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This paper introduces fast algorithms for performing group operations on twisted Edwards curves, pushing the recent speed limits of Elliptic Curve Cryptography (ECC) forward in a wide range of applications. Notably, the new addition algorithm uses 1 8M for suitably selected curve constants. In comparison, the fastest point addition algorithms for (twisted)… (More)

This paper is on efficient implementation techniques of Ellip-tic Curve Cryptography. In particular, we improve timings 1 for Jacobi-quartic (3M+4S) and Hessian (7M+1S or 3M+6S) doubling operations. We provide a faster mixed-addition (7M+3S+1d) on modified Jacobi-quartic coordinates. We introduce tripling formulae for Jacobi-quartic (4M+11S+2d),… (More)

This paper improves implementation techniques of Elliptic Curve Cryptography. We introduce new formulae and algorithms for the group law on Jacobi quartic, Jacobi intersection, Edwards, and Hessian curves. The proposed formulae and algorithms can save time in suitable point representations. To support our claims, a cost comparison is made with classic… (More)

- R.-M Mu, V S Grigoryan, Curtis R Menyuk, G M Carter, J M Jacob
- 2000

—We have developed a model that accurately predicts the dynamics of the signal pulses and the growth of amplified spontaneous emission noise in a dispersion-managed soliton pulse train propagating in a recirculating fiber-loop experiment. Theoretically predicted dependencies of the amplitude and phase margins for the marks and the amplitude margin for the… (More)

This paper provides new results about efficient arithmetic on (extended) Jacobi quartic form elliptic curves y 2 = dx 4 + 2ax 2 + 1. Recent works have shown that arithmetic on an elliptic curve in Jacobi quartic form can be performed solidly faster than the corresponding operations in Weierstrass form. These proposals use up to 7 coordinates to represent a… (More)

- Yu Sun, Ivan T Lima, Hua Jiao, Jiping Wen, Hai Xu, Heider Ereifej +2 others
- 2001

—We investigate the polarization evolution for both signal and noise in two 107-km recirculating loops with polarization dependent loss per round-trip of 0.35 dB and less than 0.1 dB, respectively. When the system is optimized, in the first case, both signal and noise are polarized, while in the second case, the signal tends to depolarize due to the noise.… (More)

—Due to the temporal drift of the fiber birefringence in an optical fiber transmission system, the polarization mode dispersion (PMD) effects measured in a time window can be quite different for different time windows of the same duration. Every 10 s for 10 days, the accumulated differential group delay (DGD) was repeatedly measured at 5000 km in a 107-km… (More)

One of the five AES finalists, MARS, makes use of a 9x32 s-box with very specific combinatorial, differential and linear correlation properties. The s-box used in the cipher was selected as the best from a large sample of pseudo randomly generated tables, in a process that took IBM about a week to compute. This paper provides a faster and more effective… (More)