We prove new bounds for sums of multiplicative characters over set with small doubling and applying this result we break the square--root barrier in a problem Balog concerning products differences field prime order.

We introduce the study of Conditional symmetry breaking in constraint programming. This arises in a sub-problem of a constraint satisfaction problem, where the sub-problem satisfies some condition under which additional symetries hold. Conditional symmetry can cause redundancy in a systematic search for solutions. Breaking this symmetry is an important part of solving a constraint satisfaction ...

Hydroxyapatite is a biocompatible ceramic and reinforcement for bone implantations. SEVA/HAP composite content HAP filler with difference particle sizes were designed. Mechanical tests like tensile modulus, UTS, strain at break and biodegradation were investigated. Results illustrated much increase tensile modulus of composites content HAP nano powders ratio to micro powders. Also UTS analysis ...

A number of different satisfaction and optimisation combinatorial problems have recently been approached with constraint programming over the domain of finite sets, for increased declarativity and efficiency. Such problems where one tries to find sets of values that satisfy some conditions often present much symmetry on variables and values. In particular, the social golfers problem encompasses...

Guess-and-determine attack is one of the general attacks on stream ciphers. It is a common cryptanalysis tool for evaluating security of stream ciphers. The effectiveness of this attack is based on the number of unknown bits which will be guessed by the attacker to break the cryptosystem. In this work, we present a relation between the minimum numbers of the guessed bits and uniquely restricted...

Multilinear map is a novel primitive which has many cryptographic applications, and GGH map is a major candidate of K-linear maps for K > 2. GGH map has two classes of applications, which are respectively applications with public tools of encoding and with hidden tools of encoding. In this paper we show that applications of GGH map with public tools of encoding are not secure, and that one appl...