Knowing that the grid cells in the dorso-lateral band of the medial enthorinal cortex are a necessary component of rat’s ability to perform path integration and homing, we explore the idea proposed by Fiete et al. (2008, J. Neurosci., 28(27):6858) that they might encode the coordinates of the rat in a Residue Number System. We show that the decoding network based on a gradient descent they prop...

In this paper, we propose a novel high speed memoryless reverse converter for the moduli set {22n+1 − 1,2n,2n − 1}. First, we simplify the traditional Chinese Remainder Theorem in order to obtain a reverse converter that only requires arithmetic mod-(22n+1 − 1). Second, we further improve the resulting architecture to obtain a reverse converter that only uses Carry Save Adders and Carry Propaga...

We present in this paper a novel general algorithm for signed number division in Residue Number Systems (RNS). A parity checking technique is used to accomplish the sign and overflow detection in this algorithm. Compared with conventional methods of sign and overflow detection, the parity checking method is more e f ficient and practical. Sign magnitude arithmetic division is implemented using ...

We show that new BRST charges in RNS superstring theory with nonstandard ghost numbers, constructed in our recent work, can be mapped to deformed pure spinor (PS) superstring theories, with the nilpotent pure spinor BRST charge QPS = ∮ λdα still retaining its form but with singular operator products between commuting spinor variables λ. Despite the OPE singularities, the pure spinor condition λ...

In many problems, modular exponentiation jxjm is a basic computation, often responsible for the overall time performance, as in some cryptosystems, since its implementation requires a large number of multiplications. It is known that jxjm 1⁄4 jxjbjuðmÞ jm for any x in 1⁄21;m 1 if m is prime; in this case the number of multiplications depends on uðmÞ instead of depending on b. It was also stated...

Modular multiplication is the main and basic operation in public key cryptography algorithms like Elliptic Curve Cryptography (ECC). By using Residue Number System (RNS) in these algorithms, large number computation is replaced by computation over the small moduli without carry propagation between moduli. Moduli selection has an important role in the efficiency of modular multiplication. Theref...

In the last years, research on Residue Number Systems (RNS) has targeted larger dynamic ranges in order to further explore their inherent parallelism. In this paper, we start from the traditional 3-moduli set f2;2 1;2þ1g, with an equivalent 3n-bit dynamic range, and propose horizontal and vertical extensions to scale the dynamic range and enhance the parallelism according to the requirements. T...

Residue Number System (RNS) is a method for representing an integer as an n-tuple of its residues with respect to a given base. Since RNS has inherent parallelism, it is actively researched to implement fast public-key cryptography using RNS. This paper derives the exact error bound of approximation on the Cox-Rower architecture which was proposed for RNS modular multiplication. This is the tig...

In this paper, we propose link-adaptive cooperative communication in wireless USB networks. To select the optimal relay node, we propose the RNS (Relay Node Selection) algorithm considering channel condition. Also, the proposed protocol can be directly applied with small overhead to the current wireless USB standard system. Furthermore, each device independently performs RNS algorithm by using ...

Recently, a lot of progress has been made in the implementation of pairings in both hardware and software. In this paper, we present two FPGA-based high speed pairing designs using the Residue Number System and lazy reduction. We show that by combining RNS, which is naturally suitable for parallel architectures, and lazy reduction, which performs one reduction for multiple multiplications, the ...