Public Key Cryptosystem

The Java Cryptography Architecture, JCA in short, was created to allow JCA-compliant cryptography providers to be plugged into a JCA-aware application at run time. This configurable feature makes JCA widely used and assures its success. However, the public key cryptographic service interfaces defined by JCA are based on the conventional public key cryptography, which is a single-sender-singlereceiver model, and does not accommodate the group-based public key cryptography well. Especially, it does not support the threshold cryptography (TC), an important type of group-based public key cryptography, which has been shown to be a useful tool to enhance system security. As a step towards the systematic application of group-based public key cryptography, this article proposes an extension to the JCA framework to integrate threshold cryptography. Under this extension, various TC providers implementing different TC primitives can be plugged into a security application at run-time. This extension also makes it easy for a existing JCA-aware application to be migrated to use threshold cryptography. An example provider of threshold RSA is implemented under this framework extension. It is our belief that such an extension would help speed up the adoption of threshold cryptography.

Assuming a cryptographically strong cyclic group G of prime order q and a random hash function H, we show that ElGamal encryption with an added Schnorr signature is secure against the adaptive chosen ciphertext attack, in which an attacker can freely use a decryption oracle except for the target ciphertext. We also prove security against the novel one-more-decyption attack. Our security proofs are in a new model, corresponding to a combination of two previously introduced models, the Random Oracle model and the Generic model. The security extends to the distributed threshold version of the scheme. Moreover, we propose a very practical scheme for private information retrieval that is based on blind decryption of ElGamal ciphertexts.

Cloud computing has become one of the migrating technology in the field of Information Technology(IT).In which user can access Infrastructure, Platform, Software, as Services anywhere from the Internet on as needed basis. The biggest challenge is to provide efficient confidentiality for the data to be stored in cloud due to this many organizations are not coming forward to store their confidential data in cloud. The typical technology used to provide data confidentiality is Cryptography system so that the data stored in third party is encrypted. In which the confidentiality is depends on the security level of the cryptography algorithm which is used. Meanwhile we should consider the efficiency (computation and storage cost) of the algorithm which increases the efficiency of cloud service. In this survey paper we look at various current researches being done to solve these issues, the current trends in storing, provide confidentiality and availability for the data in cloud and also discuss a public key cryptography scheme called Elliptic Curve Cryptography scheme which provide efficient security level by using small key, the challenges that are required to implement secure cloud data storage. This survey help to identify the future research areas.

Starting a small business with little capital can be very challenging to new business owners. Oftentimes, they resort to using trial and error in managing their finances especially when it comes to purchasing products from their suppliers. This study considered an online clothing store as a case study. The data provided by the online clothing store owners were used to estimate the parameters of the linear programming model. The LP model was solved using QM for Windows software to determine the most economical product mix to be purchased by the online clothing store owners from their suppliers and therefore provide an optimum solution. It was recommended that the owners should continue using linear programming in determining the number of each product to be purchased from the suppliers while minimizing the overall supply cost. Likewise, as their online clothing store grows, they must also explore the possibility of using linear programming to determine the optimal product mix for maximum profit.

Fiat and Shamir have proposed to use Zero-Knowledge interactive proofs to obtain secure identification mechanisms. Zero-Knowledge protocols are designed to address the identification service, by allowing a prover to demonstrate knowledge of a secret while revealing no information to be use by the verifier to convey the demonstration of knowledge to others. The invention of an efficient Zero-Knowledge identification scheme has provided anther public-key cryptosystem besides the renowned Fiat-Shamir scheme, for which in addition to the identification feature both key exchange and mutual identification are available. The availability of the elliptic curve discrete logarithm problem made the invented scheme very efficient. The purpose of this paper is to show the security level performance of our scheme and show its ability to resist the brute-force attack of an unauthorized prover.

