Index
A
Abstraction-refinement algorithm, 184–185
Adaptive chosen-ciphertext attack (CCA2), 42
arithmetic-to-Boolean transformation, 30,
31
CCA2-secured decryption, 28–29
correctness, 30, 38
cycle counts and dynamic memory
consumption, 44, 45
decoding, 31, 32
Fujisaki–Okamoto (FO) transformation, 27
masked binomial sampler, 37–38
masked PRNG, 38
MDecode algorithm, 33, 34
public-key size, 28
ring-LWE decryption, 29–30, 35–37
RLWE.CPA conversion, 28
security analysis, 33
SHAKE, 34
Targhi–Unruh variant, 27
timing-constant solution, 39
TransformPower2 algorithm, 31
Affine equivalence classes, 204, 206–207
size distribution, 208, 209
Altun–Riedel method, 160
Architectural explanation, 10
Arithmetic-to-Boolean transformation, 30, 31
ARM Cortex-M4F, 42, 44
Associativity axiom, 139, 140
Asynchronous distributed system, 6, 7
Axiomatization
Associativity axiom, 139, 140
axioms, types, 138
Commutativity axiom, 139
Distribution axiom, 139, 141
Inverter Propagation axiom, 139, 142
Majority, 139–140, 142
B
Backpropagation, 110, 112
Backtracking-based solver, 108
BDE, see Boolean differential equation
Bent functions, 83–86, 98–101
function vector, 102, 103
Gibbs coefficients, 96–97
Gibbs dyadic derivative, 103
Kronecker delta, 90
properties, 91–92
quadratic bent function, 89
Reed–Muller spectra, 89, 98
subsets, 97
Walsh spectrum, 90
Binary reversible functions, 222
Binary vector (BV), 66–68
Binomial distribution, 25
B2M algorithm, see Boolean to Majority
algorithm
Boolean differential calculus, 81
Boolean differential equation (BDE), 52
Boolean functions
affine equivalence classes, 204, 206–207
size distribution, 208, 209
arithmetic verification, 196
average translations per function, 210
class generation, CPU sec, 204, 210
1-neighbourhood of function, 210, 213
spectral equivalence classes, 211–212
classification schemes, 199, 200
cryptography, 196
© Springer Nature Switzerland AG 2020
R. Drechsler, M. Soeken (eds.), Advanced Boolean Techniques,
https://doi.org/10.1007/978-3-030-20323-8
259
A
Abstraction-refinement algorithm, 184–185
Adaptive chosen-ciphertext attack (CCA2), 42
arithmetic-to-Boolean transformation, 30,
31
CCA2-secured decryption, 28–29
correctness, 30, 38
cycle counts and dynamic memory
consumption, 44, 45
decoding, 31, 32
Fujisaki–Okamoto (FO) transformation, 27
masked binomial sampler, 37–38
masked PRNG, 38
MDecode algorithm, 33, 34
public-key size, 28
ring-LWE decryption, 29–30, 35–37
RLWE.CPA conversion, 28
security analysis, 33
SHAKE, 34
Targhi–Unruh variant, 27
timing-constant solution, 39
TransformPower2 algorithm, 31
Affine equivalence classes, 204, 206–207
size distribution, 208, 209
Altun–Riedel method, 160
Architectural explanation, 10
Arithmetic-to-Boolean transformation, 30, 31
ARM Cortex-M4F, 42, 44
Associativity axiom, 139, 140
Asynchronous distributed system, 6, 7
Axiomatization
Associativity axiom, 139, 140
axioms, types, 138
Commutativity axiom, 139
Distribution axiom, 139, 141
Inverter Propagation axiom, 139, 142
Majority, 139–140, 142
B
Backpropagation, 110, 112
Backtracking-based solver, 108
BDE, see Boolean differential equation
Bent functions, 83–86, 98–101
function vector, 102, 103
Gibbs coefficients, 96–97
Gibbs dyadic derivative, 103
Kronecker delta, 90
properties, 91–92
quadratic bent function, 89
Reed–Muller spectra, 89, 98
subsets, 97
Walsh spectrum, 90
Binary reversible functions, 222
Binary vector (BV), 66–68
Binomial distribution, 25
B2M algorithm, see Boolean to Majority
algorithm
Boolean differential calculus, 81
Boolean differential equation (BDE), 52
Boolean functions
affine equivalence classes, 204, 206–207
size distribution, 208, 209
arithmetic verification, 196
average translations per function, 210
class generation, CPU sec, 204, 210
1-neighbourhood of function, 210, 213
spectral equivalence classes, 211–212
classification schemes, 199, 200
cryptography, 196
© Springer Nature Switzerland AG 2020
R. Drechsler, M. Soeken (eds.), Advanced Boolean Techniques,
https://doi.org/10.1007/978-3-030-20323-8
259