@techreport{TR-IC-PFG-18-28,
   number = {IC-PFG-18-28},
   author = {Vitor {Falcão da Rocha} and Julio {López}},
   title = {{An Overview on Homomorphic Encryption Algorithms}},
   month = {January},
   year = {2019},
   institution = {Institute of Computing, University of Campinas},
   note = {In English, 23 pages.
    \par\selectlanguage{english}\textbf{Abstract}
       Homomorphic  encryption  is  a  cryptographic construction that
       allows  an  application to operate on ecrypted data, instead of
       the  raw data itself. The possibility of homomorphic encryption
       had  long  been  studied  due  to  the applications it enables,
       especially  the  outsourcing  of  computing  on sensitive data,
       while  preserving  the  privacy  of  the data. Not until 2009 a
       fully homomorphic encryption scheme (FHE) was proposed by Craig
       Gentry,  though  not  practical,  this scheme paved the way for
       other schemes, both based on Gentry's ideas and others based on
       new  ideas  In  parallel,  some  applications were developed to
       operate  on  data  encrypted by those FHE schemes, proving that
       FHE  could  power  practical  applications,  in  a more privacy
       preserving  fashion.  This  paper  presents  the  concepts that
       support  modern  homomorphic  encryption schemes, together with
       the   description  of  some  FHE  schemes.  In  addition,  some 
       practical   applications  for  processing  sensitive  data  are 
       presented.
  }
}