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Relation between o-equivalence and EA-equivalence for Niho bent functions
Bent function Boolean function EA-equivalence
2019/7/15
Boolean functions, and bent functions in particular, are considered up to so-called EA-equivalence, which is the most general known equivalence relation preserving bentness of functions. However, for ...
On equivalence between known families of quadratic APN functions
CCZ-equivalence EA-equivalence APN
2019/7/15
We study a question whether the currently known families of quadratic APN polynomials are pairwise different up to CCZ-equivalence. We reduce the list of these families to those CCZ-inequivalent to ea...
Extended Affine and CCZ Equivalence up to Dimension 4
boolean functions extended affine equivalence CCZ equivalence
2019/4/1
For all vectorial boolean functions up to dimension 4, we present canonical representatives for all extended affine (EA) and CCZ equivalence classes. We include the size of each class, as well as its ...
In this short note we give a polynomial-time quantum reduction from the vectorization problem (DLP) to the parallelization problem (CDHP) for group actions. Combined with the trivial reduction from pa...
Linear Equivalence of Block Ciphers with Partial Non-Linear Layers: Application to LowMC
Block cipher LowMC Picnic signature algorithm linear equivalence
2018/8/28
LowMC is a block cipher family that is optimized for practical instantiations of multi-party computation, fully homomorphic encryption, and zero-knowledge proofs. It was designed in 2015 by Albrecht e...
On CCZ-Equivalence, Extended-Affine Equivalence, and Function Twisting
Boolean functions CCZ-Equivalence EA-equivalence
2018/8/2
Two vectorial Boolean functions are ``CCZ-equivalent'' if there exists an affine permutation mapping the graph of one to the other. It preserves many of the cryptographic properties of a function such...
In this work, we discuss two notions of differential equivalence on Sboxes. First, we introduce the notion of DDT-equivalence which applies to vectorial Boolean functions that share the same differenc...
The security for authenticated encryption schemes is often captured by demanding CCA security (IND-CCA) and integrity of plaintexts (INT-PTXT). In this short note, we prove that this implies in partic...
An Improved Affine Equivalence Algorithm for Random Permutations
Affine equivalence problem block cipher Even-Mansour cipher
2018/2/1
Our algorithm is based on a new structure (called a \emph{rank table}) which is used to analyze particular algebraic properties of a function that remain invariant under invertible affine transformati...
Weakly Secure Equivalence-Class Signatures from Standard Assumptions
Structure-preserving signatures security proof standard assumptions
2018/1/11
Structure-preserving signatures on equivalence classes, or equivalence-class signatures for short (EQS), are signature schemes defined over bilinear groups whose messages are vectors of group elements...
On differential equivalence of APN functions
Boolean function Almost perfect nonlinear function Almost bent function
2017/9/25
For a given vectorial Boolean function FF from Fn2F2n to itself it was defined an associated Boolean function γF(a,b)γF(a,b) in 2n2n variables by C.~Carlet, P.~Charpin, V.~Zinoviev in 1998 that takes ...
An Equivalence Between Attribute-Based Signatures and Homomorphic Signatures, and New Constructions for Both
digital signatures homomorphic signatures attribute-based signatures
2017/7/28
In Attribute-Based Signatures (ABS; first defined by Maji, Prabhakaran and Rosulek, CT-RSA 2011) an authority can generate multiple signing keys, where each key is associated with an attribute xx. Mes...
A New Method to Investigate the CCZ-Equivalence between Functions with Low Differential Uniformity
Differentially 44-uniform function Projected differential spectrum Substitution boxes
2016/12/12
Recently, many new classes of differentially 44-uniform permutations have been constructed. However, it is difficult to decide whether they are CCZ-inequivalent or not. In this paper, we propose a new...
An Equivalence-Preserving Transformation of Shift Registers
Feedback shift register NLFSR Fibonacci configuration
2016/1/26
The Fibonacci-to-Galois transformation is useful for reducing the propagation
delay of feedback shift register-based stream ciphers and hash functions.
In this paper, we extend it to handle Galois-t...
Structure-Preserving Signatures on Equivalence Classes and their Application to Anonymous Credentials
Public key cryptography structure-preserving signatures attribute-based anonymous credentials
2016/1/7
Structure-preserving signatures are a quite recent but important building block for many
cryptographic protocols. In this paper, we introduce a new type of structure-preserving signatures, which
all...