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Index Index

\(=\quad\) is equal to
function, Definition
integers, Subsection
ordered pair, Definition
sets, Definition
\(\#\quad\) cardinality, Definition
\(\A\quad\) set of characters, Item
\(\cspace\quad\) space, Item
\(\fdiv\quad\) quotient, Definition
\(\fmod\quad\) remainder, Definition
\(\gcd\quad\) greatest common divisor, Definition
\(\ge\quad\) is greater than or equal to, Subsection
\(\gexp{b}{-1}{\bullet}\quad\) inverse
in group, Paragraph
with respect to \(\bullet\), Definition
\(\gexp{b}{0}{}=1\), Definition
\(\gexp{b}{n}{\otimes}\quad\) exponentiation in \((\Z_p^\otimes,\otimes)\), Paragraph
\(\gexp{b}{n}{\star}\quad\) exponentiation in group, Definition
\(\gexp{b}{n}{}\quad\) exponentiation of integers, Definition
\(\glog{b}{a}{\otimes}\quad\) discrete logarithm in \((\Z_p^\otimes,\otimes)\), Paragraph
\(\glog{b}{a}{\star}\quad\) discrete logarithm in group, Definition
\(\gt\quad\) is greater than, Subsection
\(\in\quad\) is element of, Definition
\(\le\quad\) is less than or equal to, Subsection
\(\lt\quad\) is less than, Subsection
\(\mid x\mid\quad\) absolute value, Definition
\(\N\quad\) set of natural numbers, Item
\(\ne\quad\) is not equal to
function, Definition
integers, Subsection
ordered pair, Definition
sets, Definition
\(\not\in\quad\) is not element of, Definition
\(\not\subseteq\quad\) is not subset of, Definition
\(\oplus\quad\) modular addition, Item
\(\otimes\quad\) modular multiplication, Item
\(\PP\quad\) set of prime numbers, Item
\(\subseteq\quad\) is subset of, Definition
\(\W\quad\) set of whole numbers, Item
\(\Z\quad\) set of integers, Item
\(\Z_n=\{0,\dots,n-1\}\), Item
\(\Z_n^\otimes=\{1,\dots,n-1\}\), Item
\(\{\,\}\quad\) empty set, Definition
\(\{\cdot,\cdot,\cdot,\cdot,\ldots\}\quad\) roster form with ellipsis, Paragraph
\(\{\cdot,\cdot,\cdot,\cdot\}\quad\) roster form, Definition
\(\{\cdot\mid \cdots\}\quad\) set builder, Paragraph
\(C\quad\) encoding function, Figure
\(C^{-1}\quad\) decoding function, Figure
\(f^{-1}\quad\) inverse function, Definition
\(n!\quad\) factorial, Definition
abelian, Paragraph
absolute value, Definition
algorithm, Algorithm
acknowledgments, Acknowledgements
addition
associative property, Item
inverse, Definition
algorithm, Definition
absolute value, Algorithm
base \(10\) to base \(2\), Algorithm
base \(10\) to base \(b\), Algorithm
discrete logarithm, Algorithm
division, Section
negative integers, Algorithm
positive integers, Algorithm
Eierkuchen, Algorithm
Euclidean, Algorithm
even or odd, Algorithm
exponentiation
fast in groups, Algorithm
naive for integers, Algorithm
naive in groups, Algorithm
factorial, Algorithm
fortytwo, Algorithm
four powers, Algorithm Algorithm
gcd, Algorithm
maximum, Algorithm
repeated squaring, Algorithm
sum of two integers, Algorithm
sum up to, Algorithm
Alice, Paragraph
Ant Attack, Figure
arithmetic
clock, Paragraph
ASCII, Paragraph
associative
addition, Item
binary operation, Definition
multiplication, Item
base, Definition
in group, Definition
base 10, Section
expansion, Paragraph
base 2, Section
counting, Subsection
expansion, Paragraph
base b, Section
expansion, Paragraph
representation, Section
binary, Section
binary operation, Chapter Definition
associative, Definition
commutative, Definition
identity element, Definition
inverse element, Definition
video, Figure
black and white, Figure
blackboard bold, Paragraph
Bob, Paragraph
Bézout's Identity
easy case, Theorem
Bézout's identity, Theorem
modular inverse, Strategy
Caesar ciphers, Paragraph
calculator long division, Strategy
cardinality
Cartesian product, Example
empty set, Definition
same, Definition
cardinality of a set, Definition
Cartesian product, Definition
cardinality, Example
image, Paragraph
character
\(\cspace\) space, Item
encoding, Section
set of, Item
check digit, Paragraph
checkpoing
repeated squaring, Checkpoint
checkpoint, Paragraph
are these commutative ?, Checkpoint
are these groups ?, Checkpoint
binary operation, Checkpoint
definition of associativity, Checkpoint
definition of commutativity, Checkpoint
definition of identity, Checkpoint
definition of inverse, Checkpoint
discrete logarithm, Checkpoint
find inverses, Checkpoint
group axioms, Checkpoint
is there an identity ?, Checkpoint
is this a group ?, Checkpoint
operation table, Checkpoint
clock arithmetic, Paragraph
code, Paragraph
codes, Chapter
coding theory, Paragraph
