US 12,483,405 B2
Method and system for error correction coding based on generalized concatenated codes with restricted error values for code-based cryptography
Juergen Freudenberger, Radolfzell (DE); Johann-Philipp Thiers, Constance (DE); and Jens Spinner, Constance (DE)
Assigned to HYPERSTONE GmbH, (DE)
Filed by HYPERSTONE GMBH, Constance (DE)
Filed on Oct. 27, 2022, as Appl. No. 17/975,360.
Claims priority of application No. 102021128031.1 (DE), filed on Oct. 27, 2021.
Prior Publication US 2023/0171102 A1, Jun. 1, 2023
Int. Cl. H04L 9/30 (2006.01)
CPC H04L 9/304 (2013.01) 21 Claims
OG exemplary drawing
 
1. An encoding method for error correction encoding of information to be carried by a channel to be stored in a memory device, the encoding method comprising:
providing a coding system; and
using the coding system to subject the information to error correction encoding to obtain encoded information to be stored in the memory device;
wherein the error correction encoding comprises:
encoding the information according to a McEliece cryptosystem or according to a Niederreiter cryptosystem, in each case using an error vector containing at most t E N non-zero error values; and
a combination of:
a permutation operation,
a scrambling operation; and
a coding operation to improve error correction capabilities that includes a generalized concatenated code (GCC) having an error correction capability t up to which it can correct all possible error patterns and the GCC comprising:
multiple outer codes A(1) with different dimensions n1 and 1=0, . . . ,N, with N ∈ custom character and n1 ∈ custom character; and
an inner code B, the inner code B being one of an error correction code over a Gaussian integer field, custom characterp,G, an error correction code over an Eisenstein integer field, custom characterp,E or a q-ary BCH error correction code over an integer field, custom characterq, where p is a prime number with p>2 in the case of the error correction codes over Gaussian integers or Eisenstein integers, and with q=pm, with m>0 being an integer, in the case of the q-ary BCH error correction code; and
wherein the alphabet used for generating the error vector in the McEliece cryptosystem or the Niederreiter cryptosystem, respectively, is selected such that each element of the alphabet is selected from a predetermined true subset of the finite fields custom characterp,G, custom characterp,E or custom characterq over which the GCC is defined.