Abstract-In this paper, we investigate a hybrid network coding technique to be used at a wireless base station (BS) or access point (AP) to increase the throughput efficiency of single-hop wireless networks. Traditionally, to provide reliability, lost packets from different flows (applications) are retransmitted separately, leading to inefficient use of wireless bandwidth. Using the proposed hybrid network coding approach, the BS encodes these lost packets, possibly from different flows together before broadcasting them to all wireless users. In this way, multiple wireless receivers can recover their lost packets simultaneously with a single transmission from the BS. Furthermore, simulations and theoretical analysis showed that when used in conjunction with an appropriate channel coding technique under typical channel conditions, this approach can increase the throughput efficiency up to 3.5 times over the Automatic Repeat reQuest (ARQ), and up to 1.5 times over the HARQ techniques.
It is widely acknowledged that efficient modular multiplication is a key to high-performance implementation of public-key cryptography, be it classical RSA, Diffie-Hellman, or (hyper-) elliptic curve algorithms. In the recent decade, practitioners have relied mainly on two popular methods: Montgomery Multiplication and regular long-integer multiplication in combination with Barrett's modular reduction technique. In this paper, we propose a modification to Barrett's algorithm that leads to a significant reduction (25% to 75%) in multiplications and additions.
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