Biblio

A multi-designated receiver authentication code (MDRA-code) with information-theoretic security is proposed as an extension of the traditional multi-receiver authentication code. The purpose of the MDRA-code is to securely transmit a message via a broadcast channel from a single sender to an arbitrary subset of multiple receivers that have been designated by the sender, and only the receivers in the subset (i.e., not all receivers) should accept the message if an adversary is absent. This paper proposes a model and security formalization of MDRA-codes, and provides constructions of MDRA-codes.

Pairings on elliptic curves are used for innovative protocols such as ID-based encryption and zk-SNARKs. To make the pairings secure, it is important to consider the STNFS which is the special number field sieve algorithm for discrete logarithms in the finite field. The Fotiadis-Konstantinou curve with embedding degree 12(FK12), is known as one of the STNFS secure curves. To an efficient pairing on the FK12 curve, there are several previous works that focus on final exponentiation. The one is based on lattice-based method to decompose the hard part of final exponentiation and addition chain. However, there is a possibility to construct a more efficient calculation algorithm by using the relations appeared in the decomposition calculation algorithm than that of the previous work. In this manuscript, the authors propose a relation of the decomposition and verify the effectiveness of the proposed method from the execution time.

We propose versatile hardware framework for ECC. The framework supports arithmetic operations over P-256, Ed25519 and Curve25519 curves, enabling easy implementation of various ECC algorithms. Framework finds its application area e.g. in FIDO2 attestation or in nowadays rapidly expanding field of hardware wallets. As the design is intended to be ASIC-ready, we designed it to be area efficient. Hardware units are reused for calculations in several finite fields, and some of them are superior to previously designed circuits in terms of time-area product. The framework implements several attack countermeasures. It enables implementation of certain countermeasures even in later stages of design. The design was validated on SoC FPGA.

The paradigm of quantum computation has led to the development of new algorithms as well variations on existing algorithms. In particular, novel cryptographic techniques based upon quantum computation are of great interest. Many classical encryption techniques naturally translate into the quantum paradigm because of their well-structured factorizations and the fact that they can be phased in the form of unitary operators. In this work, we demonstrate a quantum approach to data encryption and decryption based upon the McEliece cryptosystem using Reed-Muller codes. This example is of particular interest given that post-quantum analyses have highlighted this system as being robust against quantum attacks. Finally, in anticipation of quantum computation operating over binary fields, we discuss alternative operator factorizations for the proposed cryptosystem.

Pairings on elliptic curves which are carried out by the Miller loop and final exponentiation are used for innovative protocols such as ID-based encryption and group signature authentication. As the recent progress of attacks for finite fields in which pairings are defined, the importance of the use of the curves with prime embedding degrees \$k\$ has been increased. In this manuscript, the authors provide a method for providing efficient final exponentiation algorithms for a specific cyclotomic family of curves with arbitrary prime \$k\$ of \$k\textbackslashtextbackslashequiv 1(\textbackslashtextbackslashtextmod\textbackslashtextbackslash 6)\$. Applying the proposed method for several curves such as \$k=7\$, 13, and 19, it is found that the proposed method gives rise to the same algorithms as the previous state-of-the-art ones by the lattice-based method.

The article proposes a general approach to the implementation of encryption schemes based on the group of automorphisms of the Hermitian functional field. The three-parameter group is used with logarithmic captions outside the center of the group. This time we applied for an encryption scheme based on a Hermitian function field with homomorphic encryption. The use of homomorphic encryption is an advantage of this implementation. The complexity of the attack and the size of the encrypted message depends on the strength of the group.

We consider the anonymous mutual authentication problem, which consists of a certificate authority, single or multiple verifiers, many legitimate users (provers) and any arbitrary number of illegitimate users. The legal verifier and a legitimate user must be mutually authenticated to each other using the user's key, while the identity of the user must stay unrevealed. An attacker (illegitimate prover) as well as an illegal verifier must fail in authentication. A general interactive information theoretic framework in a finite field is proposed, where the normalized total key rate as a metric for reliability is defined. Maximizing this rate has a trade-off with establishing anonymity. The problem is studied in two different scenarios: centralized scenario (one single verifier performs the authentication process) and distributed scenario (authentication is done by N verifiers, distributively). For both scenarios, achievable schemes, which satisfy the completeness, soundness (at both verifier and prover) and anonymity properties, are proposed. Increasing the size of the field, results in the key rate approaching its upper bound.

