Related papers: Fusion Discrete Logarithm Problems
Given two elliptic curves over a finite field having the same cardinality and endomorphism ring, it is known that the curves admit an isogeny between them, but finding such an isogeny is believed to be computationally difficult. The fastest…
Generalized Discrete Logarithm Problem (GDLP) is an extension of the Discrete Logarithm Problem where the goal is to find $x\in\mathbb{Z}_s$ such $g^x\mod s=y$ for a given $g,y\in\mathbb{Z}_s$. Generalized discrete logarithm is similar but…
We present novel homomorphic encryption schemes for integer arithmetic, intended for use in secure single-party computation in the cloud. These schemes are capable of securely computing only low degree polynomials homomorphically, but this…
In this paper, we study a security problem of protecting secrets in distributed systems. Specifically, we employ discrete-event systems to describe the structure and behaviour of distributed systems, in which global secret information is…
Binary field extensions are fundamental to many applications, such as multivariate public key cryptography, code-based cryptography, and error-correcting codes. Their implementation requires a foundation in number theory and algebraic…
Encrypted computation opens up promising avenues across a plethora of application domains, including machine learning, health-care, finance, and control. Arithmetic homomorphic encryption, in particular, is a natural fit for cloud-based…
In this paper we propose a signature scheme based on two intractable problems, namely the integer factorization problem and the discrete logarithm problem for elliptic curves. It is suitable for applications requiring long-term security and…
Solving the discrete logarithm problem in a finite prime field is an extremely important computing problem in modern cryptography. The hardness of solving the discrete logarithm problem in a finite prime field is the security foundation of…
Since fully homomorphic encryption and homomorphically encrypted computing preserve algebraic identities such as 2*2=2+2, a natural question is whether this extremely utilitarian feature also sets up cryptographic attacks that use the…
Finding low-weight multiples of a binary polynomial is a difficult problem arising in the context of stream ciphers cryptanalysis. The classical algorithm to solve this problem is based on a time memory trade-off. We will present an…
Computing discrete logarithms in finite fields is a main concern in cryptography. The best algorithms in large and medium characteristic fields (e.g., {GF}$(p^2)$, {GF}$(p^{12})$) are the Number Field Sieve and its variants (special,…
Post-quantum cryptography currently rests on a small number of hardness assumptions, posing significant risks should any one of them be compromised. This vulnerability motivates the search for new and cryptographically versatile assumptions…
Homomorphic encryption is a form of encryption which allows computation to be carried out on the encrypted data without the need for decryption. The success of quantum approaches to related tasks in a delegated computation setting has…
Cryptographic Protocols (CP) are distributed algorithms intended for secure communication in an insecure environment. They are used, for example, in electronic payments, electronic voting procedures, systems of confidential data processing,…
In this paper a three fuzzy vault schemes which integrated with discrete logarithmic encryption scheme are proposed. In the first scheme, the message m is encoded with discrete logarithmic encryption scheme using randomly generated identity…
The linear complexity is a measure for the unpredictability of a sequence over a finite field and thus for its suitability in cryptography. In 2012, Diem introduced a new figure of merit for cryptographic sequences called expansion…
Full Disk Encryption (FDE) has become a widely used security feature. Although FDE can provide confidentiality, it generally does not provide cryptographic data integrity protection. We introduce an algorithm-agnostic solution that provides…
Many proofs in discrete mathematics and theoretical computer science are based on the probabilistic method. To prove the existence of a good object, we pick a random object and show that it is bad with low probability. This method is…
Since their introduction in 2004, Polynomial Modular Number Systems (PMNS) have become a very interesting tool for implementing cryptosystems relying on modular arithmetic in a secure and efficient way. However, while their implementation…
Discrete Differential Equations (DDEs) are functional equations that relate polynomially a power series $F(t,u)$ in $t$ with polynomial coefficients in a "catalytic" variable $u$ and the specializations, say at $u=1$, of $F(t,u)$ and of…