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Since Gentry’s breakthrough result was introduced in the year 2009, the homomorphic encryption has become a very popular topic. The main contribution of Gentry’s thesis [5] was, that it has proven, that it actually is possible to design a fully homomorphic encryption scheme. However ground-breaking Gentry’s result was, the designs, that employ the bootstrapping technique suffer from terrible performance both in key generation and homomorphic evaluation of circuits. Some authors tried to design schemes, that could evaluate homomorphic circuits of arbitrarily many inputs without need of bootstrapping. This paper introduces the notion of symmetric homomorphic encryption, and analyses the security of four such proposals, published in three different papers ([2], [7], [10]). Our result is a known plaintext key-recovery attack on every one of these schemes.

  • [1]

    Brakerski, Zvika and Vaikuntanathan, Vinod, Fully homomorphic encryption from ring-lwe and security for key dependent messages, in: Proceedings of the31st annual conference on Advances in cryptology, CRYPTO′11, pages 505524, Berlin, Heidelberg, 2011. Springer-Verlag.

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  • [2]

    Chan, Aldar C-F. , Symmetric-key homomorphic encryption for encrypted data processing, in: Proceedings of the 2009 IEEE international conference on Communications, ICC′09, pages 774778, Piscataway, NJ, USA, 2009. IEEE Press.

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  • [3]

    Coppersmith, Don , Small solutions to polynomial equations, and low exponent rsa vulnerabilities, J. Cryptology, 10(4) (1997), 233260.

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  • [4]

    Fan, Junfeng and Vercauteren, Frederik, Somewhat practical fully homomorphic encryption, IACR Cryptology ePrint Archive, 2012 (2012), 144.

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  • [5]

    Gentry, Craig , A fully homomorphic encryption scheme, PhD thesis, Stanford, CA, USA, 2009. AAI3382729.

  • [6]

    Gentry, Craig and Halevi, Shai, Implementing gentry’s fully-homomorphic encryption scheme, Cryptology ePrint Archive, Report 2010/520, 2010. http://www.eprint.iacr.org/.

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  • [7]

    Kipnis, Aviad and Hibshoosh, Eliphaz, Efficient methods for practical fully homomorphic symmetric-key encrypton, randomization and verification, IACRCryptology ePrint Archive, 2012 (2012), 637.

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  • [8]

    Rivest, R. L. , Adleman, L. and Dertouzos, M. L., On data banks and privacy homomorphisms, Foundations of Secure Computation, Academia Press, pages 169179, 1978.

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  • [9]

    van Dijk, Marten, Gentry, Craig, Halevi, Shai and Vaikuntanathan, Vinod, Fully homomorphic encryption over the integers, in: EUROCRYPT, pages 2443, 2010.

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  • [10]

    Xiao, Liangliang , Bastani, Osbert and Yen, I-Ling, An efficient homomorphic encryption protocol for multi-user systems, IACR Cryptology ePrint Archive, 2012 (2012), 193. Informal publication.

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Editors in Chief

Gábor SIMONYI (Rényi Institute of Mathematics)
András STIPSICZ (Rényi Institute of Mathematics)
Géza TÓTH (Rényi Institute of Mathematics) 

Managing Editor

Gábor SÁGI (Rényi Institute of Mathematics)

Editorial Board

  • Imre BÁRÁNY (Rényi Institute of Mathematics)
  • Károly BÖRÖCZKY (Rényi Institute of Mathematics and Central European University)
  • Péter CSIKVÁRI (ELTE, Budapest) 
  • Joshua GREENE (Boston College)
  • Penny HAXELL (University of Waterloo)
  • Andreas HOLMSEN (Korea Advanced Institute of Science and Technology)
  • Ron HOLZMAN (Technion, Haifa)
  • Satoru IWATA (University of Tokyo)
  • Tibor JORDÁN (ELTE, Budapest)
  • Roy MESHULAM (Technion, Haifa)
  • Frédéric MEUNIER (École des Ponts ParisTech)
  • Márton NASZÓDI (ELTE, Budapest)
  • Eran NEVO (Hebrew University of Jerusalem)
  • János PACH (Rényi Institute of Mathematics)
  • Péter Pál PACH (BME, Budapest)
  • Andrew SUK (University of California, San Diego)
  • Zoltán SZABÓ (Princeton University)
  • Martin TANCER (Charles University, Prague)
  • Gábor TARDOS (Rényi Institute of Mathematics)
  • Paul WOLLAN (University of Rome "La Sapienza")

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2020  
Total Cites 536
WoS
Journal
Impact Factor
0,855
Rank by Mathematics 189/330 (Q3)
Impact Factor  
Impact Factor 0,826
without
Journal Self Cites
5 Year 1,703
Impact Factor
Journal  0,68
Citation Indicator  
Rank by Journal  Mathematics 230/470 (Q2)
Citation Indicator   
Citable 32
Items
Total 32
Articles
Total 0
Reviews
Scimago 24
H-index
Scimago 0,307
Journal Rank
Scimago Mathematics (miscellaneous) Q3
Quartile Score  
Scopus 139/130=1,1
Scite Score  
Scopus General Mathematics 204/378 (Q3)
Scite Score Rank  
Scopus 1,069
SNIP  
Days from  85
submission  
to acceptance  
Days from  123
acceptance  
to publication  
Acceptance 16%
Rate

2019  
Total Cites
WoS
463
Impact Factor 0,468
Impact Factor
without
Journal Self Cites
0,468
5 Year
Impact Factor
0,413
Immediacy
Index
0,135
Citable
Items
37
Total
Articles
37
Total
Reviews
0
Cited
Half-Life
21,4
Citing
Half-Life
15,5
Eigenfactor
Score
0,00039
Article Influence
Score
0,196
% Articles
in
Citable Items
100,00
Normalized
Eigenfactor
0,04841
Average
IF
Percentile
13,117
Scimago
H-index
23
Scimago
Journal Rank
0,234
Scopus
Scite Score
76/104=0,7
Scopus
Scite Score Rank
General Mathematics 247/368 (Q3)
Scopus
SNIP
0,671
Acceptance
Rate
14%

 

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Studia Scientiarum Mathematicarum Hungarica
Language English
French
German
Size B5
Year of
Foundation
1966
Volumes
per Year
1
Issues
per Year
4
Founder Magyar Tudományos Akadémia  
Founder's
Address
H-1051 Budapest, Hungary, Széchenyi István tér 9.
Publisher Akadémiai Kiadó
Publisher's
Address
H-1117 Budapest, Hungary 1516 Budapest, PO Box 245.
Responsible
Publisher
Chief Executive Officer, Akadémiai Kiadó
ISSN 0081-6906 (Print)
ISSN 1588-2896 (Online)