The energy cost of asymmetric cryptography is a vital component of modern secure communications, which inhibits its wide spread adoption within the ultra-low energy regimes such as Implantable Medical Devices (IMDs) and Radio Frequency Identification (RFID) tags. The ciphertext-policy attribute-based encryption (CP-ABE) is a promising cryptographic tool, where an encryptor can decide the access policy that who can decrypt the data. Thus, the data will be protected from the unauthorized users. However, most of the existing CP-ABE schemes require huge storage and computational overheads. Moreover, CP-ABE schemes based on bilinear map loose the high efficiency over the elliptic curve cryptography because of the requirement of the security parameters of larger size. These drawbacks prevent the use of ultra-low energy devices in practice. In this paper, we aim to propose a novel expressive AND-gate access structured CP-ABE scheme with constant-size secret keys (CSSK) with the cost effici...

The object of this paper is the concrete security of recent multivariate signature schemes. A major challenge is to reconcile some "tricky" ad-hoc constructions that allow to make short signatures, with regular provable security. The paper is composed of two parts. In the first part of this paper we formalize and confront with the most recent attacks the security of several known multivariate trapdoor functions. For example the signature scheme Quartz is based on a trapdoor function G belonging to a family called HFEv-. It has two independent security parameters, and we claim that if d is big enough, no better method to compute an inverse of G than the exhaustive search is known. This will allow us to formulate our key assumption on which the provable security results can be build. In the second part, we study the security concrete security of signature schemes under our assumption. We study some general constructions, that transform a trapdoor function into a short signature scheme, and in particular these designed to obtain short signatures. On the one hand, we present generic attacks on such constructions. On the other hand, we study the possibility to prove or justify the security with some well chosen assumptions. Unfortunately for Quartz, our lower and upper security bounds do not coincide. Still the best attack known for Quartz is our generic attack using O(2 80 ) computations with O(2 80 ) of memory. We will also propose an alternative way of doing short signatures for which both bounds do coincide. Finally we also apply our results for Flash and Sflash.

In this paper we try to unify the frameworks of definitions of semantic security, indistinguishability and non-malleability by defining semantic security in comparison based framework. This facilitates the study of relations among these goals against different attack models and makes the proof of the equivalence of semantic security and indistinguishability easie r and more understandable. Besides, our proof of the equivalence of semantic security and indistinguishability does not need any intermediate goals such as non devidability to change the definition framework.

Extending the classical Legendre's result, we describe all solutions of the inequality |α -a/b| < c/b 2 in terms of convergents of continued fraction expansion of α. Namely, we show that a/b = (rpm+1 ± spm)/(rqm+1 ± sqm) for some nonnegative integers m, r, s such that rs < 2c. As an application of this result, we describe a modification of Verheul and van Tilborg variant of Wiener's attack on RSA cryptosystem with small secret exponent.

Cryptography is the study of “Mathematical Systems” involving two kinds of security protocols: Privacy and Authentication. The mathematical concepts from the branch of number theory known as Modular arithmetic, Quadratic residue are significantly useful in cryptography. Cryptography Deals with large number integers i.e. integers as big as hundred digits and more. In such situation identifying whether an integer “a” is quadratic residue modulo “p” where p is Prime can be achieved using Legendre and Jacobi Symbol. This paper introduces to the mathematical concepts of Quadratic Residue, Fermat&#39;s little theorem, Euler’s criterion and Legendre and Jacobi symbol. However it has been observed that Jacobi symbol in case of some example fails to give correct result and therefore the Limitation for predicting the quadratic residue.

Computer and network security system are needed to protect data during their transmissions and to guarantee that data are authentic. Cryptography is useful not only for proving data to be secure but also for ensuring that data have not altered. So, it is needed to implement the public key cryptosystem in computer and network security system. In cryptography, symmetric key cryptosystems are faster than public key asymmetric cryptosystems. But public key cryptosystems are more secure than symmetric key cryptosystems and widely used in computer and network security system. This describes the comparison of RSA Rivest, Shame, Adelman public key cryptosystem and ElGamal public key cryptosystem. RSA public key cryptosystem is faster than ElGamal in encryption and decryption. This paper also describes the encryption decryption time comparison of RSA and ElGamal. Kyaw Myo Thu | Kyaw Swar Hlaing | Nay Aung Aung &quot;Time Performance Analysis of RSA and Elgamal Public-Key Cryptosystems&quot; ...

