• Journal of the Korea Institute of Information Security & Cryptology
• /
• v.12 no.4
• /
• pp.115-126
• /
• 2002

This paper deals with efficient algorithms for computing a product of n distinct powers in a group(called multi-exponentiation). Four different algorithms are presented and analyzed, each of which has its own range of n for best performance. Using the best performing algorithm for n ranging from 2 to several thousands, one can achieve 2 to 4 times speed-up compared to the baseline binary algorithm and 2 to 10 times speed-up compared to individual exponentiation.

• The Journal of Korean Institute of Communications and Information Sciences
• /
• v.22 no.5
• /
• pp.1036-1044
• /
• 1997

We modify the montgomery modeular multikplication to extract the common parts in common-multiplicand multi-plications. Since the modified method computes the common parts in two modular multiplications once rather than twice, it can speed up the exponentiations and reduce the amount of storage tables in m-ary or windowexponentiation. It can be also applied to an exponentiation mehod by folding the exponent in half. This method is well-suited to the memory limited environments such as IC card due to its speed and requirement of small memory.

• Journal of KIISE:Computer Systems and Theory
• /
• v.33 no.4
• /
• pp.223-230
• /
• 2006

The method of implementing a modular multiplier for Montgomery multiplication by using an adder depends on a selected adder. When using a CPA, there is a carry propagation problem. When using a CSA, it needs an additional calculation for a final result. The Multiplier using a Multi-precision CSA can solve both problems simultaneously by combining a CSA and a CPA. This paper presents an improved MP-CSA which reduces hardware resources and operation time by changing a MP-CSA's carry chain structure. Consequently, the proposed multiplier is more suitable for the module of long bit multiplication and exponentiation using a modular multiplier repeatedly.

• The Journal of the Korea Contents Association
• /
• v.10 no.3
• /
• pp.32-43
• /
• 2010

IPTV is an emerging technology that combines both broadcasting and tele-communication technologies, and provides various multi-media contents to the service subscribers. In general, IPTV broadcasters transmit scrambled signals (multi-media contents) to the paying subscribers, and the users within the acknowledged network descramble the signals using the smart-card. That is, users are verified through communication between STB (Set-Top Box) and smart-card. In 2004, Jiang et al. proposed a secure protocol regarding the verification process. The method has been modified and enhanced by several following research works. However, all the methods that have been proposed so far required modular exponentiation operations which may raise the smart-card costs. In this paper, we propose a new efficient mutual authentication and session-key establishment protocol using only hash functions and exclusive-or operations, and show that the proposed protocol is still secure under various security attacks.