An Elliptic Divisibility Sequence is an integer sequence satisfying the following recurrence relation.
Some Example Sequences 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, …
- Page 1 and 2: Elliptic Nets How To Catch an Ellip
- Page 3 and 4: Part I: Elliptic Curves are Groups
- Page 5 and 6: A Typical Elliptic Curve E E : Y 2
- Page 7 and 8: Doubling a Point P on E Tangent Lin
- Page 9 and 10: Part II: Elliptic Divisibility Sequ
- Page 11 and 12: Example
- Page 13: So What Happens to Point Multiples?
- Page 17 and 18: Some Example Sequences 0, 1, 1, -1,
- Page 19 and 20: Some more terms… 0, 1, 1, -3, 11,
- Page 21 and 22: Take a Lattice Λ in the Complex Pl
- Page 23 and 24: Elliptic Functions Zeroes at z = a
- Page 25 and 26: Part IV: Elliptic Divisibility Sequ
- Page 27 and 28: Elliptic Divisibility Sequences: De
- Page 29 and 30: Part V: Reduction Mod p
- Page 31 and 32: Reduction Mod p 0, 1, 1, -3, 11, 38
- Page 33 and 34: Reduction Mod p 0, 1, 1, -3, 11, 38
- Page 35 and 36: Periodicity Example 0, 1, 1, 8, 0,
- Page 37 and 38: Part VI: Elliptic Nets: Jacking up
- Page 39 and 40: From Sequences to Nets It is natura
- Page 41 and 42: Definition A Elliptic Nets: Rank 2
- Page 43 and 44: ↑ Q Example 4335 5959 12016 -5528
- Page 45 and 46: ↑ Q Example 4335 5959 12016 -5528
- Page 47 and 48: ↑ Q Example 4335 5959 12016 -5528
- Page 49 and 50: Equivalence of Definitions
- Page 51 and 52: Nets are Integral
- Page 53 and 54: Divisibility Property
- Page 55 and 56: ↑ Q Example 0 4 1 3 1 2 4 4 4 4 4
- Page 57 and 58: Periodicity of Nets
- Page 59 and 60: Elliptic Curve Cryptography For cry
- Page 61 and 62: Elliptic Curve Diffie-Hellman Key E
- Page 63 and 64: Tate Pairing in Cryptography: Tripa
- Page 65 and 66:
Tate Pairing from Elliptic Nets
- Page 67 and 68:
Calculating the Net (Rank 2) Based
- Page 69 and 70:
Embedding Degree k
- Page 71 and 72:
Possible Research Directions • Ex