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Faster homomorphic encryption is not enough: improved heuristic for multiplicative depth minimization of Boolean circuits
somewhat homomorphic encryption multiplicative depth Boolean functions
2019/8/27
In somewhat homomorphic encryption schemes (e.g. B/FV, BGV) the size of ciphertexts and the execution performance of homomorphic operations depends heavily on the multiplicative depth. The multiplicat...
Hardware masked AES designs usually rely on Boolean masking and perform the computation of the S-box using the tower-field decomposition. On the other hand, splitting sensitive variables in a multipli...
Flaws in a Verifiably Multiplicative Secret Sharing Scheme from ICITS 2017
secret sharing multiplicative verifiability
2018/1/27
In this paper, we point out flaws in an existing verifiably multiplicative secret sharing (VMSS) scheme. Namely, we show that a scheme proposed by Yoshida and Obana presented at ICITS 2017 is insecure...
The Multiplicative Complexity of 6-variable Boolean Functions
Affine equivalence Boolean functions Circuit complexity
2018/1/12
The multiplicative complexity of a Boolean function is the minimum number of AND gates that are necessary and sufficient to implement the function over the basis (AND, XOR, NOT). Finding the multiplic...
A multi-start heuristic for multiplicative depth minimization of boolean circuits
boolean functions homomorphic encryption multiplicative depth
2017/6/1
In this work we propose a multi-start heuristic which aims at minimizing the multiplicative depth of boolean circuits. The multiplicative depth objective is encountered in the field of homomorphic enc...
On the Multiplicative Complexity of Boolean Functions and Bitsliced Higher-Order Masking
Higher-Order Masking Boolean Functions Multiplicative Complexity
2016/6/6
Higher-order masking is a widely used countermeasure to
make software implementations of blockciphers achieve high security levels
against side-channel attacks. Unfortunately, it often comes with a
...
MiMC: Efficient Encryption and Cryptographic Hashing with Minimal Multiplicative Complexity
distributed cryptography cryptanalysis block ciphers
2016/5/23
We explore cryptographic primitives with low multiplicative complexity. This is motivated by recent progress in practical applications of secure multi-party computation (MPC), fully homomorphic encryp...
Ultra-lightweight 8-bit Multiplicative Inverse Based S-box Using LFSR
Multiplicative Inverse AES LFSR
2016/1/26
Most of the lightweight block ciphers are nibble-oriented as
the implementation of a 4-bit S-box is much more compact than an 8-bit
S-box. This paper proposes a novel implementation of multiplicativ...
Strong Security of the Strongly Multiplicative Ramp Secret Sharing based on Algebraic Curves
ramp secret sharing multiplicative secret sharing strong security
2015/12/29
We introduce a coding theoretic criterion for Yamamoto's strong security of the ramp secret sharing scheme. After that, by using it, we show the strong security of the strongly multiplicative ramp sec...
The Multiplicative Complexity of Boolean Functions on Four and Five Variables
Affine transformation Boolean functions Circuit complexity
2015/12/23
A generic way to design lightweight cryptographic primitives is to construct simple rounds
using small nonlinear components such as 4x4 S-boxes and use these iteratively (e.g., PRESENT [1]
and SPONG...
The Number of Boolean Functions with Multiplicative Complexity 2
Affine equivalence Boolean functions Cryptography
2015/12/22
Multiplicative complexity is a complexity measure defined
as the minimum number of AND gates required to implement a given
primitive by a circuit over the basis (AND, XOR, NOT). Implementations
of ...
Multiplicative monotone span program is one of the important tools to realize secure multiparty computation. It is essential to construct multiplicative monotone span programs for secure multiparty co...
Improving Additive and Multiplicative Homomorphic Encryption Schemes Based on Worst-Case Hardness Assumptions}
homomorphic encryption secure function evaluation lattices
2012/6/14
In CRYPTO 2010, Aguilar et al. proposed a somewhat homomorphic encryption scheme, i.e. an encryption scheme allowing to compute a limited amount of sums and products over encrypted data, with a securi...
Improving Additive and Multiplicative Homomorphic Encryption Schemes Based on Worst-Case Hardness Assumptions}
homomorphic encryption secure function evaluation lattices
2012/3/22
In CRYPTO 2010, Aguilar et al. proposed a somewhat homomorphic encryption scheme, i.e. an encryption scheme allowing to compute a limited amount of sums and products over encrypted data, with a securi...
Improving Additive and Multiplicative Homomorphic Encryption Schemes Based on Worst-Case Hardness Assumptions}
homomorphic encryption secure function evaluation lattices
2012/3/21
In CRYPTO 2010, Aguilar et al. proposed a somewhat homomorphic encryption scheme, i.e. an encryption scheme allowing to compute a limited amount of sums and products over encrypted data, with a securi...