Public Key Cryptosystem Research Papers (original) (raw)

2002

Elliptic Curve Cryptography (ECC) is emerging as an attractive public-key cryptosystem for mobile/wireless environments. Compared to traditional cryptosystems like RSA, ECC offers equivalent security with smaller key sizes, which results in faster computations, lower power consumption, as well as memory and bandwidth savings. This is especially useful for mobile devices which are typically limited in terms of their CPU, power and network connectivity.

1985, Journal of the ACM

The subset sum problem is to decide whether or not the O-1 integer programming problem " C aixi = M,

E-commerce has presented a new way of doing transactions all over the world using internet. The success of ecommerce depends greatly on how its information technology is used. Over the years the rate at which ecommerce sensitive information is sent over the internet and network has increased drastically. It is for this reason that every company wants to ensure that its ecommerce information is secured. There is need for ecommerce information transmitted via the internet and computer networks to be protected. There is substantial growth in the areas of credit card fraud and identity theft because the internet is a public network with thousands of millions of users. Amongst users are crackers or hackers that carry out the credit card fraud and identity theft in numerous ways facilitated by poor internet security; a concern regarding the exchange of money securely and conveniently over the internet increases. The criticality, danger, and higher priority importance of any e-commerce money transfer makes it a hot area of research interest in modern computer science and informatics. E-commerce industry is slowly addressing security issues on their internal networks but security protection for the consumers is still in its infancy, thus posing a barrier to the development of e-commerce. There is a growing need for technological solutions to globally secure ecommerce transaction information by using appropriate data security technology. The technology solution proposed for solving this security problem is the RSA cryptosystem. This research paper focuses on securing ecommerce information sent through the computer network and internet using RSA cryptography. It elucidates the implementation of RSA algorithm and shows that ecommerce security powered with RSA cryptography is very important in ecommerce transaction. While many attacks exist, the system has proven to be very secure.

2000

This report presents a brief survey on secret key and public key cryptography algorithms. These include: block ciphers, stream ci- phers, RSA, ElGamal and Elliptic Curve Cryptosystems (ECC). Since ECC achieved security levels comparable to those of traditional public key cryptosystems using smaller keys (160 bits), this work focus more on ECC. Finally, this work also presents a survey on

2007, Journal of Systems Architecture

For the last decade, Elliptic Curve Cryptography (ECC) has gained increasing acceptance in the industry and the academic community and has been the subject of several standards. This interest is mainly due to the high level of security with relatively small keys provided by ECC. To sustain the high throughput required by applications like network servers, highspeed implementations of public-key cryptosystems are needed. For that purpose, hardware-based accelerators are often the only solution reaching an acceptable performance-cost ratio. The fundamental question that arises is how to choose the appropriate efficiency-flexibility tradeoff.

2019, IJIRAE:: AM Publications,India

Security has become one of the key features of data transmission on large database. RDBMS are used for storage purposes but with applications generating enormous amount of data, RDBMS is no longer efficient because RDBMS doesn't support quick data access and computations as it do not support processing of data in distributed manner. NoSQL databases are nowadays popular in handling the unstructured data that are available as open source databases such as MongoDB, Cassandra, etc. This paper make a detailed study on the encryption techniques of NoSQL databases especially MongoDB which becomes popular in data management. Since encryption features are not applied on handling the data in MongoDB, In this paper, security for users data is provided by using additive homomorphic asymmetric cryptosystem which encrypts the users data in MongoDB(CryptMDB) and achieve strong user's data privacy protection. This also supports the database operations over the encrypted data.

2008, Computing Research Repository - CORR

We have designed a new class of public key algorithms based on quasigroup string trans- formations using a speciflc class of quasigroups called multivariate quadratic quasigroups (MQQ). Our public key algorithm is a bijective mapping, it does not perform message expansions and can be used both for encryption and signatures. The public key consist of n quadratic polynomials with n variables where n = 140;160;:::. A particular characteristic of our public key algorithm is that it is very fast and highly parallelizable. More concretely, it has the speed of a typical modern symmetric block cipher { the reason for the phrase "A Public Key Block Cipher" in the title of this paper. Namely the reference C code for the 160{bit variant of the algorithm performs decryption in less than 11,000 cycles (on Intel Core 2 Duo { using only one processor core), and around 6,000 cycles using two CPU cores and OpenMP 2.0 library. However, implemented in Xilinx Virtex-5 FPGA that is running on ...