Network security is a general idea to ensure information transmission over PC and portable systems. Elliptic curve cryptosystems are nowadays widely used in public communication channels for network security. Their security relies upon the complexity of clarifying the elliptic curve discrete alogarithm issue. But, there are several general attacks in them. Elliptic bend number juggling is actualized over complex fields to enhance the security of elliptic curve cryptosystems. This paper starts with the qualities of elliptic curve cryptosystems and their security administrations. At that point we talk about limited field number-crunching and its properties, prime field number-crunching, twofold field math and complex number-crunching, and elliptic bend number-crunching over prime field and parallel field. This paper proposes how to execute the unpredictable number of math under prime field and double field utilizing java BigInteger class. also, we actualize elliptic bend math and elliptic bend cryptosystems utilizing complex numbers over prime field and double field and talk about our trials that got from the usage.

The article explores the question of the effective implementation of arithmetic operations with points of an elliptic curve given over a prime field. Given that the basic arithmetic operations with points of an elliptic curve are the operations of adding points and doubling points, we study the question of implementing the arithmetic operations of adding and doubling points in various coordinate systems using the weighted number system and using the Residue Number System (RNS). We have shown that using the fourmodule RNS allows you to get an average gain for the operation of adding points of the elliptic curve of 8.67% and for the operation of doubling the points of the elliptic curve of 8.32% compared to the implementation using the operation of modular multiplication with special moduli from NIST FIPS 186.

DNA cryptography becomes a burgeoning new area of study along with the fast-developing of DNA computing and modern cryptography. Point-doubling, point-addition and point-multiplication are three fundamental point-operations to construct encryption protocols in some cryptosystem over mathematical curves such as elliptic curves and conic curves. This paper proposes a DNA computing model to calculate point-doubling in conic curves cryptosystem over finite held GF(2n). By decomposing and rearranging the computing steps of point-doubling, the assembly process could be fulfilled by using 8 different types of computation tiles performing different functions with 1097 encoding ways. This model could also figure out point-multiplication if its coefficient is 2k. The assembly time complexity is 2kn+n-k-1, and the space complexity is k2n2+kn2-k2n.

Blum-Blum-Shub (BBS) is a less complex pseudorandom number generator (PRNG) that requires very large modulus and a squaring operation for the generation of each bit, which makes it computationally heavy and slow. On the other hand, the concept of elliptic curve (EC) point operations has been extended to PRNGs that prove to have good randomness properties and reduced latency, but exhibit dependence on the secrecy of point P. Given these pros and cons, this paper proposes a new BBS-ECPRNG approach such that the modulus is the product of two elliptic curve points, both primes of length, and the number of bits extracted per iteration is by binary fraction. We evaluate the algorithm performance by generating 1000 distinct sequences of 106bits each. The results were analyzed based on the overall performance of the sequences using the NIST standard statistical test suite. The average performance of the sequences was observed to be above the minimum confidence level of 99.7 percent and successfully passed all the statistical properties of randomness tests.

This paper proposes a new cryptosystem that combines Diffie-Hellman protocol implemented with hyperelliptic curves over a Galois field GF(2n) with Tree Parity Machine synchronization for a Visible Light Communication indoor channel. The proposed cryptosystem security focuses on overcoming a weakness of neuronal synchronization; specifically, the stimulus vector that is public, which allows an attacker to try to synchronize with one of the participants of the synchronization. Real data receptions of the Visible Light Communication channel are included. In addition, there is an improvement of 115% over a range of 100 $łeq$ tsync$łeq$ 400 of the average synchronization time t\_sync, compared to the classic Tree Parity Machine synchronization.

This paper proposed a feedback shift register structure which can be split, it is based on a research of operating characteristics about 70 kinds of cryptographic algorithms and the research shows that the “different operations similar structure” reconfigurable design is feasible. Under the configuration information, the proposed structure can implement the multiplication in finite field GF(2n), the multiply/divide linear feedback shift register and other operations. Finally, this paper did a logic synthesis based on 55nm CMOS standard-cell library and the results show that the proposed structure gets a hardware resource saving of nearly 32%, the average power consumption saving of nearly 55% without the critical delay increasing significantly. Therefore, the “different operations similar structure” reconfigurable design is a new design method and the proposed feedback shift register structure can be an important processing unit for coarse-grained reconfigurable cryptologic array.

This paper proposes a novel scheme for RFID anti-counterfeiting by applying bisectional multivariate quadratic equations (BMQE) system into an RF tag data encryption. In the key generation process, arbitrarily choose two matrix sets (denoted as A and B) and a base Rab such that [AB] = λRABT, and generate 2n BMQ polynomials (denoted as p) over finite field Fq. Therefore, (Fq, p) is taken as a public key and (A, B, λ) as a private key. In the encryption process, the EPC code is hashed into a message digest dm. Then dm is padded to d'm which is a non-zero 2n×2n matrix over Fq. With (A, B, λ) and d'm, Sm is formed as an n-vector over F2. Unlike the existing anti-counterfeit scheme, the one we proposed is based on quantum cryptography, thus it is robust enough to resist the existing attacks and has high security.

