Logarithm Representation Research Articles

Comments on biometric-based non-transferable credentials and their application in blockchain-based identity management

In IT-ecosystems, access to unauthorized parties is prevented with credential-based access control techniques (locks, RFID cards, biometrics, etc.). Some of these methods are ineffective against malicious users who lend their credentials to other users. To obtain non-transferability, Adams proposed a combination of biometrics encapsulated in Pedersen commitment with Brands digital credential. However, Adams’ work does not consider the Zero Knowledge Proof-of Knowledge (ZKPoK) system for Double Discrete Logarithm Representation of the credential. Besides, biometrics is used directly, without employing any biometric cryptosystem to guarantee biometric privacy, thus Adams’ work cannot be GDPR-compliant. In this paper, we construct the missing ZKPoK protocol for Adam’s work and show its inefficiency. To overcome this limitation, we present a new biometric-based non-transferable credential scheme that maintains the efficiency of the underlying Brands credential. Secondly, we show the insecurity of the first biometric-based anonymous credential scheme designed by Blanton et al.. In this context, we present a brute-force attack against Blanton’s biometric key generation algorithm implemented for fuzzy vault. Next, we integrate an Oblivious PRF (OPRF) protocol to solve the open problem in Blanton’s work and improve its efficiency by replacing the underlying signature scheme with PS-signatures. Finally, we evaluate application scenarios for non-transferable digital/anonymous credentials in the context of Blockchain-based Identity Management (BBIM). We show that our modified constructions preserve biometric privacy and efficiency, and can easily be integrated into current BBIM systems built upon efficient Brands and PS-credentials.

Advantages of q-logarithm representation over q-exponential representation from the sense of scale and shift on nonlinear systems

Addition and subtraction of observed values can be computed under the obvious and implicit assumption that the scale unit of measurement should be the same for all arguments, which is valid even for any nonlinear systems. This paper starts with the distinction between exponential and non-exponential family in the sense of the scale unit of measurement. In the simplest nonlinear model ${dy}/{dx}=y^{q}$, it is shown how typical effects such as rescaling and shift emerge in the nonlinear systems and affect observed data. Based on the present results, the two representations, namely the $q$-exponential and the $q$-logarithm ones, are proposed. The former is for rescaling, the latter for unified understanding with a fixed scale unit. As applications of these representations, the corresponding entropy and the general probability expression for unified understanding with a fixed scale unit are presented. For the theoretical study of nonlinear systems, $q$-logarithm representation is shown to have significant advantages over $q$-exponential representation.

Continued Logarithm Representation of Real Numbers

We introduce the continued logarithm representation of real numbers and prove results on the occurrence and frequency of digits with respect to this representation

Alternative Infinitesimal Generator of Invertible Evolution Families

A logarithm representation of evolution operators is defined. Generators of invertible evolution families are characterized by the logarithm representation. In this article, using the logarithm representation, a concept of evolution operators without satisfying the semigroup property is introduced. In conclusion the existence of alternative infinitesimal generator is clarified.

Small Private Key MQPKS on an Embedded Microprocessor

Multivariate quadratic ( ) cryptography requires the use of long public and private keys to ensure a sufficient security level, but this is not favorable to embedded systems, which have limited system resources. Recently, various approaches to cryptography using reduced public keys have been studied. As a result of this, at CHES2011 (Cryptographic Hardware and Embedded Systems, 2011), a small public key scheme, was proposed, and its feasible implementation on an embedded microprocessor was reported at CHES2012. However, the implementation of a small private key scheme was not reported. For efficient implementation, random number generators can contribute to reduce the key size, but the cost of using a random number generator is much more complex than computing on modern microprocessors. Therefore, no feasible results have been reported on embedded microprocessors. In this paper, we propose a feasible implementation on embedded microprocessors for a small private key scheme using a pseudo-random number generator and hash function based on a block-cipher exploiting a hardware Advanced Encryption Standard (AES) accelerator. To speed up the performance, we apply various implementation methods, including parallel computation, on-the-fly computation, optimized logarithm representation, vinegar monomials and assembly programming. The proposed method reduces the private key size by about 99.9% and boosts signature generation and verification by 5.78% and 12.19% than previous results in CHES2012.

