Abstract
In this paper, we present a new variant of the Niederreiter Public Key Encryption (PKE) scheme which is resistant against recent attacks. The security is based on the hardness of the Rank Syndrome Decoding (RSD) problem and it presents a (u|u + υ)-construction code using two different types of codes: Ideal Low Rank Parity Check (ILRPC) codes and λ-Gabidulin codes. The proposed encryption scheme benefits are a larger minimum distance, a new efficient decoding algorithm and a smaller ciphertext and public key size compared to the Loidreau’s variants and to its IND-CCA secure version.
Highlights
In 1978, McEliece introduced the first public key encryption (PKE) scheme based on coding theory using as a private key a generator matrix of a binary Goppa code [26]
We propose a new variant of the Niederreiter-PKE scheme based on the Rank Syndrome Decoding (RSD) problem
We present a new family of (u|u + v) codes constructed by two different types: Ideal Low Rank Parity Check (ILRPC) codes and λ-Gabidulin codes
Summary
In 1978, McEliece introduced the first public key encryption (PKE) scheme based on coding theory using as a private key a generator matrix of a binary Goppa code [26]. Niederreiter proposed another PKE scheme using linear codes wherein the private key is the parity-check matrix of the code instead of its generator matrix [27]. Both of these schemes are based on equivalent N P-complete problems [7] and they have an equivalent security levels for the same set of parameters. Gaborit et al proposed in [9] a PKE scheme based on Low Rank Parity Check (LRPC) codes They proved that their scheme is resistant to message attack and structural attacks on the key. Al Shehhi et al was proposed in [2] an IND-CCA secure version of Loidreau’s PKE scheme with an overhead of 23% in the computational cost for encryption algorithm
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