In this paper we propose an ecient multivariate public key cryptosystem based on per- mutation p-polynomials over finite fields. We first characterize a class of permutation p- polynomials over finite fields Fqm and then construct a trapdoor function using this class of permutation p-polynomials. The complexity of encryption in our public key cryptosystem is O(m3) multiplication which is equivalent to other multivariate public key cryptosystems. However the decryption is much faster than other multivariate public key cryptosystems. In decryption we need O(m2) left cyclic shifts and O(m2) xor operations.

2007, Journal of Systems Architecture

2001

This paper presents a new proposed message digest algorithm 0). Many of its characteristics (applications domain, performance and implementation structure) are similar to those of MDCfamily of hash functions. The proposed algorithm takes as input a message of arbitrary length and produces as output a 128/160-bit fugerprint or message digest. New features of the proposed algorithm include the heavy use of data-dependent rotations, and the inclusion of integer multiplication as an additional primitive operation. These proposed features are expected to provide high security level with enhancement in throughput. The proposed algorithm is intended for digital signature applications, where a large fde must be compressed in a secure manner before being signed (encrypted) with a private secret key under a public-key cryptosystem. The proposed algorithm is designed to be quite fast on 32-bit machines. In addition, it does not require any large substitution tables, so that the algorithm can be coded quite compactly. We describe the general characteristics, architecture and implementation, and give a complete specifcation for MD-160/128. Several test vectors are used for inspecting the validity of the proposed algorithm. Also, we compare the software performance of several MDCbased algorithms, which is of independent interest. Simulation results show that the throughput of the proposed MD-128 is about 76.4 Mbitlsec while in RIPEMD-128 is about 69.8 Mbitlsec.

math.gc.cuny.edu

Most common public key cryptosystems and public key exchange protocols presently in use, such as the RSA algorithm, Diffie-Hellman, and elliptic curve methods are number theory based and hence depend on the structure of abelian groups. The strength of computing machinery has made these techniques theoretically susceptible to attack and hence recently there has been an active line of research to develop cryptosystems and key exchange protocols using noncommutative cryptographic platforms. This line of investigation has been given the broad title of noncommutative algebraic cryptography. This was initiated by two public key protocols that used the braid groups, one by Ko, Lee et.al.and one by Anshel, Anshel and Goldfeld. The study of these protocols and the group theory surrounding them has had a large effect on research

2011

Securing data over wireless medium got significant importance because of inherent problems of power, memory and processing constraints. Hyper elliptic curve cryptosystem (HECC) is an emerging public key cryptosystem suitable for such resource constrained environment due to its high efficiency and shorter key size, HECC can be used for digital signatures and encryption to provide confidentiality and authenticity. In this paper, we proposed a resource efficient signcryption schemes based on Hyperelliptic curve cryptosystem. Compared with existing schemes our proposed scheme can save up to 40% computational cost and a minimum of 40% of Communication Overhead.

In current scenario everything is being transferred on the web and other communication medium. So that we need to make our data secure from all other attacker and unauthorized person. So that we have to give lot of protection to the transmitting data. For that we have lots of cryptography algorithm .But all of then do not provide level best protection in today‟s world as there are lots of ways to make that algorithm cracked and the cryptanalyst can retrieve the plain text so easily. So that with reference to the RSA and other famous algorithms as Diffie Hellman and N-prime RSA we have tried to give one more level of security by the use of Magic Rectangle. And by the use of Magic Rectangle we can have different cipher text for the same character. So by these many reasons this approach give enhancement to the public key cryptosystem. And Magic Rectangle have different approach that can unable to get the plain text without the knowledge of generation of Magic Rectangle.

2004, Microprocessors and Microsystems

Secure electronic and internet transactions require public key cryptosystems to establish and distribute shared secret information for use in the bulk encryption of data. For security reasons, key sizes are in the region of hundred's of bits. This makes cryptographic procedures slow in software. Hardware accelerators can perform the computationally intensive operations far quicker. Field-Programmable Gate Arrays are well-suited for this application due to their reconfigurability and versatility. Elliptic Curve Cryptosystems over GF( p) have received very little attention to date due to the seemingly more attractive finite field GF(2 m ). However, we present a GF( p) Arithmetic Logic Unit which can perform 160-bit arithmetic at clock speeds of up to 50 MHz. q

1996, Designs, Codes and Cryptography

McEliece proposed a public-key cryptosystem based on algebraic codes, in particular binary classical Goppa codes. Actually, his scheme needs only a class of codes with a good decoding algorithm and with a huge number of inequivalent members with given parameters. In the present paper we look at various aspects of McEliece's scheme using the new and much larger class of q-ary algebraic-geometric Goppa codes.

