Index

(n, t)-threshold scheme 1

GF(pⁿ) 1

3-colouring 1

abelian group 1

abelianization 1

active attacker 1

adaptive chosen message attack 1

AES 1

affine cipher 1

Ajtai-Dwork cryptosystem 1

Ajtai hash function 1

AKS algorithm 1

Alberti code 1

algebraic attack 1

– ciphertext-only 1

– known plaintext 1

– public key system 1

algebraic closure 1

algebraic element 1, 2

algebraic eraser method 1

algebraic extension 1

algebraically closed 1

amalgam factors 1

Artin presentation 1

associated subgroups 1

asymmetric cryptography 1

asymptotically equal 1

Atabash code 1

attack 1, 2

– length based 1

authentication 1, 2, 3

authentication protocol 1

average case complexity 1

Babai’s algorithm 1

baby step giant step algorithm 1

base 1

base field equation 1

base field ideal 1

Big O-Little o Notation 1

Blakely scheme 1

block cipher 1, 2

braid group on n strands 1

broken cryptosystem 1

Buchberger’s algorithm 1

Buchberger’s criterion 1, 2

Buchberger’s procedure 1

– for modules 1

Buchberger-Moller algorithm 1

caesar code 1

Carmichael number 1

Cayley Table 1

CCM Mode 1

characteristic of a field 1

characteristic term attack 1

Chinese Remainder Theorem 1

chosen ciphertext attack 1, 2

chosen plaintext attack 1

cipher text only attack 1

ciphertext 1

classical cryptography 1

closest vector problem 1

closest vector secret sharing protocol 1

closest vector theorem 1

code 1

collision resistant 1

combinatorial group theory 1

commutative ring 1

commutator subgroup 1

complete lattice 1

component elimination module 1

computational security 1

congruence modulo n 1

congruence motion 1

conjugacy problem 1

conjugate subgroups 1

conjugator search problem 1, 2

coprime 1

cracking problem 1

critical pair 1

cryptanalysis 1, 2, 3

cryptographic protocol 1, 2

cryptography 1, 2

– classical 1

– public key 1, 2

– symmetric key 1, 2

cryptology 1, 2

cryptosystem 1, 2

– commutative Gröbner basis 1

– Courtois toy cipher 1

– free group 2

– graph 1

– colouring 2

– graph p-colouring 1

– graph perfect code 1

– Gröbner basis 1

– Polly Cracker 1

– Polly Two 2

cuttingnumber 1

CVP 1

cyclic group 1

cyclic subgroup 1, 2

data rate 1

decision Diffie-Hellman problem 1

decryption 1

decryption key 1, 2

decryption map 1, 2

defining relator 1

degree of a divisor 1

degree of an extension 1

DES 1

diagonal ideal 1

Diffie-Hellman Key Exchange 1

Diffie-Hellman Problem 1

Diffie-Hellman zero-knowledge protocol 1

digest 1

digital envelope 1, 2

digital forgeries 1

digital signature 1, 2, 3, 4

digital signature protocol 1

digital signing algorithm 1

dihedral group 1, 2, 3

– infinite 1

discrete log problem 1, 2, 3

discrete logarithm 1

discriminant 1

division algorithm 1, 2

– non-commutative 1

divisor 1

ECB Mode 1

ECDSA 1

ECES 1

ElGamal encryption 1, 2

ElGamal Signature Method 1

elimination ideal 1

elimination ordering 1

elliptic curve 1, 2, 3

elliptic curve cryptosystem 1

elliptic curve ElGamal cryptosystem 1

elliptic curve elliptography 1

elliptic curve encryption scheme 1

elliptic curve group 1, 2

embedding degree 1

encryption 1

encryption key 1, 1

encryption map 1, 2

Enigma Machine 1

enumerative procedure 1

enveloping algebra 1

Euclidean algorithm 1

Euclidean group 1

Euler phi function 1

Euler’s Theorem 1

exhaustive search 1, 1

exponential time algorithm 1

exponential time problem 1

extension field 1

F-isomorphism 1

factor group 1

factorization problem 1

fair strategy 1

Feistel network 1

Fermat factorization method 1

Fermat’s primality test 1

Fermat’s theorem 1

field 1, 2

finite extension 1

free abelian group 1

free associative algebra 1

free basis 1

free group 1

– rank 1

free group cryptosystem 1

free length 1

free monoid 1

free part 1

free products 1, 2

free products with amalgamation 1, 2

free reduction 1

freely reduced 1

Friedman test, 1

Friedmann Coincidence Index 1

Frobenius map 1, 2

Fuchsian group 1

Fundamental Theorem of Algebra 1

Galois field 1

Garside normal form 1

gaussian heuristic 1

general linear group 1, 2

generators 1

generic case complexity 1

generic complexity 1

geometry of numbers 1

GGH cryptosystem 1

Gram-Schmidt process 1

graph 1

ground field 1

group 1, 2

– abelian 1

– cyclic 1

– finite 1

– finitely generated 1

– finitely presented 1

– finitely related 1

– generating system 1

– generators 1, 2

– infinite 1

– order 1, 2

– presentation 1, 2

– relations 1

– relator 1

group amalgams 1

group based cryptography 1

group decision problems 1

group homomorphism 1

group presentation 1, 2

group products 1

group ring 1

group table 1

Grobner basis 1, 2, 3

– partial 1

GSO 1

hadamard ratio 1

handle 1

handle reduction 1

hash function 1, 2, 3, 4

hash value 1

HFE challenge 1

HKZ algorithm 1

HNN extension 1

ideal 1

– base field 1

– diagonal 1

– elimination 1

– finitely generated 1

– leadingword 1

– left 1

– right 1

– two-sided 1

– zero set 1

ideal membership test 1, 2

indeterminate 1