With the emergence of technological revolution to host services over Internet, secure communication over World Wide Web becomes critical. Cryptographic protocols are being in practice to secure the data transmission over network. Researchers use complex mathematical problem, number theory, prime numbers etc. to develop such cryptographic protocols. RSA and Diffie Hellman public key crypto systems have proven to be secure due to the difficulty of factoring the product of two large primes or computing discrete logarithms respectively. With the advent of quantum computers a new paradigm shift on public key cryptography may be on horizon. Since superposition of the qubits and entanglement behavior exhibited by quantum computers could hold the potential to render most modern encryption useless. The aim of this chapter is to analyze the implications of quantum computing power on current public key cryptosystems and to show how these cryptosystems can be restructured to sustain in the new ...

The proposed technique is used to provide maximum security for data over the network and minimize time consumption in encryption and decryption. In this technique we used two key pair, one small size key pair for data encryption and one large size key pair to encrypt key component(n=p*q) of small size key pair. In proposed system every communicating party needs just two key pairs for communicating with any number of other communicating parties. Once someone obtains key pairs, he /she can communicate with anyone else. RSA is a well known public key cryptography algorithm and was one of the first great advances in public key cryptography.

A new digital multisignature scheme using bijective public-key cryptosystems that overcomes the problems of previous signature schemes used for multisignatures is proposed. The principal features of this scheme are (1) the length of a multisignature message is nearly equivalent to that for a singlesignature message; (2) by using a one-way hash function, multisignature generation and verification are processed in an efficient manner; (3) the order of signing is not restricted; and (4) this scheme can be constructed on any bijective public-key cryptosystem as well as the RSA scheme. In addition, it is shown that the new scheme is considered as safe as the public-key cryptosystem used in this new scheme. Some variations based on the scheme are also presented.

A new digital multisignature scheme using bijective public-key cryptosystems that overcomes the problems of previous signature schemes used for multisignatures is proposed. The principal features of this scheme are (1) the length of a multisignature message is nearly equivalent to that for a singlesignature message; (2) by using a one-way hash function, multisignature generation and verification are processed in an efficient manner; (3) the order of signing is not restricted; and (4) this scheme can be constructed on any bijective public-key cryptosystem as well as the RSA scheme. In addition, it is shown that the new scheme is considered as safe as the public-key cryptosystem used in this new scheme. Some variations based on the scheme are also presented.

Using the Burnside ring theoretic methods a new setting and a complete description of the Artin exponent A(G) of finite p-groups was obtained in [4]. In this paper, we compute A(G) for any finite group G -hence providing the global version of [4].

Quantum computers are able to destroy most, if not absolutely all conventional cryptosystems that are widely used in practice, specifically, systems based on the problem of factoring integers (e.g., RSA). Some cryptosystems like RSA system with 4 000bit keys are considered useful to protect classic computers from attacks, but probably absolutely useless against attacks on quantum computers. One of the alternatives are post-quantum systems, systems based on lattices. These systems are known for high security levels based on the worst-case hardness. They are based on the complexity of the problems grids, the main of which is the problem of the shortest vector (SVP). In fact, we consider the approximate option when we find a lattice vector, with the length of (n) times more than the shortest nonzero vector. ±(n) is the approximation coefficient, n is the lattice size. The best known algorithm for grids problems is LLL algorithm. This algorithm needs polynomial time with approximation ...

