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CryptoBook
CryptoBook
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Fundamentals
Mathematical Notation
Division and Greatest common divisor
Modular Arithmetic
Continued Fractions
Number Theory
Ideals
Polynomials With Shared Roots
Integer Factorization
Abstract algebra
Groups
Rings
Fields
Polynomials
Elliptic Curves
Untitled
Lattices
Introduction
LLL reduction
Lattice reduction
Applications
Hard lattice problems
Lattices of interest
Cryptographic lattice problems
Interactive fun
Resources and notations
Asymmetric Cryptography
RSA
Diffie-Hellman
Elliptic Curve Cryptography
Symmetric Cryptography
Encryption
The One Time Pad
AES
Hashes
Introduction / overview
The Birthday paradox / attack
Isogeny Based Cryptography
Introduction to Isogeny Cryptography
Isogenies
Isogeny and Ramanujan Graphs
Appendices
Sets and Functions
Probability Theory
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Fields
A set
F
F
F
with two binary operations
+
,
⋅
:
F
×
F
→
F
+,\cdot:F\times F\to F
+
,
⋅
:
F
×
F
→
F
is a
field
if the following holds:
R
,
+
R,+
R
,
+
is a commutative group with identity
0
0
0
R
−
{
0
}
,
⋅
R-\{0\},\cdot
R
−
{
0
}
,
⋅
is a commutative group with identity
1
1
1
.
Distributivity:
a
(
b
+
c
)
=
a
b
+
a
c
,
(
a
+
b
)
c
=
a
c
+
b
c
a(b+c)=ab+ac,(a+b)c=ac+bc
a
(
b
+
c
)
=
ab
+
a
c
,
(
a
+
b
)
c
=
a
c
+
b
c
// field extensions, algebraic elements
Abstract algebra - Previous
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5mo ago
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