The Fermat-type equation with signature (2, 2, n) and Bunyakovsky conjecture by Sawian Jaidee, Korakot Saosoong

“…We first discuss the Fermat-type equation with signature (2, 𝑚, 𝑛), which is the Diophantine equation in the shape 𝑥 2 + 𝑦 𝑚 = 𝑧 𝑛 , where 𝑥, 𝑦 and 𝑧 are unknown integers, and 𝑚, 𝑛 are fixed positive integers greater than 1. …”

Cryptanalysis of El-Gamal AAs cryptosystem by Mandangan, Arif

“…Those attacks are the exhaustive search attack on the secret parameters and the linear Diophantine equation attack. We show that these attacks fail to get the correct secret parameters efficiently. …”
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Heterotic string compactification and quiver gauge theory on toric geometry by Sun, C

“…After explicitly computing the Diophantine equation of five block cases, we use this structure to re-organize the result in a form that can be applied to arbitrary block numbers. …”

Factorization strategies of N = pq and N = pʳq and relation to its decryption exponent bound by Abubakar, Saidu Isah

“…The major RSA underlying security problems rely on the difficulty of factoring a very large composite integer N into its two nontrivial prime factors of p and q in polynomial time, the ability to solve a given Diophantine equation ed = 1 + kφ (N) where only the public key e is known and the parameters d, k and φ (N) are un- known and finally the failure of an adversary to compute the decryption key d from the public key pair (e, N). …”
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Cryptanalysis on the modulus N=p2q and design of rabin-like cryptosystem without decryption failure by Asbullah, Muhammad Asyraf

“…In this thesis, we also develop a new cryptographic hard problem based on a special instance of a linear Diophantine equation in two variables, with some provided restrictions and carefully selected parameters. …”
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Optimization of the multivariate polynomial public key for quantum safe digital signature by Randy Kuang, Maria Perepechaenko

“…The optimal key-recovery attack reduces to a Modular Diophantine Equation Problem or MDEP with more than one unknown variables for a single equation. …”
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Snake Graphs Arising from Groves with an Application in Coding Theory by Agustín Moreno Cañadas, Gabriel Bravo Rios, Robinson-Julian Serna

“…Furthermore, perfect matchings of snake graphs have also been used to find closed formulas for cluster variables of some cluster algebras and solutions of the Markov equation, which is a well-known Diophantine equation. Recent results prove that snake graphs give rise to some <i>string modules</i> over some path algebras, connecting snake graph research with the theory of representation of algebras. …”
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