Words and Transcendence

Is it possible to distinguish algebraic from transcendental real numbers by considering the $b$-ary expansion in some base $b\ge2$? In 1950, \'E. Borel suggested that the answer is no and that for any real irrational algebraic number $x$ and for any base $g\ge2$, the $g$-ary expansion of $x$ should satisfy some of the laws that are shared by almost all numbers. There is no explicitly known example of a triple $(g,a,x)$, where $g\ge3$ is an integer, $a$ a digit in $\{0,...,g-1\}$ and $x$ a real irrational algebraic number, for which one can claim that the digit $a$ occurs infinitely often in the $g$-ary expansion of $x$. However, some progress has been made recently, thanks mainly to clever use of Schmidt's subspace theorem. We review some of these results

An information privacy taxonomy for collaborative environments

Purpose: Information Privacy is becoming an increasingly important field of research with many new definitions and terminologies. Along similar rates of increase are the use, uptake and expansion of Collaborative Environments. There is a need for a better understanding and classification of information privacy concepts and terms. The pur-pose of this paper is to provide a taxonomy of Information Privacy in Collaborative Environments. The knowledge provided from an information privacy taxonomy can be used to formulate better information privacy policies, practices, and privacy enhancing technologies (PET?s).Approach: Through the hierarchical classification and categorization of information privacy concepts and principles an organized representation of these components has been produced. Each area was well surveyed and researched and then classified into a number of sub-categories according to their nature and relevance.Findings: A taxonomy was successfully developed with the identification of three high level dimensions of information privacy. Within each dimensional view a further three sub-classifications were proposed each with their own unique nature.Originality: This paper provides an Information Privacy taxonomy for Collaborative Environments, the first of its kind to be proposed. A number of new Information Pri-vacy terms are defined that make up the categorization and classification of Informa-tion Privacy concepts and components

Polytopic Cryptanalysis

Standard differential cryptanalysis uses statistical dependencies between the difference of two plaintexts and the difference of the respective two ciphertexts to attack a cipher. Here we introduce polytopic cryptanalysis which considers interdependencies between larger sets of texts as they traverse through the cipher. We prove that the methodology of standard differential cryptanalysis can unambiguously be extended and transferred to the polytopic case including impossible differentials. We show that impossible polytopic transitions have generic advantages over impossible differentials. To demonstrate the practical relevance of the generalization, we present new low-data attacks on round-reduced DES and AES using impossible polytopic transitions that are able to compete with existing attacks, partially outperforming these

DES i AES

Data Encryption Standard (DES) je naziv za simetrični kriptosustav šifriranja elektronskih podataka, objavljen od strane američkog instituta za standarde (NBS) 15. siječnja 1977. godine, nakon 4 godine dugog natječaja i procesa standardiziranja. Razvio ga je IBM-ov tim, na čelu s Horstom Feistelom, 1974. godine. DES primjenjuje ključ duljine 56 bitova na 64-bitne blokove podataka. Proces se odvija u nekoliko faza i uključuje 16 rundi operacija. Mnogi kriptoanalitičari su pokušali pronaći razne brze metode razbijanja DES-a. Početkom 1997. godine, zajedničkim snagama internetske populacije od 14000 korisnika računala koji su isprobavali razne šifre, jedna poruka je konačno dešifrirana otkrivanjem ključa nakon isprobavanja samo 18 od mogućih 72 kvadrilijuna mogućih ključeva. NIST je kasnije objavio da DES neće ponovno dobiti certifikat kao standard i da će prihvaćati prijedloge za njegove zamjene. Sljedeći prihvaćeni standard će biti poznat pod imenom Advanced Encryption Standard. The Advanced Encryption Standard (AES) je specifikacija za način šifriranja elektronskih podataka, objavljen od strane američkog instituta za standarde i tehnologiju (NIST) 26. studenog 2001. godine, nakon petogodišnjeg procesa natječaja i standardizacije u kojem se natjecalo 15 kandidata, od kojih je Rijndael procijenjen najboljim i odabran kao budući standard. Svaki AES šifrat se sastoji od blokova veličine 128-bitova i ključeva veličine 128, 192 i 256 bitova. AES je mnogo puta analiziran što je dovelo do upotrebe na svjetskoj razini, kao što je to bila situacija i s njegovim prethodnikom, Data Encryption Standard-om. AES je prvi javno objavljeni i u potpunosti dostupni način šifriranja podataka, odobren i od američke sigurnosne agencije NSA.The Data Encryption Standard (DES) is a specification for a symmetric-key algorithm for the encryption of electronic data adopted by the U.S. National Bureau of Standards (NBS) on January 15, 1977 after a 4 year-long contest and standardization process. It was developed by an IBM team, with Horst Feistel’s lead, around 1974. DES applies a 56-bit key to each 64-bit block of data. The process can run in several modes and involves 16 rounds or operations. Many cryptanalysts have attempted to find shortcuts for breaking the system. Early in 1997, a cooperative effort on the Internet of over 14,000 computer users trying out various keys finally deciphered the message, discovering the key after running through only 18 quadrillion of the 72 quadrillion possible keys. NIST has later indicated DES that will not be recertified as a standard and submissions for its replacement are being accepted. The next standard will be known as the Advanced Encryption Standard (AES). The Advanced Encryption Standard (AES) is a specification for the encryption of electronic data adopted by the U.S. National Institute of Standards and Technology (NIST) on November 26, 2001 after a 5-year standardization process in which fifteen competing designs were presented and evaluated before Rijndael was selected as the most suitable. Each AES cipher has a 128-bit block size, with key sizes of 128, 192 and 256 bits. The AES ciphers have been analyzed extensively and are now used worldwide, as was the case with its predecessor, the Data Encryption Standard (DES). AES is the first publicly accessible and open cipher approved by the NSA