The rise of Internet of Things (IoT) networks has highlighted vulnerabilities related to devices' limited resources. As a result, it has become essential to delegate encryption services to cloud and fog platforms. Encryption as a Service (EaaS) offers a comprehensive range of cryptographic services to end-users, helping them manage their constrained resources and processing capabilities.

This paper reviews the current research on EaaS platforms and categorizes them based on the types of encryption algorithms they employ. Additionally, we present different EaaS architectures depending on the locations of their key components. To our knowledge, no existing surveys in this field have addressed these specific features.

Up to now, any attempt to use Gröbner bases in the design of public key cryptosystems has failed, as anticipated by a classical paper of B. Barkee et al.; we show why, and show that the only residual hope is to use binomial ideals, i.e. lattices. We propose two lattice-based cryptosystems that will show the usefulness of multivariate polynomial algebra and Gröbner bases in the construction of public key cryptosystems. The first one tries to revive two cryptosystems Polly Cracker and GGH, that have been considered broken, through a hybrid; the second one improves a cryptosystem (NTRU) that only has heuristic and challenged evidence of security, providing evidence that the extension cannot be broken with some of the standard lattice tools that can be used to break some reduced form of NTRU. Because of the bounds on length, we only sketch the construction of these two cryptosystems, and leave many details of the construction of private and public keys, of the proofs and of the security considerations to forthcoming technical papers.

Using Gröbner bases for the construction of public key cryptosystems has been often attempted, but has always failed. We review the reason for these failures, and show that only ideals generated by binomials may give a successful cryptosystem. As a consequence, we concentrate on binomial ideals that correspond to Euclidean lattices. We show how to build a cryptosystem based on lattice ideals and their Gröbner bases, and, after breaking a simple variant, we construct a more elaborate one. In this variant the trapdoor information consists in a ''small'' change of coordinates that allows one to recover a ''fat'' Gröbner basis. While finding a change of coordinates giving a fat Gröbner basis is a relatively easy problem, finding a small one seems to be a hard optimization problem. This paper develops the details and proofs related to computer algebra, the cryptographic details related to security, the comparison with other lattice cryptosystems and discusses the implementation.

Institute of Applied Mathematics, National Chung Hsing UniversityTaichung, Taiwan 402, R.O.C.Received: October 2000Abstract. Peyravian and Zunic (2000) proposed a password transmission scheme and a passwordchange scheme over an insecure network. Their proposed solutions do not require the use of anysymmetric-key or public-key cryptosystems. However, this article points out that their schemeshave several security flaws for practical applications. A slight improvement on their schemes isproposed in this paper to remove the security flaws.Key words: cryptography, password, hash function, discrete logarithm.

The zero-knowledge proof of knowledge, first defined by Fiat, Fiege and Shamir, was used by Galil, Haher and Yung as a means of constructing (out of a trapdoor function) an interactive public-key cryptosystem provably secure against chosen ciphertext attack. We introduce a revised setting which permits the definition of a non-interactive analogue, the non-interactive zereknowledge proof of knowledge, and show how it may be constructed in that setting from a non-interactive zeroknowledge proof system for N P (of the type introduced by Blum, Feldman and Micali). We give a formalization of chosen ciphertext attack in our model which is stronger than the "lunchtime attack" considered by Naor and Yung, and prove a non-interactive public-key cryptosystem based on non-interactive zero-knowledge proof of knowledge to be secure against it.

We present a new algorithm based on binary quadratic forms to factor integers of the form N = pq 2. Its heuristic running time is exponential in the general case, but becomes polynomial when special (arithmetic) hints are available, which is exactly the case for the so-called NICE family of public-key cryptosystems based on quadratic fields introduced in the late 90s. Such cryptosystems come in two flavours, depending on whether the quadratic field is imaginary or real. Our factoring algorithm yields a general key-recovery polynomial-time attack on NICE, which works for both versions: Castagnos and Laguillaumie recently obtained a total break of imaginary-NICE, but their attack could not apply to real-NICE. Our algorithm is rather different from classical factoring algorithms: it combines Lagrange's reduction of quadratic forms with a provable variant of Coppersmith's lattice-based root finding algorithm for homogeneous polynomials. It is very efficient given either of the following arithmetic hints: the public key of imaginary-NICE, which provides an alternative to the CL attack; or the knowledge that the regulator of the quadratic field Q(√ p) is unusually small, just like in real-NICE.

