In standardizing a new mode of operation the first two goals are security and efficiency. Security should be demonstrated in the reduction-based provable-security paradigm: the belief that AES (say) is a good PRP should be enough to conclude that some MAC based on it is secure. This has become the generally-accepted way of demonstrating security. One might even say that a MAC design that fails ...

These are lecture notes of a 20-hour course at the International Summer School Mathematical Methods and Technologies in Com-Loosely speaking, a T-function is a map of n-bit words into n-bit words such that each i-th bit of image depends only on low-order bits 0,. .. , i of the pre-image. For example, all arithmetic operations (addition , multiplication) are T-functions, all bitwise logical oper...

We define an operation called transposition on words of fixed length. This operation arises naturally when the letters of a word are considered as entries of a matrix. Words that are invariant with respect to transposition are of special interest. It turns out that transposition invariant words have a simple interpretation by means of elementary group theory. This leads us to investigate some p...

Pseudomonomials and ideals generated by pseudomonomials (pseudomonomial ideals) are a central object of study in the theory of neural rings and neural codes. In the setting of a polynomial ring, we define the polarization operation ρ sending pseudomonomials to squarefree monomials and a further polarization operation P sending pseudomonomial ideals to squarefree monomial ideals. We show for a p...

In the [16] has been proven that the multiplicative group Z/pZ∗ is a cyclic group. Likewise, finite subgroup of the multiplicative group of a field is a cyclic group. However, finite subgroup of the multiplicative group of a field being a cyclic group has not yet been proven. Therefore, it is of importance to prove that finite subgroup of the multiplicative group of a field is a cyclic group. M...

We prove that the property of admitting no cosmetic crossing changes is preserved under the operation of inserting full twists in the strings of closed braids and the operation of forming certain satellites of winding number zero. As a consequences of the main results, we prove the nugatory crossing conjecture for twisted fibered braids, for closed 3-braids and for Whitehead doubles of prime no...

We present influence games, a class of non-cooperative games that we designed to model behavior resulting from influence among individual entities in large, networked populations such as social networks. While inspired by threshold models in sociology, our model is fundamentally different from models based on contagion or diffusion processes and concentrates on significant strategic aspects of ...

The semi-direct product of arbitrary two monoids and a presentation for this product have received considerable attention, see for instance [12], [14] and [15]. In [15], Wang defined a trivialiser set of the Squier complex associated with this presentation. In this paper, as a main result, we discuss necessary and sufficient conditions for the standard presentation of the semi-direct product of...

In this paper, we present the results of computing the Tate pairing using a supersingular elliptic curve defined over a prime field. The aim of this work is to demonstrate the feasibility of the primitives of identity based cryptosystem for application in embedded processors such as a smartcard. The most computationally intensive operation in an Identity Based Protocol is the calculation of a p...

In the implementation of many public key schemes, there is a need to perform modular arithmetic. Typically this consists of addition, subtraction, multiplication and (occasionally) division with respect to a prime modulus. To resist certain side-channel attacks it helps if implementations are “constant time”. As the calculations proceed there is potentially a need to reduce the result of an ope...