Pseudo-probabilistic block ciphers and their randomization

  • Moldovyan Nikolay Andreevich
  • Moldovyan Alexander Andreevich
  • Tam Nguyen Duc
  • Hai Nguyen Nam
  • Manh Cong Tran
  • Minh Nguyen HieuEmail author
Original Research


There is considered implementation of the plan-ahead share-key deniable encryption algorithms that produce the cryptogram that satisfy criterion of the computational indistinguishability from probabilistic encryption of the fake message. This paper introduces a general design of the pseudo-probabilistic block ciphers. The proposed method includes encryption of the secret message block and the fake message block followed by a transformation procedure mapping the pair of intermediate ciphertext blocks into a single block of the output ciphertext. The transformation procedure is implemented in the following two variants: (1) simultaneous encryption of the intermediate ciphertext blocks and (2) solving the system of two linear congruencies. The second variant provides natural possibility to construct pseudo-probabilistic block ciphers in which recovering fake or secret message is performed using the same single decryption algorithm. To provide higher security there are proposed randomized pseudo-probabilistic ciphers. There are also considered designs with different size of the input data blocks corresponding to fake and secret messages.


Block ciphers Plan-ahead deniable encryption Shared-key deniable encryption Pseudo-probabilistic cipher Randomization 



The reported study was funded by Russian Foundation for Basic Research (project #18-57-54002-Viet_a) and by Vietnam Academy of Science and Technology (project # QTRU01.08/18-19).


  1. Barakat TM (2014) A new sender-side public-key deniable encryption scheme with fast decryption. KSII Trans Internet Inf Syst 8(9):3231–3249. Google Scholar
  2. Canetti R, Dwork C, Naor M, Ostrovsky R (1997) Deniable encryption. In: Kaliski BS (ed) Advances in cryptology—CRYPTO ’97. Springer, Berlin, pp 90–104. Google Scholar
  3. Dürmuth M, Freeman DM (2011) Deniable encryption with negligible detection probability: an interactive construction. In: Paterson KG (ed) Advances in cryptology—EUROCRYPT 2011. Springer, Berlin, pp 610–626. CrossRefGoogle Scholar
  4. Ishai Y, Kushilevitz E, Ostrovsky R, Prabhakaran M, Sahai A (2011) Efficient non-interactive secure computation. In: Paterson KG (ed) Advances in cryptology—EUROCRYPT 2011. Springer, Berlin, pp 406–425. CrossRefGoogle Scholar
  5. Meng B (2009) A secure internet voting protocol based on non-interactive deniable authentication protocol and proof protocol that two ciphertexts are encryption of the same plaintext. J Netw 4(5):370–377. Google Scholar
  6. Moldovyan NA, Moldovyan AA (2006) Innovative cryptography (programming series). Charles River Media Inc, RocklandGoogle Scholar
  7. Moldovyan NA, Moldovyan AA (2007) Data-driven block ciphers for fast telecommunication systems, 1st edn. Auerbach Publications, Boca RatonCrossRefzbMATHGoogle Scholar
  8. Moldovyan AA, Moldovyan DN, Shcherbacov VA (2015) Stream deniable-encryption algorithm satisfying criterion of the computational indistinguishability from probabilistic ciphering. Workshop Found Inf I:318–330MathSciNetGoogle Scholar
  9. Moldovyan NA, Moldovyan AA, Moldovyan DN, Shcherbacov VA (2016) Stream deniable–encryption algorithms. Comput Sci J Moldova 24(1(70)):68–82MathSciNetzbMATHGoogle Scholar
  10. Moldovyan NA, Shcherbacov VA, Eremeev MA (2017) Deniable encryption protocols based on commutative ciphers. Quasigroups Relat Syst:95–108.Google Scholar
  11. O’Neill A, Peikert C, Waters B (2011) Bi-deniable public-key encryption. In: Rogaway P (ed) Advances in cryptology—CRYPTO 2011. Springer, Berlin, pp 525–542. CrossRefGoogle Scholar
  12. Pieprzyk J, Hardjono T, Seberry J (2002) Fundamentals of computer security. Springer, Berlin. zbMATHGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.St. Petersburg Institute for Informatics and AutomationRussian Academy of SciencesSt. PetersburgRussia
  2. 2.ITMO UniversitySt. PetersburgRussia
  3. 3.Academy of Cryptography TechniquesHanoiVietnam
  4. 4.Le Quy Don Technical UniversityHanoiVietnam

Personalised recommendations