codomain, Definition
colors, Section
darker, Subsection
grey, Subsection
interactive, Figure
lighter, Subsection
video, Figure
commutative
addition, Example
binary operation, Definition
group, Definition
multiplication, Item
complexity analysis, Paragraph
composite
function, Definition
integer, Definition
compound statement, Subsection
conjecture, Paragraph
twin prime, Conjecture
conversion
base 10 to base 2, Section
base 10 to base b, Section
base 2 to base 10, Paragraph
base b to base 10, Paragraph
character to number, Section
image to numbers, Section
text to number, Section
countably infinite set, Definition
counterexample, Paragraph
counting in base 2, Subsection
cryptography
Caesar ciphers, Paragraph
Diffie Hellman key exchange, Section
ElGamal encryption system, Paragraph
frequency analysis, Paragraph
public key, Chapter
substitution ciphers, Section
symmetric key, Paragraph
cubed, Paragraph
darker colors, Subsection
decimal, Section
expansion, Paragraph
representation, Section
decoder disc, Figure
decoding function \(C^{-1}\), Figure
definition, Paragraph
difference, Definition
Diffie Hellman key exchange, Section
diagram, Figure
interactive, Example
video
color mixing, Figure
example, Figure
how it works, Figure
digital signatures, Subsection
discrete logarithm, Definition
algorithm, Algorithm
video, Figure
distributive, Paragraph
distributive property, Example
divides, Definition
other formulations, Definition
divisibility, Section
division, Chapter Paragraph
algorithm, Section Subsection
negative integers, Algorithm
positive integers, Algorithm
calculator long, Strategy
long, Section
negative integers, Paragraph
divisor, Definition
domain, Definition
Eierkuchen, Algorithm
El Gamal encryption system
diagram, Figure
ElGamal encryption system, Paragraph
interactive, Example
video, Figure
ellipses, Paragraph
empty set, Definition
cardinality, Definition
encoding
character, Section
function \(C\), Figure
text to number, Section
equal
function, Definition
integers, Paragraph
ordered pair, Definition
sets, Definition
Eratosthenes, sieve of, Section
Euclid's theorem, Theorem
Euclidean algorithm, Algorithm
video, Figure
evaluation, Subsection
Eve, Paragraph
even, Definition
example, Paragraph
expansion
base 10, Paragraph
base 2, Paragraph
base b, Paragraph
decimal, Paragraph
exponent, Definition
in group, Definition
exponentiation
algorithm
fast in groups, Algorithm
naive for integers, Algorithm
naive in groups, Algorithm
fast in groups, Section
in groups, Section
integers, Definition
properties, Subsection
expression, Paragraph
factor, Definition
factorial, Definition
algorithm, Algorithm
Factoring the Time, Figure
false, Paragraph
fast exponentiation, Section
algorithm, Algorithm
fifty shades of grey, Figure
finite set, Definition
for all, Subsection
frequency analysis, Paragraph
full, Quotation
function, Definition
composite, Definition
equal, Definition
identity, Definition
inverse, Definition
invertible, Definition
trapdoor, Definition
video, Figure
algorithm, Algorithm
video, Figure Figure
given any, Subsection
greatest common divisor, Definition
video, Figure
grey, Subsection
group, Definition
hex triplet, Paragraph
identity
binary operation, Definition
function, Definition
modular
additive, Item
multiplicative, Item
if (if_then), Section
image
Cartesian product, Paragraph
of an element under a function, Item
to numbers, Section
interactive, Figure
strategy, Strategy
video, Figure
infinite
countably, set, Definition
infinitude of primes, Theorem
input, Item
instruction
if (if_then), Section
let (let_:=), Section
repeat (repeat_until), Section
return, Section
integer, Paragraph
composite, Definition
even, Definition
exponentiation, Definition
negative, Paragraph
operation, Subsection
positive, Paragraph
prime, Definition
set of, Item
interactive
algorithm
(naive) exponentiation, Example
base \(10\) to base \(2\), Example
base \(10\) to base \(b\), Example
division of negative integers, Example
division of positive integers, Example
eighth power, Example
Euclidean, Example
fast exponentiation, Example
sum, Example
colors, Figure
Diffie Hellman key exchange, Example
ElGamal encryption system, Example
image to numbers, Figure
sieve of Eratosthenes, Figure
inverse
additive, Definition
binary operation, Definition
function, Definition
in group, Paragraph
modular
additive, Item
multiplicative, Strategy
uniqueness, Theorem
with respect to binary operation, Definition
