Reduction of a curve mod p (0,-3) 6 5 4 3 2 1 0 X 0 1 2 3 4 5 6
Reduction Mod p 0, 1, 1, -3, 11, 38, 249, -2357, 8767, 496035, -3769372, -299154043, -12064147359, 632926474117, -65604679199921, -6662962874355342, -720710377683595651, 285131375126739646739, 5206174703484724719135, -36042157766246923788837209, 14146372186375322613610002376, … 0, 1, 1, 8, 0, 5, 7, 8, 0, 1, 9, 10, 0, 3, 7, 6, 0, 3, 1, 10, 0, 1,10, 8, 0, 5, 4, 8, 0, 1, 2, 10, 0, 3, 4, 6, 0, 3, 10, 10, 0, 1, 1, 8, 0, 5, 7, 8, 0, … This is the elliptic divisibility sequence associated to the curve reduced modulo 11
- 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 and 14: So What Happens to Point Multiples?
- Page 15 and 16: Some Example Sequences 0, 1, 2, 3,
- 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: Part V: Reduction Mod p
- 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