New Hardware Algorithms and Designs for Montgomery Modular Inverse Computation in Galois Fields GF(p) and GF(2n)

الموضوعات

علوم تطبيقية وتكنولوجية

الملخص

The computation of the inverse of a number in finite fields, namely Galois Fields GF(p) or GF(2n), is one of the most complex arithmetic operations in cryptographic applications. In this work, we investigate the GF(p) inversion and present several phases in the design of efficient hardware implementations to compute the Montgomery modular inverse. We suggest a new correction phase for a previously proposed almost Montgomery inverse algorithm to calculate the inversion in hardware. It is also presented how to obtain a fast hardware algorithm to compute the inverse by multi-bit shifting method. The proposed designs have the hardware scalability feature, which means that the design can fit on constrained areas and still handle operands of any size. In order to have long-precision calculations, the module works on small precision words. The word-size, on which the module operates, can be selected based on the area and performance requirements. The upper limit on the operand precision is dictated only by the available memory to store the operands and internal results. The scalable module is in principle capable of performing infinite-precision Montgomery inverse computation of an integer, modulo a prime number. We also propose a scalable and unified architecture for a Montgomery inverse hardware that operates in both GF(p) and GF(2n) fields. We adjust and modify a GF(2n) Montgomery inverse algorithm to benefit from multi-bit shifting hardware features making it very similar to the proposed best design of GF(p) inversion hardware. We compare all scalable designs with fully parallel ones based on the same basic inversion algorithm. All scalable designs consumed less area and in general showed better performance than the fully parallel ones, which makes the scalable designs more efficient.

روابط وملفات

التعريف والنوع

رقم الوثيقة

0feb9ce8-cf66-491e-ad1a-168fc4bf796b

رقم العقد

0

نوع الوسائط

Crawler

نوع المحتوى

الرسائل العلمية

صيغة المصدر

رسائل دكتوراة

نوع الملف

pdf text

أسماء الملفات

851078_1.pdf

بيانات النشر

ألقاب المؤلفين

[{"name_ar":"Adnan Abdul-Aziz Gutub ","title_ar":"اعداد","title_en":"Preparation"},{"name_ar":"Alexandre Ferreira Tenca","title_ar":"اشراف","title_en":"Supervision"},{"name_ar":"Ҫetin Kaya Koҫ","title_ar":"اشراف","title_en":"Supervision"}]

اللغة

English

المصدر والدورية

اسم المصدر

New Hardware Algorithms and Designs for Montgomery Modular Inverse Computation in Galois Fields GF(p) and GF(2n)

المحتوى والصفحات

عدد الصفحات

0

كلمات الباحثين

Montgomery modular inverse, Galois Fields, Scalable hardware architecture, Cryptography, Multi-bit shifting, Modular arithmetic

إشراف وإعداد

الإشراف

Alexandre Ferreira Tenca, Ҫetin Kaya Koҫ

الإعداد

Adnan Abdul-Aziz Gutub

الاقتباسات الببليوغرافية