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In this paper we study a problem which emerged during an attempt to apply a differential cryptanalysis method to the <> algorithm. We obtained a general formula of distribution in the differenc...
We propose new algorithms for constructing multidimensional differential addition chains and for performing multidimensional scalar point multiplication based on these chains. Our algorithms work in a...
This paper presents parallel scalar multiplication techniques for elliptic curve cryptography using q-based addition-subtraction k-chain which can also effectively resist side-channel attack. Many tec...
Addition chain calculations play a critical role in determining the efficiency of cryptosystems based on isogenies on elliptic curves. However, finding a minimal length addition chain is not easy; a g...
The operation of modular addition modulo a power of two is one of the most applied operations in symmetric cryptography. For example, modular addition is used in RC6, MARS and Twofish block ciphers...
Modular addition modulo a power of two, is one of the most applicable operators in symmetric cryptography; therefore, investigating cryptographic properties of this operator has a significant role ...
Linear approximations of modular addition modulo a power of two was studied by Wallen in 2003. He presented an efficient algorithm for computing linear probabilities of modular addition. In 2013 Scult...
A common countermeasure to thwart side-channel analysis attacks is algorithmic masking. For this, algorithms that mix Boolean and arithmetic operations need to either apply two different masking sc...
An elliptic curve addition law is said to be complete if it correctly computes the sum of any two points in the elliptic curve group. One of the main reasons for the increased popularity of Edwards ...
The aim of this paper is to present a new way of computing short addition-subtraction chains using the generalized continued fractions where subtraction is allowed. We will recover the most used ways ...
In this note, we give a simple proof of the combinatorial conjecture proposed by Tang, Carlet and Tang, based on which they constructed two classes of Boolean functions with many good cryptographic pr...
In this paper, we give a generalization of Lucas addition chains, where subtraction is allowed. We call them ''Lucas addition-subtraction chain''.
In this paper, we give a generalization of Lucas addition chains, where subtraction is allowed. We call them ''Lucas addition-subtraction chain''. We also show that this new method gives minimal addit...
In this paper we study the number of carries occurring while performing an addition modulo $2^k-1$. For a fixed modular integer $t$, it is natural to expect the number of carries occurring when adding...
In this paper we study the number of carries occurring while performing an addition modulo $2^k-1$. For a fixed modular integer $t$, it is natural to expect the number of carries occurring when adding...

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