2010, International journal of Network Security & Its Applications

Quantum Cryptography or Quantum key distribution (QKD) is a technique that allows the secure distribution of a bit string, used as key in cryptographic protocols. When it was noted that quantum computers could break public key cryptosystems based on number theory extensive studies have been undertaken on QKD. Based on quantum mechanics, QKD offers unconditionally secure communication. Now, the progress of research in this field allows the anticipation of QKD to be available outside of laboratories within the next few years. Efforts are made to improve the performance and reliability of the implemented technologies. But several challenges remain despite this big progress. The task of how to test the apparatuses of QKD For example did not yet receive enough attention. These devises become complex and demand a big verification effort. In this paper we are interested in an approach based on the technique of probabilistic model checking for studying quantum information. Precisely, we use the PRISM tool to analyze the security of BB84 protocol and we are focused on the specific security property of eavesdropping detection. We show that this property is affected by the parameters of quantum channel and the power of eavesdropper.

metronu.ulb.ac.be

2014, International Journal of Advanced Computer Science and Applications

RSA is one of the most important public key cryptosystems for information security. The security of RSA depends on Integer factorization problem, it relies on the difficulty of factoring large integers. Much research has gone into problem of factoring a large number. Due to advances in factoring algorithms and advances in computing hardware the size of the number that can be factorized increases exponentially year by year. The General Number Field Sieve algorithm (GNFS) is currently the best known method for factoring large numbers over than 110 digits. In this paper, a parallel GNFS implementation on a BA-cluster is presented. This study begins with a discussion of the serial algorithm in general and covers the five steps of the algorithm. Moreover, this approach discusses the parallel algorithm for the sieving step. The experimental results have shown that the algorithm has achieved a good speedup and can be used for factoring a large integers.

2017, International Journal of Computer Science, Engineering and Applications (IJCSEA)

Using passwords only has rapidly become a security risk. Another approach to security is visual cryptography (VC), which divides paper documents into several encrypted papers managed by multiple people. Decryption occurs by stacking these papers, i.e., they cannot be decrypted individually. In our work, we consider a system for decrypting text encrypted by VC on digital devices. Furthermore, we propose a method for automatically recognizing encrypted portions using images captured by a digital device's camera. Our system has several advantages, including no actual text in communication and enabling users to use different passwords or secret questions at each use. Furthermore, our method is implementable on wearable glasses-like devices, thus enabling wearers to decrypt text simply by looking at encrypted portions. We conducted experiments regarding recognition accuracy and performance and obtained results showing that our proposed method was able to achieve a high recognition rate at a low cost.

2006, Applied Reconfigurable Computing

This paper presents a reconfigurable hardware architecture for Public-key cryptosystems. By changing the connections of coarse grain Carry-Save Adders (CSAs), the datapath provides a high perfor- mance for both RSA and Elliptic Curve Cryptography (ECC). In addi- tion, we introduce another reconfigurability for the flip-flops in order to make the best of hardware resources. The results of FPGA implemen- tation

2007

Over the past few years, much research attention has been afforded to the application of remote patient monitoring using embedded mobile devices. However, relatively little research has been done to investigate the security aspects of such scenarios. The present work describes the implementation of a cryptographic algorithm based on elliptic curves on an embedded mobile device useful for healthcare purposes. A personal digital assistant (PDA) has been chosen to be the hardware platform for the implementation as it is particularly suitable for remote patient monitoring applications. The motivation for this paper was to formulate a secure protocol which comprises of signature, encryption and authentication (SEA) as a combined ingredient of secure remote patient monitoring application using mobile devices. This needed to be easy to use and computationally efficient in order to be acceptable to both clinicians and patients and the results indicate a positive outcome.

