Searching for Best Karatsuba Recurrences

Çalık, Çağdaş; Dworkin, Morris J.; Dykas, Nathan; Peralta, René

doi:10.1007/978-3-030-34029-2_22

Cited by 4 publications

(1 citation statement)

References 10 publications

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“…No _page-end_page  Speeding up the Karatsuba algorithm [2]  Searching for Best Karatsuba Recurrences [3]  On the Complexity of Hybrid n-Term Karatsuba Multiplier for Trinomials [4]  Decoupling for moment manifolds associated to Arkhipov-Chubarikov-Karatsuba systems [5] Perhatian utama pada penelitian ini adalah pada bagian base case dari algoritma Karatsuba. Base case adalah tingkatan paling rendah pada proses divide and conquer dan recursive call.…”

Section: Pendahuluanunclassified

Analisis Pengaruh Base Case pada Algoritma Karatsuba terhadap Tingkat Efisiensi Waktu Eksekusi

Felix¹,

Irviantina²

2021

J. Sifo Mikrosk.

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Algoritma Karatsuba adalah algoritma perkalian yang masih banyak diteliti oleh peneliti Ilmu Komputer dan Matematika meskipun telah berusia lebih dari setengah abad. Algoritma ini merupakan algoritma yang menerapkan konsep Divide Conquer. Oleh karena itu terdapat nilai base case (BC) yang dapat diganti. Hipotesisnya adalah nilai BC ketika ditingkatkan akan mengurangi waktu eksekusi sampai mencapai suatu nilai x. Setelah melewati nilai x, waktu eksekusi akan bertambah. Pada penelitian ini dilakukan dengan 36 percobaan dengan kombinasi dari 3 pilihan digit, 3 kasus, dan 4 BC. Pilihan digitnya adalah 2000, 4000, dan 6000 digit. Kasus yang digunakan adalah angka acak yang dikalikan dengan angka acak itu sendiri. BC yang digunakan adalah 1010^n dengan nilai n = {0, 1, 2, 3}. Penelitian ini menghasilkan fakta yang berlawanan dengan hipotesis. Semakin besar BC membutuhkan waktu eksekusi yang lebih singkat. Hal ini diduga karena di dalam Python sendiri sudah menerapkan algoritma Karatsuba secara implisit.

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Section: Pendahuluanunclassified

Analisis Pengaruh Base Case pada Algoritma Karatsuba terhadap Tingkat Efisiensi Waktu Eksekusi

Felix¹,

Irviantina²

2021

J. Sifo Mikrosk.

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Toffoli gate count optimized space-efficient quantum circuit for binary field multiplication

Kim,

Kim

et al. 2024

Quantum Inf Process

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Progressive and efficient verification for digital signatures: extensions and experimental results

Boschini,

Fiore,

Pagnin

et al. 2024

J Cryptogr Eng

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Digital signatures are widely deployed to authenticate the source of incoming information, or to certify data integrity. Common signature verification procedures return a decision (accept/reject) only at the very end of the execution. If interrupted prematurely, however, the verification process cannot infer any meaningful information about the validity of the given signature. This limitation is due to the algorithm design solely, and it is not inherent to signature verification. In this work, we provide a formal framework to extract information from prematurely interrupted signature verification, independently of why the process halts: we propose a generic verification procedure that progressively builds confidence on the final decision. Our transformation builds on a simple but powerful intuition and applies to a wide range of existing schemes considered to be post-quantum secure, including some lattice-based and multivariate equations based constructions. We demonstrate the feasibility of our approach through an implementation on off-the-shelf resource-constrained devices. In particular, an intensive testing activity has been conducted measuring the increase of performance on three IoT boards—i.e., Arduino, Raspberry, and Espressif—and a consumer-grade laptop. While the primary motivation of progressive verification is to mitigate unexpected interruptions, we show that verifiers can leverage it in two innovative ways. First, progressive verification can be used to intentionally adjust the soundness of the verification process. Second, our transformation splits verification into a computationally intensive offline set-up (run once), and an efficient online verification that is faster than the original algorithm. We conclude showing how to tweak our compiler for progressive verification to work on a wide range of signatures with properties, on three real-life use cases, and in combination with efficient verification.

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Searching for Best Karatsuba Recurrences

Cited by 4 publications

References 10 publications

Analisis Pengaruh Base Case pada Algoritma Karatsuba terhadap Tingkat Efisiensi Waktu Eksekusi

Analisis Pengaruh Base Case pada Algoritma Karatsuba terhadap Tingkat Efisiensi Waktu Eksekusi

Toffoli gate count optimized space-efficient quantum circuit for binary field multiplication

Progressive and efficient verification for digital signatures: extensions and experimental results

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