Document Open Access Logo

Two-Round Perfectly Secure Message Transmission with Optimal Transmission Rate

Authors Nicolas Resch , Chen Yuan

Thumbnail PDF


  • Filesize: 0.77 MB
  • 20 pages

Document Identifiers

Author Details

Nicolas Resch
  • Informatics' Institute, University of Amsterdam, The Netherlands
Chen Yuan
  • School of Electronic Information and Electrical Engineering, Shanghai Jiao Tong University, China


CY would also like to thank Serge Fehr for introducing him to this problem.

Cite AsGet BibTex

Nicolas Resch and Chen Yuan. Two-Round Perfectly Secure Message Transmission with Optimal Transmission Rate. In 4th Conference on Information-Theoretic Cryptography (ITC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 267, pp. 1:1-1:20, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2023)


In the model of Perfectly Secure Message Transmission (PSMT), a sender Alice is connected to a receiver Bob via n parallel two-way channels, and Alice holds an 𝓁 symbol secret that she wishes to communicate to Bob. There is an unbounded adversary Eve that controls t of the channels, where n = 2t+1. Eve is able to corrupt any symbol sent through the channels she controls, and furthermore may attempt to infer Alice’s secret by observing the symbols sent through the channels she controls. The transmission is required to be (a) reliable, i.e., Bob must always be able to recover Alice’s secret, regardless of Eve’s corruptions; and (b) private, i.e., Eve may not learn anything about Alice’s secret. We focus on the two-round model, where Bob is permitted to first transmit to Alice, and then Alice responds to Bob. In this work we provide upper and lower bounds for the PSMT model when the length of the communicated secret 𝓁 is asymptotically large. Specifically, we first construct a protocol that allows Alice to communicate an 𝓁 symbol secret to Bob by transmitting at most 2(1+o_{𝓁→∞}(1))n𝓁 symbols. Under a reasonable assumption (which is satisfied by all known efficient two-round PSMT protocols), we complement this with a lower bound showing that 2n𝓁 symbols are necessary for Alice to privately and reliably communicate her secret. This provides strong evidence that our construction is optimal (even up to the leading constant).

Subject Classification

ACM Subject Classification
  • Security and privacy → Mathematical foundations of cryptography
  • Secure transmission
  • Information theoretical secure
  • MDS codes


  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    PDF Downloads


  1. Saurabh Agarwal, Ronald Cramer, and Robbert de Haan. Asymptotically optimal two-round perfectly secure message transmission. In Cynthia Dwork, editor, Advances in Cryptology - CRYPTO 2006, 26th Annual International Cryptology Conference, Santa Barbara, California, USA, August 20-24, 2006, Proceedings, volume 4117 of Lecture Notes in Computer Science, pages 394-408. Springer, 2006. URL:
  2. Danny Dolev, Cynthia Dwork, Orli Waarts, and Moti Yung. Perfectly secure message transmission. J. ACM, 40(1):17-47, 1993. URL:
  3. Matthew Franklin and Rebecca N Wright. Secure communication in minimal connectivity models. Journal of Cryptology, 13(1):9-30, 2000. Google Scholar
  4. Kaoru Kurosawa and Kazuhiro Suzuki. Truly efficient 2-round perfectly secure message transmission scheme. In Annual International Conference on the Theory and Applications of Cryptographic Techniques, pages 324-340. Springer, 2008. Google Scholar
  5. Hasan Md. Sayeed and Hosame Abu-Amara. Efficient perfectly secure message transmission in synchronous networks. Inf. Comput., 126(1):53-61, 1996. URL:
  6. Gabriele Spini and Gilles Zémor. Perfectly secure message transmission in two rounds. In Theory of Cryptography Conference, pages 286-304. Springer, 2016. Google Scholar
  7. K. Srinathan, Arvind Narayanan, and C. Pandu Rangan. Optimal perfectly secure message transmission. In Matthew K. Franklin, editor, Advances in Cryptology - CRYPTO 2004, 24th Annual International CryptologyConference, Santa Barbara, California, USA, August 15-19, 2004, Proceedings, volume 3152 of Lecture Notes in Computer Science, pages 545-561. Springer, 2004. URL:
  8. Lloyd R Welch and Elwyn R Berlekamp. Error correction for algebraic block codes, December 1986. US Patent 4,633,470. Google Scholar
Questions / Remarks / Feedback

Feedback for Dagstuhl Publishing

Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail