THECLA CHRYSALUS, EDWARDS, AND ITS VARIETY CITIMA, HENRY EDWARDS

11 Edwards

Binary Edwards Curves

This paper presents a new shape for ordinary elliptic curves over fields of characteristic 2. Using the new shape, this paper presents the first complete addition formulas for binary elliptic curves, i.e., addition formulas that work for all pairs of input points, with no exceptional cases. If n ≥ 3 then the complete curves cover all isomorphism classes of ordinary elliptic curves over F2n . Th...

Batch Binary Edwards

This paper sets new software speed records for high-security Diffie-Hellman computations, specifically 251-bit elliptic-curve variablebase-point scalar multiplication. In one second of computation on a $200 Core 2 Quad Q6600 CPU, this paper’s software performs 30000 251-bit scalar multiplications on the binary Edwards curve d(x + x + y + y) = (x + x)(y + y) over the field F2[t]/(t 251 + t + t +...

Twisted Edwards Curves Revisited

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 8M for suitably selected curve constants. In comparison, the fastest point addition algorithms for (twisted) Edwards curves stated in the literature ...

Edwards' Syndrome (Trisomy 18)

The Edwards' syndrome phenotype results from full, mosaic or partial trisomy 18q. Full trisomy 18 is the most common form occurring in about 94% of cases. In full trisomy every cell contains three full copies of chromosome 18. Mosaics can occur in about 5% of cases in which some cells are normal with 46 chromosomes and others have the extra chromosome. Partial trisomy 18 can (rarely) occur if a...