İkili Kuadratik Formlar İle Çarpanlara Ayırma (Factorization with Binary Quadratic Forms)

Year 2018, Volume: 3 Issue: 3, 165 - 171, 29.12.2018

Kübra Nari Enver Özdemir Ergün Yaraneri

https://doi.org/10.30931/jetas.473727

Abstract

TR

Bu makalede diskriminantı pozitif olan ikili kuadratik formlar incelenmiştir. Özellikle diskriminantı iki asal sayının çarpımı olan sınıf grubunun etkisiz elemanına ait çevrimin ilginç özellikler taşıdığı gözlemlenmiştir. Bu özelliklerden yararlanarak bir çarpanlara ayırma algoritması tasarlanmış ve özellikle RSA açık anahtarlı şifreleme sisteminin anahtarlarını kırmada etkili olabileceği gösterilmiştir.

EN

In this work we investigated binary quadratic forms that have positive discriminant. Binary quadratic forms of the same discriminant have a equivalence relation among them and this equivalence relationship construct a cycle structure. There exist interesting characteristic specification in the cycle belonging identity element of class group whose the discriminant has just two factors. We designed a factorization algorithm using these features. We show that this method can be effective for breaking the keys of the public key cryptosystem RSA.

Keywords

binary quadratic forms, integer factorization

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