Kriptografske Boolove funkcije in teorija grafov / Cryptographic Boolean Functions and Graph Theory
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Naziv Tittle |
Kriptografske Boolove funkcije in teorija grafov / Cryptographic Boolean Functions and Graph Theory |
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Akronim Acronim |
BI-US/15-16-028 |
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Opis Description |
(SI) Število internetnih aplikacij se neprestano povečuje, s tem pa je tudi vedno večja potreba po elektronskih transakcijah. Preden pa se uporabi določen šifrirni algoritem, je treba preučiti uporabljeno matematiko, da se ugotovi, kako težko je zlomiti ta sistem. Ideja v ozadju je preprosta: spremenimo ali zašifriramo sporočilo oziroma plaintext v vmesno obliko oziroma ciphertext, v katerem so vsebovani vsi podatki originalnega sporočila, vendar so zavarovani. Ta diskusija vodi k vprašanjema:
1) Kakšne druge invariante Cayleyjevih grafov bi nam pomagale pri razločevanju med raznimi (afnimi) družinami ukrivljenih funkcij (oziroma kar Boolovih funkcij na splošno)?
2) Kaj bi poleg nelinearnosti še vplivalo na to, da je Clayleyjeveggraf, asociiran Boolovi funkciji, krepko regularen? (EN) The number of internet applications is constantly increasing, and so is the need for electronic transactions. However, before a particular encryption algorithm is used, the mathematics involved must be studied to determine how difficult it is to break that system. The idea behind it is simple: we transform or encrypt a message, or plaintext, into an intermediate form, or ciphertext, which contains all the data of the original message but is secured. This discussion leads to the questions: 1) What other invariants of Cayley graphs would help us to distinguish between different (affine) families of curved functions (or just Boolean functions in general)? 2) What else, besides nonlinearity, would make a Clayley graph associated to a Boolean function boldly regular? |
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Trajanje Duration |
01/03/2015 - 31/12/2016 |
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Vodja projekta Project Leader |
Enes Pasalic |
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Sodelujoče organizacije Participating organizations |
Department of Applied Mathematics, Naval Postgraduate School |
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Oddelek Department |
Oddelek za matematiko IAM |