Cryptosystems based on the knapsack problem were among the first public-key systems to be invented. Their high encryption/ decryption rate attracted considerable interest until it was noticed that the underlying knapsacks often had a low density, which made them vulnerable to lattice attacks, both in theory and practice. To prevent low-density attacks, several designers found a subtle way to increase the density beyond the critical density by decreasing the weight of the knapsack, and possibly allowing non-binary coefficients. This approach is actually a bit misleading: we show that low-weight knapsacks do not prevent efficient reductions to lattice problems like the shortest vector problem, they even make reductions more likely. To measure the resistance of low-weight knapsacks, we introduce the novel notion of pseudodensity, and we apply the new notion to the Okamoto-Tanaka-Uchiyama (OTU) cryptosystem from Crypto '00. We do not claim to break OTU and we actually believe that this system may be secure with an appropriate choice of the parameters. However, our research indicates that, in its current form, OTU cannot be supported by an argument based on density. Our results also explain why Schnorr and Hörner were able to solve at Eurocrypt '95 certain high-density knapsacks related to the Chor-Rivest cryptosystem, using lattice reduction.

A breach of the unprotected electronic data might result in sensitive or confidential information being taken, changed, copied, sent, viewed, or used without authority. This study focuses on having security testing of Rijindael, Rivest Cipher4 and Format Preserving Algorithms in VB.Net Using simulation Comparison Techniques by comparing three (3) encryption algorithms by simulation method to know the most secured algorithm in VB.Net of different minimum and maximum key sizes to determine the security. The study also evaluate the three most common encryption algorithms like Rijandael, Rivest Cipher4 and Format Preserving Encryption Algorithm. A simulation comparison were conducted for those three (3) encryption algorithms at different settings for each algorithm such as minimum and maximum key size change to know which among those algorithms performs cryptography in the most secured way. Results from simulation analysis showed that Rivest Cipher4 (RC4) is the best algorithm in terms of security among the other compared contenders using the higher key size and lower key size as it maintain an average time for each key size both (Min & Max) followed by Rijandael and format preserving algorithm. This study therefore recommend the adoption of Rivest Cipher4 (RC4) in VB.Net in terms of secured cryptography.

In this thesis we present a new method for building pairs of HFE polynomials of high degree, in such a way that the map constructed with this pair is easy to invert. The inversion is accomplished using a low degree polynomial of Hamming weight three, which is derived from a special reduction via Hamming weight three polynomials produced by these two HFE polynomials. This allows us to build new candidates for multivariate trapdoor functions in which we use the pair of HFE polynomials to fabricate the core map. Using this new multivariate trapdoor function we derive an encryption scheme in a similar way as the HFE scheme is created. We show that this encryption scheme is relatively efficient and that it resists the attacks that have threatened the security of HFE. Finally, we propose parameters for a practical implementation of our cryptosystem. 1HFE stands for Hidden Field Equations.

We review the well-known relation between Lucas sequences and exponentiation. This leads to the observation that certain public-key cryptosystems that are based on the use of Lucas sequences have some elementary properties their re-inventors were apparently not aware of. In particular, we present a chosen-message forgery for 'LUC' (cf. [21; 25]), and we show that 'LUCELG' and 'LUCDIF ' (cf. [22, 261) are vulnerable to subexponential time attacks. This proves that various claims that were made about Lucas-based cryptosystems are incorrect. 'messagedependent' keys. The main selling point of the Lucas-based cryptosystems aa presented in these later publications (cf. [21; 22; 25; 261) is that they are not formulated in terms of exponentiation. This would make them unsusceptible to various wellknown attacks that threaten the security of more traditional exponentiationbased cryptosystems like 'RSA ' (cf. [19]) and 'Diffie-Hellman ' (cf. [4]). This is illustrated by the following quotes from 1211: This opens RSA to a cryptographic attack known as adaptive chosenmessage forgery. ... LUC is not multiplicative and therefore not susceptible to this attack.

