# American Institute of Mathematical Sciences

doi: 10.3934/amc.2020021

## Dual-Ouroboros: An improvement of the McNie scheme

 1 University of Limoges, Limoges, France 2 Sogang University, Seoul, South Korea 3 Chosun University, Gwangju, South Korea

* Corresponding author: Jon-Lark Kim

Received  June 2018 Revised  November 2018 Published  September 2019

Fund Project: The work of Jon-Lark Kim was supported by Samsung Science and Technology Foundation under Project Number SSTF-BA1602-01

McNie [8] is a code-based public key encryption scheme submitted to the NIST Post-Quantum Cryptography standardization [10] as a candidate. In this paper, we present Dual-Ouroboros, an improvement of McNie, which can be seen as a dual version of the Ouroboros-R protocol [1], another candidate to the NIST competition. This new improved protocol permits, first, to avoid an attack proposed by Gaborit [7] and second permits to benefit from a reduction security to a standard problem (as the original Ouroboros protocol).

Citation: Philippe Gaborit, Lucky Galvez, Adrien Hauteville, Jon-Lark Kim, Myeong Jae Kim, Young-Sik Kim. Dual-Ouroboros: An improvement of the McNie scheme. Advances in Mathematics of Communications, doi: 10.3934/amc.2020021
##### References:

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##### References:
Suggested parameters and key sizes in bytes for Dual-Ouroboros
 $n$ $k$ $l$ $q$ $m$ $d$ $r$ Failure PK SK CT Security 94 47 47 2 67 5 7 -28 788 1181 1181 128 142 71 71 2 91 5 6 -54 1616 2423 2423 128 194 97 97 2 91 5 7 -78 2207 3311 3311 128 106 53 53 2 101 5 8 -30 1339 2008 2008 192 158 79 79 2 101 5 8 -58 1995 2993 2993 192 194 97 97 2 101 5 8 -76 2450 3674 3674 192 134 67 67 2 107 6 9 -30 1793 2689 2689 256 158 79 79 2 131 6 8 -56 2588 3881 3881 256 202 101 101 2 131 6 8 -78 3308 4962 4962 256
 $n$ $k$ $l$ $q$ $m$ $d$ $r$ Failure PK SK CT Security 94 47 47 2 67 5 7 -28 788 1181 1181 128 142 71 71 2 91 5 6 -54 1616 2423 2423 128 194 97 97 2 91 5 7 -78 2207 3311 3311 128 106 53 53 2 101 5 8 -30 1339 2008 2008 192 158 79 79 2 101 5 8 -58 1995 2993 2993 192 194 97 97 2 101 5 8 -76 2450 3674 3674 192 134 67 67 2 107 6 9 -30 1793 2689 2689 256 158 79 79 2 131 6 8 -56 2588 3881 3881 256 202 101 101 2 131 6 8 -78 3308 4962 4962 256
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