Elliptic Curve Cryptography (ECC) is a promising public key cryptography, probably takes the place of RSA. Not only ECC uses less memory, key pair generation and signing are considerably faster, but also ECC's key size is less than that of RSA while it achieves the same level of security. However, the magic behind RSA and its friends can be easily explained, is also widely understood, the foundations of ECC are still a mystery to most of us. This paper's aims are to provide detailed mathematical foundations of ECC, especially, the subgroup and its generator (also called base point) formed by one elliptic curve are researched as highlights, because they are very important for practical ECC implementation. The related algorithms and their implementation details are demonstrated, which is useful for the computing devices with restricted resource, such as embedded systems, mobile devices and IoT devices.

In this paper, a dual-field elliptic curve cryptographic processor is proposed to support arbitrary curves within 576-bit in dual field. Besides, two heterogeneous function units are coupled with the processor for the parallel operations in finite field based on the analysis of the characteristics of elliptic curve cryptographic algorithms. To simplify the hardware complexity, the clustering technology is adopted in the processor. At last, a fast Montgomery modular division algorithm and its implementation is proposed based on the Kaliski's Montgomery modular inversion. Using UMC 90-nm CMOS 1P9M technology, the proposed processor occupied 0.86-mm2 can perform the scalar multiplication in 0.34ms in GF(p160) and 0.22ms in GF(2160), respectively. Compared to other elliptic curve cryptographic processors, our design is advantageous in hardware efficiency and speed moderation.

AES algorithm or Rijndael algorithm is a network security algorithm which is most commonly used in all types of wired and wireless digital communication networks for secure transmission of data between two end users, especially over a public network. This paper presents the hardware implementation of AES Rijndael Encryption and Decryption Algorithm by using Xilinx Virtex-7 FPGA. The hardware design approach is entirely based on pre-calculated look-up tables (LUTs) which results in less complex architecture, thereby providing high throughput and low latency. There are basically three different formats in AES. They are AES-128, AES-192 and AES-256. The encryption and decryption blocks of all the three formats are efficiently designed by using Verilog-HDL and are synthesized on Virtex-7 XC7VX690T chip (Target Device) with the help of Xilinx ISE Design Suite-14.7 Tool. The synthesis tool was set to optimize speed, area and power. The power analysis is made by using Xilinx XPower Analyzer. Pre-calculated LUTs are used for the implementation of algorithmic functions, namely S-Box and Inverse S-Box transformations and also for GF (28) i.e. Galois Field Multiplications involved in Mix-Columns and Inverse Mix-Columns transformations. The proposed architecture is found to be having good efficiency in terms of latency, throughput, speed/delay, area and power.

Secure group communication systems have become increasingly important for many emerging network applications. An efficient and robust group key management approach is indispensable to a secure group communication system. Motivated by the theory of hyper-sphere, this paper presents a new group key management approach with a group controller (GC). In our new design, a hyper-sphere is constructed for a group and each member in the group corresponds to a point on the hyper-sphere, which is called the member's private point. The GC computes the central point of the hyper-sphere, intuitively, whose “distance” from each member's private point is identical. The central point is published such that each member can compute a common group key, using a function by taking each member's private point and the central point of the hyper-sphere as the input. This approach is provably secure under the pseudo-random function (PRF) assumption. Compared with other similar schemes, by both theoretical analysis and experiments, our scheme (1) has significantly reduced memory and computation load for each group member; (2) can efficiently deal with massive membership change with only two re-keying messages, i.e., the central point of the hyper-sphere and a random number; and (3) is efficient and very scalable for large-size groups.

Blind Source Separation (BSS) deals with the recovery of source signals from a set of observed mixtures, when little or no knowledge of the mixing process is available. BSS can find an application in the context of network coding, where relaying linear combinations of packets maximizes the throughput and increases the loss immunity. By relieving the nodes from the need to send the combination coefficients, the overhead cost is largely reduced. However, the scaling ambiguity of the technique and the quasi-uniformity of compressed media sources makes it unfit, at its present state, for multimedia transmission. In order to open new practical applications for BSS in the context of multimedia transmission, we have recently proposed to use a non-linear encoding to increase the discriminating power of the classical entropy-based separation methods. Here, we propose to append to each source a non-linear message digest, which offers an overhead smaller than a per-symbol encoding and that can be more easily tuned. Our results prove that our algorithm is able to provide high decoding rates for different media types such as image, audio, and video, when the transmitted messages are less than 1.5 kilobytes, which is typically the case in a realistic transmission scenario.