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All Journal Journal of the Indonesian Mathematical Society Journal of ICT Research and Applications
Fajar Yuliawan
Department Of Mathematics, Institut Teknologi Bandung
Computer Science & IT Mathematics

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Composite Field Multiplier based on Look-Up Table for Elliptic Curve Cryptography Implementation Marisa W. Paryasto; Budi Rahardjo; Fajar Yuliawan; Intan Muchtadi Alamsyah; Kuspriyanto Kuspriyanto
Journal of ICT Research and Applications Vol. 6 No. 1 (2012)
Publisher : LPPM ITB

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/itbj.ict.2012.6.1.4

Abstract

Implementing a secure cryptosystem requires operations involving hundreds of bits. One of the most recommended algorithm is Elliptic Curve Cryptography (ECC). The complexity of elliptic curve algorithms and parameters with hundreds of bits requires specific design and implementation strategy. The design architecture must be customized according to security requirement, available resources and parameter choices. In this work we propose the use of composite field to implement finite field multiplication for ECC implementation. We use 299-bit keylength represented in GF((213)23) instead of in GF(2299). Composite field multiplier can be implemented using different multiplier for ground-field and for extension field. In this paper, LUT is used for multiplication in the ground-field and classic multiplieris used for the extension field multiplication. A generic architecture for the multiplier is presented. Implementation is done with VHDL with the target device Altera DE2. The work in this paper uses the simplest algorithm to confirm the idea that by dividing field into composite, use different multiplier for base and extension field would give better trade-off for time and area. This work will be the beginning of our more advanced further research that implements composite-field using Mastrovito Hybrid, KOA and LUT.
On The Adjoint of Bounded Operators On A Semi-Inner Product Space Respitawulan, R.; Pangestu, Qori Y.; Kusniyanti, Elvira; Yuliawan, Fajar; Astuti, Pudji
Journal of the Indonesian Mathematical Society VOLUME 29 NUMBER 3 (NOVEMBER 2023)
Publisher : IndoMS

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22342/jims.29.3.1598.311-321

Abstract

The notion of semi-inner product (SIP) spaces is a generalization of inner product (IP) spaces notion by reducing the positive definite property of the product to positive semi-definite. As in IP spaces, the existence of an adjoint of a linear operator on a SIP space is guaranteed when the operator is bounded. However, in contrast, a bounded linear operator on SIP space can have more than one adjoint linear operators. In this article we give an alternative proof of those results using the generalized Riesz Representation Theorem in SIP space. Further, the description of all adjoint operators of a bounded linear operator in SIP space is identified.
Explicit Formulas for the Anti-Trace of 3-by-3 Matrix Powers via Generating Functions Jeriko Gormantara; Devi Fitri Ferdania; Fajar Yuliawan; Hanni Garminia
Journal of the Indonesian Mathematical Society Vol. 32 No. 3 (2026): SEPTEMBER
Publisher : IndoMS

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22342/jims.v32i3.2260

Abstract

We study the anti-trace—the sum of anti-diagonal entries—of powers of 3-by-3 matrices. Unlike the ordinary trace, the anti-trace has no spectral characterization, so closed forms for the anti-trace of matrix powers are valuable. Starting from the Cayley--Hamilton recurrence for matrix powers and solving a trivariate generating function, we derive explicit closed-form expressions whose coefficients are signed multinomial combinations of the sums of principal minors and their anti-principal counterparts. The formulas are purely algebraic and remain valid over any commutative ring. As a structural application, we analyze block anti-diagonal matrices of size 3m-by-3m.
Co-Authors Budi Rahardjo Devi Fitri Ferdania Hanni Garminia Intan Muchtadi Alamsyah Jeriko Gormantara Kusniyanti, Elvira KUSPRIYANTO Marisa W. Paryasto Pangestu, Qori Y. PUDJI ASTUTI Respitawulan, R