The discrete logarithm in a finite group of large order has been widely applied in public key cryptosystem. In this paper, we investigate attempts to solve the discrete logarithm problem, leading towards finding the current computationally best algorithms for performing the backwards computation. Several proposed algorithms for computing discrete logarithms are known and we briefly discuss some of them. Furthermore, we present the most powerful general-purpose algorithm that is known today, called the index-calculus algorithm, and analyze its asymptotic performance. Finally, we discuss several technical issues that are important to the performance of the index-calculus algorithm, such as rapid methods to solve the systems of linear equations that arise in it.

We present a code-based public-key cryptosystem, in which we use Reed-Solomon codes over an extension field as secret codes and disguise it by considering its expanded code over the base field. Considering the expanded codes provide a safeguard against distinguisher attacks based on the Schur product. Moreover, without using cyclic or quasi-cyclic structure we obtain a key size reduction of nearly 60% compared to the classic McEliece cryptosystem proposed by Bernstein et al.

Resumen El proyecto que se presenta es una herramienta grafica didáctica utilizando el complemento Guide de Matlab. Para esto hemos dividido la interfaz en dos partes: la primera que será de comparación visual, donde la persona aplica los diferentes operadores morfológicos conocidos (dilatación, erosión, cierre y apertura), a una imagen con su respectivo elemento estructurante, y observara de manera visual el efecto que produce el operador morfológico en la imagen resultante y la parte de aplicación, en la cual podremos obtener la cantidad de objetos que presenta la imagen, con sus respectivas áreas y perímetros de cada forma o estructura que muestre la imagen.

In an AI-driven era, data the board is reliant on security confirmation and open commerce. A standard datasharing organization stage is important in the current datasharing courses of action, and clients transmit their information to a cloud server for limitation and dispersion. Customers, on the other hand, would lose control of their data the instant it was sent off the server, making security and insurance a major worry. Even though data encryption and access control are regarded as cutting-edge innovations for storing individual data on cloud servers, they only go so far. Regardless, it continues to depend heavily on an external source of validity, the Cloud Service Provider (CSP). To tackle this challenge, they combined blockchain, 3DES ciphertext technology, ECC, and the Interplanetary File System (IPFS). This research focuses on BTDEC, a Blockchain-based Trible Data Elliptic Curve Crypto System for Personal Data. The data holder encrypts the sharing data and saves it on IPFS in this customer-driven way, boosting the decentralization of the arrangement. The standardized data area and unscrambling key will be coupled utilizing 3DES with ECC, and the data owner will disseminate his data-related information and send on keys to data customers using blockchain, according to the built-up confirmation method. The data may only be downloaded and interpreted by the data client whose credits fulfill the confirmation conditions. BTDEC enables the data owner to deny a particular data client at the individual dimension without affecting others, providing him fine-grained network access over his data. When obtaining data, the ciphertext phrase search is almost usually utilized to secure the data customer's security. They investigated BTDEC's security and recreated our technology on the EOS blockchain, proving the concept's validity. Meanwhile, they investigated the limitation and overhead and determined that BTDEC performed well.

