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- Publications
- Influence

Analyzing and comparing Montgomery multiplication algorithms

- Ç. K. Koç, Tolga Acar, B. S. Kaliski
- Computer Science
- IEEE Micro
- 1 June 1996

Montgomery multiplication methods constitute the core of modular exponentiation, the most popular operation for encrypting and signing digital data in public-key cryptography. In this article, we… Expand

Montgomery Multiplication in GF(2k)

- Ç. K. Koç, Tolga Acar
- Mathematics, Computer Science
- Des. Codes Cryptogr.
- 1 April 1998

We show that the multiplication operation c=a · b · r-1 in the field GF(2k can be implemented significantly faster in software than the standard multiplication, where r is a special fixed element of… Expand

Affine Pairings on ARM

- Tolga Acar, Kristin E. Lauter, M. Naehrig, D. Shumow
- Computer Science, Mathematics
- Pairing
- 16 May 2012

We report on relative performance numbers for affine and projective pairings on a dual-core Cortex A9 ARM processor. Using a fast inversion in the base field and doing inversion in extension fields… Expand

Cryptographic Agility and Its Relation to Circular Encryption

- Tolga Acar, M. Belenkiy, M. Bellare, D. Cash
- Computer Science
- EUROCRYPT
- 30 May 2010

We initiate a provable-security treatment of cryptographic agility. A primitive (for example PRFs, authenticated encryption schemes or digital signatures) is agile when multiple, individually secure… Expand

Fast software exponentiation in GF(2/sup k/)

- Ç. K. Koç, Tolga Acar
- Mathematics, Computer Science
- Proceedings 13th IEEE Sympsoium on Computer…
- 6 March 1997

The authors present a new algorithm for computing a/sup e/ where a/spl isin/GF(2/sup k/) and e is a positive integer. The proposed algorithm is more suitable for implementation in software, and… Expand

Montgomery Multiplication in Gf2

- C. K. Ko, Tolga Acar
- 1998

We show that the multiplication operation c = a br ,1 in the eld GF2 k can be implemented signiicantly faster in software than the standard multiplication, where r is a special xed element of the… Expand

- 8
- 2
- Open Access

Blind MIMO System Estimation Based on PARAFAC Decomposition of Higher Order Output Tensors

- Tolga Acar, Y. Yu, A. Petropulu
- Mathematics, Computer Science
- IEEE Transactions on Signal Processing
- 1 November 2006

We present a novel framework for the identification of a multiple-input multiple-output (MIMO) system driven by white, mutually independent unobservable inputs. Samples of the system frequency… Expand

Accumulators and U-Prove Revocation

- Tolga Acar, S. Chow, Lan Nguyen
- Computer Science
- Financial Cryptography
- 1 April 2013

This work introduces the most efficient universal accumulator known today. For the first time, we have an accumulator which does not depend on hidden order groups, does not require any… Expand

Modular Reduction without Pre-computation for Special Moduli

- Tolga Acar, D. Shumow
- Mathematics
- 2010

We present Montgomery modular multiplication algorithms for special moduli that do not require the pre-computation step. We generalize previous approaches and remove pre-computation steps where the… Expand

- 13
- 1
- Open Access