T. Yu. Zyryanova ◽  
◽  
N. A. Raspopov ◽  
Keyword(s):  
Block Cipher ◽  
Public Key Infrastructure ◽  
Public Key ◽  
Avalanche Effect ◽  
The Public ◽  
Diffie Hellman

This article discusses the implementation of the Diffie-Hellman protocol in an unprotected channel. The essence of this method is to use steganography to transmit the public key in an unsecured channel. The public key is encrypted using a block cipher and encoded into the pic-ture using the LSB method. The uniqueness of the picture and the impossibility of changing the key is ensured by the avalanche effect. The implementation of the Diffie-Hellman protocol in an insecure channel has long remained relevant, although there is a solution in the form of public key infrastructure, but in this article a new solution to this problem was proposed.

scholarly journals Modification of Traditional RSA into Symmetric-RSA Cryptosystems

Cryptography ◽  
2020 ◽  
pp. 120-128
Author(s):  
Prerna Mohit ◽  
G. P. Biswas
Keyword(s):  
Digital Signature ◽  
Discrete Logarithm ◽  
Prime Numbers ◽  
Public Key ◽  
Key Exchange Protocol ◽  
Factorization Problem ◽  
Rsa Algorithm ◽  
Diffie Hellman ◽  
Diffie Hellman Key Exchange ◽  
Rsa Cryptography

This paper addresses the modification of RSA cryptography namely Symmetric-RSA, which seem to be equally useful for different cryptographic applications such as encryption, digital signature, etc. In order to design Symmetric-RSA, two prime numbers are negotiated using Diffie-Hellman key exchange protocol followed by RSA algorithm. As the new scheme uses Diffie-Hellman and RSA algorithm, the security of the overall system depends on discrete logarithm as well as factorization problem and thus, its security is more than public-key RSA. Finally, some new cryptographic applications of the proposed modifications are described that certainly extend the applications of the existing RSA.

scholarly journals A Visual Cryptographic Technique for Transferring Secret Image in Public Cloud

2020 ◽  
Vol 9 (3) ◽  
pp. 2257-2260
Keyword(s):  
Computational Cost ◽  
Visual Cryptography ◽  
Public Key ◽  
Public Cloud ◽  
Secret Key ◽  
The Public ◽  
Secret Image ◽  
Private Key ◽  
Diffie Hellman ◽  
Client System

The use of “Asymmetric Cryptography” provides the way to avail the feature of non-repudiation, encryption of data and defining the user digital identity to map with the authenticating user in the Public Cloud. A security technique is to be provided for the data even before it is stored on the Cloud. The public key certificate can be transferred into key server for encrypting the data by other users or devices in the public cloud. By using OpenPGP standard (PGP)/GNU Privacy Guard (GnuPG), public key certificate and the private key certificate can be generated by the user in the client system itself. The client private key can never be moved out from the client system and users only responsibility is to decrypt their data like images. This methodology will be very much suitable for authenticating, transferring, accessing and storing the images in the Public Cloud. The computational cost for encrypting the whole image with public key will be huge and so the hybrid methodology is proposed with visual cryptography technique and Elliptic-Curve Diffie–Hellman (ECDH) methodology. This paper proposes secure transfer of secret image by using visual cryptography technique and thereby modifying any one of the visual shares into encrypted data with ECDH secret key and finally converted those two shares into base64 format. The proposed algorithm is implemented by using the Python language and their results are discussed with sample images.

Modification of Traditional RSA into Symmetric-RSA Cryptosystems

2017 ◽  
Vol 13 (1) ◽  
pp. 66-73
Author(s):  
Prerna Mohit ◽  
G. P. Biswas
Keyword(s):  
Digital Signature ◽  
Discrete Logarithm ◽  
Prime Numbers ◽  
Public Key ◽  
Key Exchange Protocol ◽  
Factorization Problem ◽  
Rsa Algorithm ◽  
Diffie Hellman ◽  
Diffie Hellman Key Exchange ◽  
Rsa Cryptography

This paper addresses the modification of RSA cryptography namely Symmetric-RSA, which seem to be equally useful for different cryptographic applications such as encryption, digital signature, etc. In order to design Symmetric-RSA, two prime numbers are negotiated using Diffie-Hellman key exchange protocol followed by RSA algorithm. As the new scheme uses Diffie-Hellman and RSA algorithm, the security of the overall system depends on discrete logarithm as well as factorization problem and thus, its security is more than public-key RSA. Finally, some new cryptographic applications of the proposed modifications are described that certainly extend the applications of the existing RSA.

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