Finite fields are well studied discrete structures with a vast array of useful properties and are indispensable in the theory and application of cryptography. Arithmetic in finite field is an integral part of many public key algorithms. The performance of elliptic curve based schemes depends on the efficient arithmetic in the underlying field. ; Cryptography is one of the most prominent application areas of finite field arithmetic. Most of public-key cryptographic algorithms including the recent algorithms such as elliptic curve and pairing-based cryptography rely heavily on finite field arithmetic, which needs to be performed efficiently to meet the execution speed and design space constraints. These objectives constitute massive challenges that necessitate research efforts that will render the best algorithms, architectures, implementations, and design practices. This paper aims to provide a concise perspective for efficient finite field arithmetic in the most widely used finite f...

This research paper aims to attach a signature scheme that enables signature generation and verification to a well-defined cryptosystem. So, the new system combines key generation, encryption, signature generation, signature verification, and decryption algorithms. The Michael O. Rabin signature scheme uses random padding to validate signatures. Analogously, the proposed cryptographic technique utilizes the same padding system and additional components, such as quadratic residue plus the floor value of the quadratic quotient. The only difference is that Michael O. Rabin's signature may double or triple in some cases, whereas the proposed model uses a four-tuple signature system. The Michael O. Rabin cryptosystem's ability to produce multiple plaintexts from a single ciphertext and identical ciphertexts from distinct plaintexts is one of its potential ambiguities. To address this issue, I constructed a cryptosystem proposing a mathematical solution. Specifically, I created a mathematical model to distinguish identical encrypted text generated from different plaintexts in the Michael O. Rabin cryptosystem. However, that model lacked an authentication mechanism to verify the authenticity of the sender and the message, as it had no signature scheme. The proposed crypto-intensive technique uses a two-time security key by slightly altering the Diffie-Hellman key exchange protocol. Through a signature verification mechanism of the suggested method, the intended recipient can recover the original plaintext, and the sender has the advantage of using the encrypted text to create a signature. The above-mentioned cryptographic technique provides secure protection against man-in-the-middle attacks. It is unforgeable, whereas Rabin’s signature is forgeable in a forgery attack. By the way, the initial research initiative was to review different cryptosystem construction techniques and signature schemes and then apply those mathematical concepts to construct an effective cryptographic technique. This research begins with an exploratory research approach and ends with a computational research method. I utilized data collection methods such as conducting a literature review, employing critical thinking strategies, solving various computational math problems, and facilitating focus group discussions. The research population includes academic professors and graduate students.

Post-quantum cryptography (PQC) is a trend that has a deserved NIST status, and which aims to be resistant to quantum computers attacks like Shor and Grover algorithms. In this paper, we propose a method for designing post-quantum provable IND-CPA/IND-CCA2 public key cryptosystems based on polynomials over a non-commutative algebraic extension ring. The key ideas of our proposal is that (a) for a given non-commutative ring of rank-3 tensors, we can define polynomials and take them as the underlying work structure (b) we replace all numeric field arithmetic with GF(2 8) field operations. By doing so, it is easy to implement Rpropped Diffie-Helman-like key exchange protocol and consequently ElGamal-like cryptosystems. Here R stands for Rijndael as we work over the AES field. This approach yields secure post-quantum protocols since the resulting multiplicative monoid is immune against quantum algorithms and resist classical linearization attacks like Tsaban's Algebraic Span or Roman'kov. The protocols have been proved to be semantically secure. Finally, we present numerical examples of the proposed R-Propped protocols.

