Monoidal Encryption over \((\mathbb {F}_2,\cdot )\)

  • Mugurel Barcau
  • Vicenţiu PaşolEmail author
  • Cezar Pleşca
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11359)


In this paper we study monoid homomorphic encryption schemes over \((\mathbb {F}_2,\cdot )\). Such encryption schemes occur naturally by forgetting the addition operation in a Ring Homomorphic Encryption scheme over \(\mathbb {F}_2\) (if it exists). We study the structure of such schemes and analyze their security against quantum adversaries. We also present the only two monoid homomorphic encryption schemes over \((\mathbb {F}_2,\cdot )\) that exist in the literature and we raise the question of the existence of other such schemes. For one of the two schemes we present experimental results that show its performance and efficiency.


Homomorphic encryption scheme Quantum security Monoid 



We are very grateful to Mihai Togan for his comments and suggestions. This research was partially supported by the Romanian National Authority for Scientific Research (CNCS-UEFISCDI) EUREKA 62 / 2017 under the project PN-III-P3-3.5-EUK-2016-0038.


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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Mugurel Barcau
    • 1
    • 2
  • Vicenţiu Paşol
    • 1
    • 2
    Email author
  • Cezar Pleşca
    • 1
    • 3
  1. 1.certSIGN - Research and DevelopmentBucharestRomania
  2. 2.Institute of Mathematics “Simion Stoilow” of the Romanian AcademyBucharestRomania
  3. 3.Military Technical AcademyBucharestRomania

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