Paper 2015/1192

A Guide to Fully Homomorphic Encryption

Frederik Armknecht, Colin Boyd, Christopher Carr, Kristian Gjøsteen, Angela Jäschke, Christian A. Reuter, and Martin Strand


Fully homomorphic encryption (FHE) has been dubbed the holy grail of cryptography, an elusive goal which could solve the IT world's problems of security and trust. Research in the area exploded after 2009 when Craig Gentry showed that FHE can be realised in principle. Since that time considerable progress has been made in finding more practical and more efficient solutions. Whilst research quickly developed, terminology and concepts became diverse and confusing so that today it can be difficult to understand what the achievements of different works actually are. The purpose of this paper is to address three fundamental questions: What is FHE? What can FHE be used for? What is the state of FHE today? As well as surveying the field, we clarify different terminology in use and prove connections between different FHE notions.

Note: Updated the acknowledgements.

Available format(s)
Public-key cryptography
Publication info
Preprint. MINOR revision.
Fully Homomorphic Encryption
Contact author(s)
reuter @ uni-mannheim de
2016-09-14: last of 3 revisions
2015-12-16: received
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Creative Commons Attribution


      author = {Frederik Armknecht and Colin Boyd and Christopher Carr and Kristian Gjøsteen and Angela Jäschke and Christian A.  Reuter and Martin Strand},
      title = {A Guide to Fully Homomorphic Encryption},
      howpublished = {Cryptology ePrint Archive, Paper 2015/1192},
      year = {2015},
      note = {\url{}},
      url = {}
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