In this paper, we present a new approach for sharing images between l players by exploiting the additive and multiplicative homomorphic properties of two well-known public key cryptosystems, i.e. RSA and Paillier. Contrary to the traditional schemes, the proposed approach employs secret sharing in a way that limits the influence of the dealer over the protocol and allows each player to participate with the help of his key-image. With the proposed approach, during the encryption step, each player encrypts his own key-image using the dealer's public key. The dealer encrypts the secret-to-be-shared image with the same public key and then, the l encrypted key-images plus the encrypted to-be shared image are multiplied homomorphically to get another encrypted image. After this step, the dealer can safely get a scrambled image which corresponds to the addition or multiplication of the l + 1 original images (l key-images plus the secret image) because of the additive homomorphic property of the Paillier algorithm or multiplicative homomorphic property of the RSA algorithm. When the l players want to extract the secret image, they do not need to use keys and the dealer has no role. Indeed, with our approach, to extract the secret image, the l players need only to subtract their own key-image with no specific order from the scrambled image. Thus, the proposed approach provides an opportunity to use operators like multiplication on encrypted images for the development of a secure privacy preserving protocol in the image domain. We show that it is still possible to extract a visible version of the secret image with only l-1 key-images (when one key-image is missing) or when the l key-images used for the extraction are different from the l original key-images due to a lossy compression for example. Experimental results and security analysis verify and prove that the proposed approach is secure from cryptographic viewpoint.

This work develops an open source library in Python with applications in academic settings, for educational purposes. It can also be used for general software development. It allows users to implement Number Theory applications commonly employed in Cryptography and Information System Security. Improvements in teaching quality, user software readability, and time savings at the encoding stage could be expected.

The emerging trend now in network security is lightweight cryptography which is due to the growth of wireless technology. Lightweight cryptography is defined as cryptographic algorithm used to achieve higher security with limited resources. Generally, these wireless systems are in demand of security and resource(power). In order to meet these constraints an important lightweight scheme called signcryption is proposed with security features such as confidentiality, integrity(originality of sender and receiver), message and user authentication, nonrepudiation, forward secrecy and public verifiability. Signcryption fulfils the functions of signature and encryption in one logical. Strength of security and privacy of any cryptographic mechanisms that use random numbers require that the random numbers generated have two important properties namely 1.Uniform distribution and 2.Independence [9]. One idea proposed is to use sensor data as seed for Random Number Generator (RNG) to generate th...

This paper describes a hardware implementation of an arithmetic processor which is efficient for elliptic curve (EC) cryptosystems, which are becoming increasingly popular as an alternative for public key cryptosystems based on factoring. The modular multiplication is implemented using a Montgomery modular multiplication in a systolic array architecture, which has the advantage that the clock frequency becomes independent of the bit length m.

Goldreich-Goldwasser-Halevi (GGH) public key cryptosystem is an instance of lattice-based cryptosystems whose security is based on the hardness of lattice problems. In fact, GGH cryptosystem is the lattice version of the first code-based cryptosystem, proposed by McEliece. However, it has a number of drawbacks such as; large public key length and low security level. On the other hand, Low Density Lattice Codes (LDLCs) are the practical classes of lattice codes which can achieve capacity on the additive white Gaussian noise (AWGN) channel with low complexity decoding algorithm. This paper introduces a public key cryptosystem based on LDLCs to withdraw the drawbacks of GGH cryptosystem. To reduce the key length, we employ the generator matrix of the used LDLC in Hermite normal form (HNF) as the public key. Also, by exploiting the linear decoding complexity of the used LDLC, the decryption complexity is decreased compared with GGH cryptosystem. These increased efficiencies allow us to use the bigger values of security parameters. Moreover, we exploit the special Gaussian vector whose variance is upper bounded by the Poltyrev limit as the perturbation vector. These techniques can resist the proposed scheme against the most efficient attacks to the GGH-like cryptosystems.

In my first paper on the expansion to Dirichilet's theorem, the "Exemption Rule" allowed for us to identify which terms in an arithmetic progression described by an+b, where gcd(a,b)=1, would be prime. In the RSA algorithm, we require semi-prime numbers, which are products of two prime numbers p and q, where p and q can be either distinct or identical. The exemption rule allows us to generate n-values that would lead an+b to be of the form P(2k+1), a product of two odd numbers, and the exemption rule ensures that the two numbers are prime. To further enhance the security of the algorithm, at the end of the process, we can implement dynamic mapping functions which adds another layer of complexity, and with machine learning capabilities, create a modern enigma machine, in which the configurations are changing periodically.