Abstract: The story behind the Euclidean algorithm and its relationship to the solution of the Diophantine equation is examined in this article. The Euclidean algorithm appears in Proposition 2 in ...
Crypto thrives on cutting-edge technology, but quantum computing could challenge the cryptographic foundations that keep Bitcoin secure. As quantum advancements accelerate, concerns about risks to ...
There’s a rather beautiful algorithm for finding the greatest common divisor of two positive integers. For example, the greatest common divisor of 120 and 105 is 15. It’s clear that 15 is a divisor of ...
Thomas Jefferson’s first draft of the Declaration of Independence read: “We hold these truths to be sacred and undeniable . . . ” It was supposedly Benjamin Franklin who suggested instead announcing ...
Google, Microsoft, Amazon, and IBM are some of the biggest companies currently researching and developing quantum computer technology. Dr. XinXin Fan, the head of cryptography at IoTeX, recently ...
ABSTRACT: 1) Fermat has proved that x 4 + y 4 = z 2 has no positive integer solution, and in 2011, J. Cullen [1] reported that x,y∈{ 0,1,⋯, 10 7 } , x 4 + y 4 +1 is not a square greater than 1, and ...
Yubico has released a security advisory addressing a side-channel vulnerability in Infineon’s cryptographic library, which several Yubico devices use. These devices include the YubiKey 5 Series, ...
The YubiKey 5, the most widely used hardware token for two-factor authentication based on the FIDO standard, contains a cryptographic flaw that makes the finger-size device vulnerable to cloning when ...
In this paper, a new mathematical method is used to study the indefinite equations of binary quadratic and binary arbitrary order, the problem of judging and solving these indefinite equations with or ...
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