The present disclosure discloses a new coding scheme, which is constructed by superimposing together a pair of basic codes in a twisted manner. A SCL decoding algorithm is proposed for the TPST codes, which may be early terminated by a preset threshold on the empirical divergence functions (EDF) to trade off performance with decoding complexity. The SCL decoding of TPST is based on the efficient list decoding of the basic codes, where the correct candidate codeword in the decoding list is distinguished by employing a typicality-based statistical learning aided decoding algorithm. Lower bounds for the two layers of TPST are derived, which may be used to predict the decoding performance and to show the near-ML performance of the proposed SCL decoding algorithm. The construction of TPST codes may be generalised by allowing different basic codes for the two layers.

The present disclosure discloses a new coding scheme, which is constructed by superimposing together a pair of basic codes in a twisted manner. A SCL decoding algorithm is proposed for the TPST codes, which may be early terminated by a preset threshold on the empirical divergence functions (EDF) to trade off performance with decoding complexity. The SCL decoding of TPST is based on the efficient list decoding of the basic codes, where the correct candidate codeword in the decoding list is distinguished by employing a typicality-based statistical learning aided decoding algorithm. Lower bounds for the two layers of TPST are derived, which may be used to predict the decoding performance and to show the near-ML performance of the proposed SCL decoding algorithm. The construction of TPST codes may be generalised by allowing different basic codes for the two layers.

Systems and methods are described for low power error correction coding (ECC) for embedded universal flash storage (eUFS) are described. The systems and methods may include identifying a first element of an algebraic field; generating a plurality of lookup tables for multiplying the first element; multiplying the first element by a plurality of additional elements of the algebraic field, wherein the multiplication for each of the additional elements is performed using an element from each of the lookup tables; and encoding information according to an ECC scheme based on the multiplication.

Systems and methods are described for low power error correction coding (ECC) for embedded universal flash storage (eUFS) are described. The systems and methods may include identifying a first element of an algebraic field; generating a plurality of lookup tables for multiplying the first element; multiplying the first element by a plurality of additional elements of the algebraic field, wherein the multiplication for each of the additional elements is performed using an element from each of the lookup tables; and encoding information according to an ECC scheme based on the multiplication.

This invention discloses a method and system for generating a private key and a corresponding public key. These keys can be used for encrypting a message into a ciphertext for transmission through an insecure communication channel, and for decrypting said ciphertext into a clear plaintext. The goal of the present invention is to provide encryption and decryption methods of the McEliece type which are capable of improving the security level of a post-quantum cryptosystem. In one embodiment, this object is achieved by three methods: a method for creating a public key from a private linear code generator matrix, a method for encrypting a message into a ciphertext and a method for decrypting the ciphertext into a plaintext. The key generation and encryption methods of the present invention comprises the following steps: selecting an [n, k] linear code generator matrix G.sub.s=[g.sub.0, . . . , g.sub.n] over GF(q) as the private key, where k, r, n and q are positive integers and where g.sub.0, . . . , g.sub.n1 are length k column vectors; selecting kr random matrices C.sub.0, . . . , C.sub.n1; selecting a kk non-singular matrix S; selecting an n(r+1)n(r+1) matrix A; selecting an n(r+1)n(r+1) permutation matrix P; and setting the public key as G=S[g.sub.0, C.sub.0, . . . , g.sub.n1, C.sub.n1]AP. receiving a public key G, which is a kn(r+1) matrix over a finite field GF(q); generating an error vector e having elements in GF(q) and having a predetermined weight t; and encrypting a message vector m to a ciphertext vector y=mG+e.
The main difference between the proposed cryptosystem and known variants of the McEliece cryptosystem consists in the way the private generator matrix is disguised into the public one by inserting and mixing random columns within the private generator matrix.