2004, Ieee Transactions on Information Theory

We present a new family of so-called reducible rank codes which are a generalization of rank product codes [2]. This family includes maximal rank distance (MRD) codes for lengths in the field . We give methods for encoding and decoding... more

2003, ACM SIGARCH Workshop on MEmory …

As an increasing number of Internet hosts are wireless, handheld devices with small memory and strict CPU-latency constraints, the performance of cryptography methods has become critical for high transaction throughput. Elliptic Curve Cryptography (ECC) is emerging as an attractive public-key system for constrained environments, because of the small key sizes and computational efficiency, while preserving the same security level as the standard methods. The memory performance of ECC algorithms was scarcely investigated. We have developed a set of kernel benchmarks to examine performance of standard and corresponding elliptic curve public-key methods. In this paper, we characterize the operations and their memory impact on performance in Diffie-Hellman key exchange, digital signature algorithm, ElGamal, and RSA publickey cryptosystem, as well as elliptic curve Diffie-Hellman key exchange, elliptic curve digital signature algorithm and elliptic curve El-Gamal algorithm. We modeled a typical mobile device based on the Intel XScale architecture, which utilizes an ARM processor core and studied the benchmark set on that target. Different possible variations for the memory hierarchy of such basic architecture were considered. We compared our benchmarks with MiBench/Security, another widely accepted benchmark set, in order to provide a reference for our evaluation.

1978, Communications of The ACM

An encryption method is presented with the novel property that publicly revealing an encryption key does not thereby reveal the corresponding decryption key. This has two important consequences: (1) Couriers or other secure means are not needed to transmit keys, since a message can be enciphered using an encryption key publicly revealed by the intended recipient. Only he can decipher the message, since only he knows the corresponding decryption key.

2004, Proceedings of the 14th ACM Great …

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.

2006

A Diffie-Hellman public-key cryptography based on chaotic attractors of neural networks is described in the paper. There is a one-wayfunction between chaotic attractors and initial states in an Overstoraged Hopfield Neural Network (OHNN). If the synaptic matrix of OHNN is changed, each attractor and its corresponding domain ofinitial state attraction will be changed. Then, we regard the neural synaptic matrix as a trap door, and change it with commutative random permutation matrix. A new Diffie-Hellman public-key cryptosystem can be implemented, namely keeping the random permutation operation of the neural synaptic matrix as the secret key, and the neural synaptic matrix after permutation as public-key. In order to explain the practicability of the encryption scheme, Security and encryption efficient ofthe scheme are discussed. The scheme of application for Internet secure communications is implemented by using Java program. The experimental results show that the proposed cryptography is feasible, and has a good performance of encryption and decryption speed to ensure the real time ofIPng secure communications.

2008

The efficiency of the core Galois field arithmetic improves the performance of elliptic curve based public key cryptosystem implementation. This paper describes the design and implementation of a reconfigurable Galois field multiplier, which is implemented using field programmable gate arrays (FPGAs). The multiplier of Galois field based on karatsuba’s divide and conquer algorithm allows for reasonable speedup of the top-level public key algorithms. Binary Karatsuba multiplier is more efficient if it is truncated at n-bit multiplicand level and use an efficient classic multiplier algorithm. In these work three levels to truncate Binary karatsuba algorithm (4 bits, 8 bits and 16 bits) are chosen showing that 8 bits is the best level for minimum number of slices and time delay to truncate Binary karatsuba algorithm which is designed on a Xilinx VirtexE XCV2600 FPGA device. The VHDL hardware models are building using Xilinx ISE foundation software. This work is able to compute GF(2191) multiplication in 45.889 ns.

2004, Topics in Cryptology–CT-RSA 2004

This paper presents a scalable hardware implementation of both commonly used public key cryptosystems, RSA and Elliptic Curve Cryptosystem (ECC) on the same platform. The introduced hardware accelerator features a design which can be varied from very small (less than 20 Kgates) targeting wireless applications, up to a very big design (more than 100 Kgates) used for network security. In latter option it can include a few dedicated large number arithmetic units each of which is a systolic array performing the Montgomery Modular Multiplication (MMM). The bound on the Montgomery parameter has been optimized to facilitate more secure ECC point operations. Furthermore, we present a new possibility for CRT scheme which is less vulnerable to side-channel attacks.

2005, AA

Abstract:-We propose a public key cryptosystem based on block upper triangular matrices. This system is a variant of the Discrete Logarithm Problem with elements in a finite group, capable of increasing the difficulty of the problem while... more

2003, Computers & Education

Modern cryptography can achieve levels of security and authentication that non-specialists find literally incredible. Techniques including information-hiding protocols, zero-knowledge proofs and public key cryptosystems can be used to support applications like digital signatures, digital cash, on-line poker and secure voting in ways that are provably secure-far more secure than the traditional systems they replace. This paper describes simple versions of such applications that have been used to give school-children and the general public a broad understanding of what can be achieved, and how. The material has been extensively and successfully used by the authors in schools, science festivals and with undergraduates, and even postgraduate specialists. #

