262
Index
G
Galois field, 179
Gibbs coefficients, 84, 87
Gibbs dyadic derivative, 86
bent functions
Kronecker delta, 90
properties, 91–92
quadratic bent function, 89
Reed–Muller expression, 89
Walsh spectrum, 90
definition, 87
diagonal matrix, 87
discrete Walsh functions, 88
Gibbs coefficients, 87
Gibbs differentiator, 87
Gibbs matrix, 88
matrix notation, 87
partial Gibbs derivative, 89
Gibbs permutation matrices
bent functions, 98–101
function vector, 102, 103
Gibbs coefficients, 96–97
Gibbs dyadic derivative, 103
Reed–Muller spectra, 98
subsets, 97
definition, 92
sparse matrices, 93
structure
function vector, 94, 95
matrix elements, 94
requirements, 93
submatrices, 93–94, 96
H
Hadamard transform matrix, 197
Hamming weight, 84
Hash functions, 23
Heuristics
probability heuristics, 119–120
scoring heuristics, 117–119
analysis, 120–122
asymmetric search tree, 124
average maximum symmetry ratio, 125,
126
benchmark problems, 126–127
characteristics, 129
exploration constants, 127–129
preprocessing approach, 125, 130
sub tree, 125
I
Independence function, 56, 64–65
Independence matrix (IDM), 61–63, 65–67
k-fold derivative operation, 77–80
single derivative operation, 72–75
vectorial derivative operation, 68, 69
Inverse number-theoretic transform (INNT),
24–26
Inverter Propagation axiom, 139, 142
K
Karnaugh-map
k-fold derivative operation, 80, 81
single derivative operation, 76
vectorial derivative operation, 72
Key encapsulation mechanisms, 23
k-fold derivative operation, 76–81
Kronecker product, 85
L
Lattice-based encryption schemes
ARM Cortex-M4F, 42, 44
attacker models, 23
CCA, 24
CCA2, 24 (see also Adaptive chosenciphertext attack (CCA2))
CPA, 24
cryptographic key-exchange mechanisms,
21, 22
dynamic power consumption, 22
hash functions, 23
implementation, 40–41
key encapsulation mechanisms, 23
linear codes, 22
LWE problem, 22
masking schemes, 22
multivariate quadratics, 22
NIST, 22
NNT
INTT, 24
learning with errors, 25–26
polynomials, 23
PQC, 22
quantum algorithms, 22
Shor’s algorithm, 21
side-channel attacks
DPA, 26–27
hiding, 27
masking, 27
timing attacks, 26
side-channel evaluation, 41–43
standardization process, 22
Learning with errors (LWE) problem, 22,
25–26
Index
G
Galois field, 179
Gibbs coefficients, 84, 87
Gibbs dyadic derivative, 86
bent functions
Kronecker delta, 90
properties, 91–92
quadratic bent function, 89
Reed–Muller expression, 89
Walsh spectrum, 90
definition, 87
diagonal matrix, 87
discrete Walsh functions, 88
Gibbs coefficients, 87
Gibbs differentiator, 87
Gibbs matrix, 88
matrix notation, 87
partial Gibbs derivative, 89
Gibbs permutation matrices
bent functions, 98–101
function vector, 102, 103
Gibbs coefficients, 96–97
Gibbs dyadic derivative, 103
Reed–Muller spectra, 98
subsets, 97
definition, 92
sparse matrices, 93
structure
function vector, 94, 95
matrix elements, 94
requirements, 93
submatrices, 93–94, 96
H
Hadamard transform matrix, 197
Hamming weight, 84
Hash functions, 23
Heuristics
probability heuristics, 119–120
scoring heuristics, 117–119
analysis, 120–122
asymmetric search tree, 124
average maximum symmetry ratio, 125,
126
benchmark problems, 126–127
characteristics, 129
exploration constants, 127–129
preprocessing approach, 125, 130
sub tree, 125
I
Independence function, 56, 64–65
Independence matrix (IDM), 61–63, 65–67
k-fold derivative operation, 77–80
single derivative operation, 72–75
vectorial derivative operation, 68, 69
Inverse number-theoretic transform (INNT),
24–26
Inverter Propagation axiom, 139, 142
K
Karnaugh-map
k-fold derivative operation, 80, 81
single derivative operation, 76
vectorial derivative operation, 72
Key encapsulation mechanisms, 23
k-fold derivative operation, 76–81
Kronecker product, 85
L
Lattice-based encryption schemes
ARM Cortex-M4F, 42, 44
attacker models, 23
CCA, 24
CCA2, 24 (see also Adaptive chosenciphertext attack (CCA2))
CPA, 24
cryptographic key-exchange mechanisms,
21, 22
dynamic power consumption, 22
hash functions, 23
implementation, 40–41
key encapsulation mechanisms, 23
linear codes, 22
LWE problem, 22
masking schemes, 22
multivariate quadratics, 22
NIST, 22
NNT
INTT, 24
learning with errors, 25–26
polynomials, 23
PQC, 22
quantum algorithms, 22
Shor’s algorithm, 21
side-channel attacks
DPA, 26–27
hiding, 27
masking, 27
timing attacks, 26
side-channel evaluation, 41–43
standardization process, 22
Learning with errors (LWE) problem, 22,
25–26