index calculus method 1

industrial grade primes 1

information-theoretic security 1

integer programming attack 1

integral lattice 1

intermediate field 1

irreducible polynomial 1

isometry 1

isomorphism problem 1

iterated block cipher 1

Kasiski test 1

key exchange 1, 2

key exchange protocol 1

key generation algorithm 1

key only attack 1

key space 1

key stream 1

key transport 1, 2

keystream gemerator 1

keyword 1, 2

known message attack 1

known plaintext attack 1

Korselt citerion 1

Kronecker’s Theorem 1

Lagrange’s theorem 1

lattice 1

– determinant 1

– fundamental domain 1

– good basis 1

lattice based cryptography 1

lattice basis 1

lattice basis reduction 1

lattice redcution algorithm 1

leading coefficient 1,2,3

leading monomial 1,2

leading term 1, 2

leading term ideal 1

leading term module 1

leading word 1

leading word ideal 1

Legendre symbol 1

length based attack 1

letter 1

linear algebra attack 1,2

linear congruence generator 1

linear shift feedback generator 1

LLL algorithm 1

Lucas-Lehmer test 1

Macaulay’s basis theorem 1, 2, 3

Magnus representation 1

man in the middle attack 1, 2

mathematical cryptography 1

MCA 1

Meneses-Vanstone Cryptosystem 1

Mersenne prime 1

message authentication code 1

message expansion 1

message unit 1

minimal polynomial 1

Minkowski’s theorem 1

mixed encyrption 1, 2

modular arithmetic 1, 2

modular group 1

modular ring 1, 2

modular square root 1

multiplicative function 1

multiplicative relation 1

Nielsen-Schreier Theorem 1

non-commutative algebraic cryptography 1

non-commutative cryptography 1

non-deterministic polynomial time 1

normal form 1, 2

normal remainder 1, 2

normal subgroup 1

NP Complete 1

NP-hard 1

NTRU cryptosystem 1

obstruction 1

– withoutoverlap 1

one-time pad 1

one-way function 1, 2, 3, 4

order ideal 1

order of an element 1

order of magnitude 1

P=NP 1

padding 1

passive attacker 1

perfect code 1

perfect security 1

permutation 1

permutation cipher 1, 2

permutation group 1

plaintext 1

Pollard algorithm 1

Polly Cracker cryptosystem 1

polyalphabetic ciphers 1

polynomial 1

– degree 1

– logical representation 1

polynomial ring 1

– non-commutative 1

polynomial time algorithm 1

polynomial time problem 1

practical security 1

preimage resistant 1

primality test

– deterministic 1

– probabilistic 1

primality testing 1

primitive element 1, 2

principal divisor 1

principal ideal 1

private key 1

probabilistic algorithm 1, 2

probable primes 1

product cipher 1

pseudoprime 1

public key 1

public key cryptography 1, 2, 3, 4

public key encryption map 1

quadratic residue 1

quadratic sieve 1

quantum algorithm 1

quotient group 1

Rabin Cryptosystem 1

Rabin Encryption 1

Reidemeister-Schreier Process 1

relations 1

relatively prime 1

residue 1

residue class 1

Rijnadel cipher 1

ring 1

– commutative 1

root of a polynomial 1

round 1

round keys 1

RSA Algorithm 1

RSA cryptanalysis 1

RSA decryption exponent 1, 2

RSA encryption exponent 1, 2

RSA Modulus 1, 2

RSA Problem 1

RSA Protocol 1

RSA secure primes 1

RSA Signature Method 1

S-box 1

S-polynomial 1, 2

S-vector 1

SAT attack 1

secret key 1

secret sharing 1, 2

secret sharing scheme 1

security reduction 1

secutity proof 1

self-obstruction 1

semantic security 1

semi-decision procedure 1

session key 1, 2, 3

Shamir Secret Sharing Scheme 1

shift cipher 1

Shor’s algorithm 1

shortest vector problem 1

side channel attack 1

sieve 1

Sieve of Eratosthenes 1

sieving methods 1

signature 1

social security control group 1

soundness error 1

special linear group 1

splits 1

splitting field 1

SQ-universality 1

stabilizer 1

stable letters 1

standard conversion strategy 1

statistical frequency attack 1

stream cipher 1

– softwaregeneration 1

stream ciphers 1

strong pseudoprime 1

subalgebra membership problem 1

subgroup 1

– conjugate 1

substitution cipher 1

substitution-permutation network 1

subword 1

successful attack 1

summit set 1

SVP 1

syllable length 1

symmetric group 1

symmetric key cryptography 1, 2, 3

symmetry group 1

system of generators 1

syzygy module 1

– computation 1

Tate pairing 1

term 1, 2

term ordering 1

– component elimination 1

– degree reverse lexicographic 1

– lexicographic 1

– module 1

The Class NP 1

The Fermat Primality Test 1

The Modular Group 1

The MOV Algorithm 1

theoretical security 1

transcendental element 1, 2

transcendental extension 1

transposition 1

trapdoor function 1, 2, 3, 4

unit 1, 2

unit group 1, 2

vanishing ideal 1, 2

verification 1

vernam ciphers 1

Vernam key-pad 1

Vigenere code 1

Vigenere cryptosystems 1

Weierstrass form 1

Weil-pairing 1

well-ordering 1

witness 1

word 1, 2

– cyclically reduced 1

– empty 1

– length 1

– reduced 1

– trivial 1

word ordering 1

– elimination 1

– length-lexicographic 1

– lexicographic 1

word problem 1, 2

– generalized 1

worst case complexity 1, 2

XOR Operation 1

zero of a polynomial 1

zero-knowledge proof 1, 2, 3