2004

This paper showed that, Wong's watermarking scheme suffers from a serious security leak. The main reason of this leak is that, the authors made a fundamental mistake of assuming that the plaintext size determines ciphertext size. We demonstrated in this paper that, it is the key size that determines ciphertext size. Therefore, if a small key is applied to produce a small ciphertext that can be embedded in the small image blocks, the scheme will be insecure. And if a long key is used, the Wong's scheme will always give misleading results. This paper has come up with an elegant solution to tackle this leak. A larger image block was recommended to hold the entire watermark. A new method of applying the cryptographic hash function MD5 is utilized to achieve a high-level of localization accuracy. This solution moved the Wong technique from a cryptographically insecure system to a reliable and secures one. 0-7803-8554-3/04/$20.00 ©2004 IEEE.

2004, IEEE Transactions on Computers

The focus of this technical report is implementation issues for three separate but related topics of interest in elliptic curve point arithmetic. The first concerns use of single-instruction multipledata (SIMD) capabilities to speed field... more

2001, Lecture Notes in Computer Science

Non-Interactive Zero Knowledge (NIZK), introduced by Blum, , is a fundamental cryptographic primitive which has attracted considerable attention in the last decade and has been used throughout modern cryptography in several essential ways. For example, NIZK plays a central role in building provably secure public-key cryptosystems based on general complexity-theoretic assumptions that achieve security against chosen ciphertext attacks. In essence, in a multi-party setting, given a fixed common random string of polynomial size which is visible to all parties, NIZK allows an arbitrary polynomial number of Provers to send messages to polynomially many Verifiers, where each message constitutes an NIZK proof for an arbitrary polynomial-size NP statement.

2009, 2009 Fourth International Conference on Computer Sciences and Convergence Information Technology

This paper aims to provide a practical implementation of a probabilistic cipher by extending on the algorithms by Fuchsbauer, Goldwasser and Micali. We provide details on designing and implementing the cipher and further support our understanding by providing a statistical analysis of our implementation for the key generation, encryption, and decryption times taken by the cipher for key sizes of 1024, 2048, and 4096 bits for varying message spaces of 750, 1500, 3000, and 5000 bits. The concept of 'inter-bit operating time' is introduced for the cipher which calculates time elapsed between two instances of an operation. We show the working of a probabilistic cipher purely from a practical standpoint to justify if its original algorithm is practically implementable.

2008

This paper proposes a public key cryptosystem based on the symmetric group S n , and validates its theoretical foundation. The proposed system benefits from the algebraic properties of S n such as non commutative, high computational speed and high flexibility in selecting keys which make the Discrete Logarithm Problem (DLP) resistant to attacks by algorithms such as Pohlig-Hellman. Against these properties, the only disadvantage of the scheme is its relative large memory and bandwidth requirements. Due to the similarities in the algebraic structures, many other cryptosystems can be translated to their symmetric group analogs, and the proposed cryptosystem is in fact the Generalized El-Gamal cryptosystem which is based on S n instead of GF(p).

2019, Jurnal Matematika Integratif

Abstrak Protokol tanda tangan digital ElGamal mengaplikasikan ring Zp pada kunci asimetri dan fungsi hash. Pada makalah ini, konsep ring Zp akan digantikan dengan konsep general linear group GL (n, Zp) yaitu himpunan semua matriks yang... more

2004, Journal of Systems and Software

trations (E-Government) give rise to the important question, how to reliably exchange confidential data via public communication networks such as the Internet. Any data transfer must be protected from a fraudulent access by third parties in the sense that it has to be ensured that exchanged documents are neither read nor modified during the data transfer. Furthermore, the author-document relationships have to be known and unique at any point in time. The fundamental technology for document protection during public data transfer is known as public key cryptography. Digital signature schemes are probably the most common occurrence of public key cryptosystems. This paper addresses public key cryptosystems based on elliptic curves, which are aimed to high-performance digital signature schemes. Elliptic curve (EC) algorithms are characterized by the fact that one can work with considerably shorter keys compared to the RSA approach at the same level of security. A general and highly efficient method for mapping the most time-critical operations to a configurable co-processor is proposed. By means of real-time measurements the resulting performance values are compared to previously published state of the art hardware im-

2004, Icics

We present a novel public key encryption scheme semantically secure in the standard model under the intractability assumption of a subgroup membership problem related to the factorization problem.

