# Project

Back to overview

## New Cryprosystems based on Algebra

 English title New Cryprosystems based on Algebra Rosenthal Joachim 132256 Project funding (Div. I-III) Institut für Mathematik Universität Zürich University of Zurich - ZH Mathematics 01.10.2010 - 31.12.2012 134'431.00
Show all

### Keywords (10)

cryptography; one-way trapdoor function; asymmetric encryption; public-key cryptosystem; discrete logarithm problem; algebraic geometry; semirings; iteration of maps; asymmetric encryption-key cryptosystem; One-way function

### Lay Summary (English)

Lay summary
Cryptography has been the object of a very fast expansion over the past years. Today more than ever, being able to safely communicate in a private way is extremely important. For example, we daily rely on the Internet for bank access and transactions for communication and we use ATMs to access our money.Cellular phones are protected by cryptographic protocols in order to ensure privacy of the communication and correct billing of the users.Cryptography is also used for the authentication of messages via digital signatures and it ensures the identity of parties doing transactions over the Internet.At this point many cryptographic protocols rely on the hardness of the integer factorization problem. It is however not clear if these protocols remain secure with ever improving hardware and algorithms. The project is concerned with the creation and the study of new one-way trapdoor functions. This would ultimately lead to the construction of new public-key cryptosystems and hence also new signature schemes and identification protocols. The research continues the research of SNF project no. 121874.
 Direct link to Lay Summary Last update: 21.02.2013

### Responsible applicant and co-applicants

Name Institute
 Rosenthal Joachim Institut für Mathematik Universität Zürich

### Employees

Name Institute
 Schipani Davide Institut für Mathematik Universität Zürich

### Publications

Publication
Schipani D., Elia M. (2012), Additive decompositions induced by multiplicative characters over finite fields, Amer. Math. Soc., Providence, RI, 579, 179-186.
Schipani D., Elia M. (2012), Gauss sums of cubic character over {$\Bbb F_{p^r},\ p$}} odd, in Bull. Pol. Acad. Sci. Math., 60(1), 1-19.
Elia M., Rosenthal J., Schipani D. (2012), Polynomial evaluation over finite fields: new algorithms and complexity bounds, in Appl. Algebra Engrg. Comm. Comput., 23(3-4), 129-141.
Baldi M., Bianchi M., Chiaraluce F., Rosenthal J., Schipani D. (2011), A variant of the McEliece cryptosystem with increased public key security., in Proceedings of the Seventh International Workshop on Coding and Cryptography (WCC) 2011.
Schipani D., Elia M. (2011), Gauss sums of the cubic character over {${\rm GF}(2^m)$}}: an elementary derivation, in Bull. Pol. Acad. Sci. Math., 59(1), 11-18.
Baldi M., Bianchi M., Chiaraluce F., Rosenthal J., Schipani D. (2011), On fuzzy syndrome hashing with {LDPC} coding, in ISABEL '11 Proceedings of the 4th International Symposium on Applied Sciences in Biomedical and Comm, ACM.
Schipani D., Elia M., Rosenthal J. (2011), On the decoding complexity of cyclic codes up to the {BCH} bound, in Proceedings of IEEE International Symposium on Information Theory (ISIT).

### Associated projects

Number Title Start Funding scheme
 121874 New Public-Key Cryptosystems based on Algebra 01.10.2008 Project funding (Div. I-III)

### Abstract

The project is a continuation of the funded project New Public-Key Cryptosystems based on Algebra, SNF Project no.121874. The project has two major goals. First we would like tocontinue our study in the construction of new oneway trapdoorfunctions. Second we would like to continue the study ofiteration of multivariate polynomial maps and their connectionsin the construction of cryptographic primitives. This is thedissertation topic of Ms Ostafe who is currently supported bygrant no. 121874.
-