Identification Protocols based on Discrete Log Representation Problem

Identification protocols are powerful tools in many areas of cryptography. A prover's identity (ID) has n distinct secrets which in total construct her identity. When a prover, Peggy, wants to prove to a verifier, Victor, that she is the holder of a certain identity ID and at the same time, she is not willing to reveal these secrets due to privacy concerns, Peggy must prove to Victor that she indeed knows n witnesses that are related to the public instances that form her identity. The simplest way to prove this knowledge of n witnesses is to run an identification protocol for n times. This naive method results in protocols that have communication and computational complexities that are linear in the number of secrets. In this paper, we propose an identification protocol based on proof of knowledge of Discrete Logarithm (DL) representation. This protocol allows the prover to prove her knowledge of some personal information (encoded in a certain identity ID) without revealing any/some of this information to the verifier, at the same time, prevent the verifier from impersonating the prover in the future. Furthermore, we tackle the issue of reducing communication and computation costs.

A Secure Reed–Solomon Code Incentive Scheme for Commercial Ad Dissemination Over VANETs

A recent surge of research on vehicular ad hoc networks (VANETs) has given us new opportunities and challenges. Aside from safety-related applications, commercial applications also find their way to fully utilize these networks. One of the promising applications is the dissemination of commercial advertisements over VANETs. However, there are uncooperative vehicles that may disrupt the spreading of these advertisements. To encourage cooperation, we want to address proper incentives and security measurements. In this paper, we use Reed-Solomon codes (RS-codes) to construct our incentive scheme and enhance its security by introducing one discrete logarithm representation problem. Our construction yields a secure and practical commercial advertisement dissemination scheme over VANETs.

Delegatable secret handshake scheme

Abstract Secret handshake, which was introduced by Balfanz et al., is proposed for mutually anonymous authentication among untrusted parties. In this paper, a new secret handshake scheme is designed for supporting delegations. The definitions and security requirements are first formalized for delegatable secret handshakes. Based on a variant of message recoverable signature without public verification, a delegatable secret handshake scheme is presented. By assuming the intractability of the Discrete Logarithm Representation Problem and the q-Strong Diffie–Hellman Problem, our new scheme is proven secure under the random oracle model.

Speculatively Redundant Continued Logarithm Representation

Continued logarithms, as originally introduced by Gosper, represent a means for exact rational arithmetic, but their application to exact real arithmetic is limited by the uniqueness of their representation. This is quite unfortunate, as this representation seems promising for efficient hardware implementation. We propose an idea of making the representation redundant using speculative recognition of noncomputable cases. This approach solves the problem of real number computability, preserves most of the beneficial properties of continued logarithms, and only moderately affects complexity of arithmetic algorithms, thus, keeping the prospect of efficient implementation.

A Discrete Logarithm Number System for Integer Arithmetic Modulo 2^{k}: Algorithms and Lookup Structures

We present a k-bit encoding of the k-bit binary integers based on a discrete logarithm representation. The representation supports a discrete logarithm number system (DLS) that allows integer multiplication to be reduced to addition and integer exponentiation to be reduced to multiplication. We introduce right-to-left bit serial conversion, deconversion, and unified conversion/deconversion algorithms between binary and DLS. The conversion algorithms utilize O(k) additions, do not require the use of a multiplier, and are applicable at least up to 128-bit integers. We illustrate the use of the representation in determining a novel and efficient integer power modulo 2k operation |xy|2 k and compare hardware performance with a current state-of-the-art method. Furthermore, we describe properties of the conversion mappings that allow compact table lookup structures to be employed for direct conversion to and deconversion from the DLS encoding. Our lookup architecture allows 16-bit conversion and deconversion mappings to be realized with table sizes of order 2-8 Kbytes, which is up to a 64\times size reduction of the 128 Kbytes of an arbitrary 16-bits-in, 16-bits-out function table. Performance and area results that demonstrate the effectiveness of the table lookup architecture are given. The lookup methodology extends to other 16-bit integer functions such as multiplicative inverse and squaring operations.