1993, IEEE Journal on Selected Areas in Communications

This paper presents three methods for strengthening public key cryptosystems in such a way that they become secure against adaptively chosen ciphertext attacks. In an adaptively chosen ciphertext attack, an attacker can query the deciphering algorithm with any ciphertexts, except for the exact object ciphertext to be cryptanalyzed. The first strengthening method is based on the use of one-way hash functions, the second on the use of universal hash functions, and the third on the use of digital signature schemes. Each method is illustrated by an example of a public key cryptosystem based on the intractability of computing discrete logarithms in finite fields. Seeurity of the three example cryptosystems is formally proved. Two other issues, namely, applications of the methods to public key cryptosystems based on other intractable problems and enhancement of information authentication capability to the cryptosystems, are also discussed.

2010, Advances in Mathematics of Communications

. A simple elliptic curve

2003

We propose a practical scheme based on factoring and semantically secure (IND-CPA) in the standard model. The scheme is obtained from a modi.cation of the so called RSA-Paillier [5] scheme. This modification is reminiscent of the ones applied by Rabin [22] and Williams [25] to the well-known RSA cryptosystem. Thanks to the special properties of such schemes, we obtain efficiency similar to that of RSA cryptosystem, provably secure encryption (since recovering plaintext from ciphertext is as hard as factoring) and indistinguishability against plaintext attacks. We also construct a new trapdoor permutation based on factoring, which has interest on its own. Semantic security of the scheme is based on an appropiate decisional assumption, named as Decisional Small 2e-Residues assumption. The robustness of this assumption is also discussed. Compared to Okamoto-Uchiyama's scheme [18], the previous IND-CPA cryptosystem in the standard model with onewayness based on factoring, our scheme is drastically more efficient in encryption, and presents higher bandwith, achieving the same expansion factor as Paillier or El Gamal schemes. We believe the new scheme could be an interesting starting point to develop efficient IND-CCA schemes in the standard model with one-wayness based on factoring.

1978, Communications of The ACM

R o g e r M . N e e d h a m a n d M i c h a e l D . S c h r o e d e r X e r o x P a l o A l t o R e s e a r c h C e n t e r Use of encryption to achieve authenticated communication in computer networks is discussed. Example protocols are presented for the establishment of authenticated connections, for the management of authenticated mail, and for signature verification and document integrity guarantee. Both conventional and public-key encryption algorithms are considered as the basis for protocols.

1978, Communications of The ACM

1995, IMA Conference on Cryptography and Coding

this report, the use of hiding matrices is proposed to modify all the abovePKC. The modified open keys are as follows:

2010

The efficiency of the core Galois field arithmetic improves the performance of elliptic curve based public key cryptosystem implementation. This paper describes the design and implementation of a reconfigurable Galois field multiplier, which is implemented using field programmable gate arrays (FPGAs). The multiplier of Galois field based on Karatsuba's divide and conquer algorithm allows for reasonable speedup of the top-level public key algorithms. Binary Karatsuba multiplier is more efficient if it is truncated at n-bit multiplicand level and use an efficient classic multiplier algorithm. In these work three levels to truncate Binary Karatsuba algorithm (4 bits, 8 bits and 16 bits) are chosen showing that 8 bits is the best level for minimum number of slices and time delay to truncate Binary Karatsuba algorithm which is designed on an Xilinx VirtexE XCV2600 FPGA device. The VHDL hardware models are building using Xilinx ISE foundation software. This work is able to compute GF(2191) multiplication in 45.889 ns. experimental results of comparing block and stream ciphers when used to secure VoIP in terms of end-to-end delay and subjective quality of perceived voice.

The performance of today's public key cryptosystems depends mainly on the efficiency of the underlying finite field arithmetic, especially the modular multiplication. In this work we propose a new modular multiplication algorithm for GF(P ) which has a complexity of only n 2 + 7n. To our knowledge this is superior to the complexity values of any other modular multiplication algorithm for GF(P ).

2003

At the beginning some results from the field of graph theory are presented. Next we show how to share a secret that is proper n-coloring of the graph, with the known structure. The graph is described and converted to the form, where colors assigned to vertices form the number with entries from Z n . A secret sharing scheme (SSS) for the graph coloring is proposed. The proposed method is applied to the public-key cryptosystem called "Polly Cracker". In this case the graph structure is a public key, while proper 3-colouring of the graph is a private key. We show how to share the private key. Sharing particular n-coloring (colorto-vertex assignment) for the known-structure graph is presented next.

2010, … Communication Technology (ICACT), 2010 The 12th …

. A simple elliptic curve

1996, Designs, Codes and Cryptography

2011, Optics Communications

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.