invertible function, Definition
iteration, Paragraph
let (let_:=), Section
lighter colors, Subsection
logarithm
discrete, Definition
long division, Section
operation, Section
modular
addition, Item
arithmetic, Definition
multiplication, Item
multiple, Definition
multiplication, Definition
associative property, Item
natural number, Paragraph
set of, Item
negative integers, Paragraph
non-negative, Definition
number
line, Figure Figure
of elements in a set, Definition
of subsets, Section
to text, Strategy
operation
binary, Definition
integers, Subsection
mod, Section
order of operations, Subsection
ordered pair, Definition
equal, Definition
output, Item
padlock analogue, Example
perfect square, Paragraph
pixel, Paragraph
placeholder, Section
positive integer, Paragraph
power
of group element, Definition
of integer, Definition
preimage, Item
prime, Definition
factorization, Section
infinitude, Theorem
set of, Item
twin, Definition
conjecture, Conjecture
video, Figure
video, Figure
problem, Paragraph
product, Definition
Cartesian, Definition
proof, Paragraph
public key cryptography, Chapter
diagram, Figure
repeat (repeat_until), Section
repeated squaring, Section
algorithm, Algorithm
representation
base 2, Section
base b, Section
binary, Section
return (return), Section
RGB, Paragraph
hex triplet, Paragraph
video, Figure
root, Definition
roster form, Definition
-builder notation, Paragraph
countably infinite, Definition
empty, Definition
equal, Definition
finite, Definition
infinite, Definition
of characters, Item
of integers, Item
of natural numbers, Item
of primes, Item
of whole numbers, Item
roster form, Definition
special, Section
subset, Definition
well-defined, Paragraph
sieve of Eratosthenes, Section
interactive, Figure
strategy, Strategy
video, Figure
SLOs, Chapter
space, Paragraph
special sets, Section
square, Definition
perfect, Paragraph
root, Definition
squared, Paragraph
statement, Section
compound, Subsection
strategy
calculator long division, Strategy
comparing shades of grey, Strategy
image to numbers, Strategy
modular inverse, Strategy
numbers to text, Strategy
sieve of Eratosthenes, Strategy
text to number, Strategy
student learning outcomes, Chapter
subset, Definition
number of, Section
substitution ciphers, Section
symmetric key cryptography, Paragraph
text to number, Section
strategy, Strategy
then (if_then), Section
theorem, Paragraph
Euclid's, Theorem
trapdoor function, Definition
triplet, Paragraph
true, Paragraph
twin prime, Definition
conjecture, Conjecture
video, Figure
Unicode, Paragraph
uniqueness
identity, Theorem
inverse, Theorem
until (repeat_until), Section
variable, Section
video, Section
algorithms, Figure
assignment let, Figure
associativity, Figure
base 10 to base 2, Figure
base 10 to base b, Figure
binary operations, Figure
caesar cipher, Figure
cardinality, Figure
cardinality of Cartesian products, Figure
clock arithmetic, Figure
colors, Figure
commutativity, Figure
compute mod, Figure
conditional if_then, Figure
decoder disc, Figure
Diffie Hellman
color mixing, Figure
example, Figure
how it works, Figure
discrete logarithm, Figure
division algorithm, Figure
ElGamal encryption system, Figure
encoding, Figure
Euclidean algorithm, Figure
exponentiation (of integers), Figure
fast exponentiation, Figure
frequency analysis, Figure
functions, Figure
gcd, Figure
greatest common divisor, Figure Figure
groups, Figure
additive, Figure
examples, Figure
multiplicative, Figure
identity, Figure
image to numbers, Figure
infinite sets, Figure
integers, Figure
definition and statements, Figure
inverses, Figure
ISBN, Figure
long division, Figure
loop repeat_until, Figure
membership and equality, Figure
naive exponentiation, Figure
number of subsets, Figure
operation mod, Figure
other substitution ciphers, Figure
prime, Figure
factorization, Figure
infinitude, Figure
twin, Figure
quotients and remainders, Figure
repeated squaring, Figure
algorithm, Figure
roster form, Figure
set builder, Figure
sets (definition), Figure
sieve of Eratosthenes, Figure
special sets, Figure
subsets, Figure Figure
symmetric key cryptography, Figure
variables, Figure
well-defined, Paragraph
whole number
set of, Item
xkcd, Section
1 to 10, Figure
Alice and Bob, Figure
Certainty, Figure
Code Talkers, Figure
Forgot Algebra, Figure
Loop, Figure
Mnemonics: order of operations, Figure
privacy opinions, Figure
Protocol, Figure
random number, Figure
Su Doku, Figure