Ideals over a non-commutative ring and their application in cryptology
EM Gabidulin, AV Paramonov, OV Tretjakov - Advances in Cryptology …, 1991 - Springer
A new modification of the McEliece public-key cryptosystem is proposed that employs the so-called
maximum-rank-distance (MRD) codes in place of Goppa codes and that hides the …
maximum-rank-distance (MRD) codes in place of Goppa codes and that hides the …
Reducible rank codes and their applications to cryptography
EM Gabidulin, AV Ourivski, B Honary… - IEEE Transactions on …, 2003 - ieeexplore.ieee.org
We present a new family of so-called reducible rank codes which are a generalization of
rank product codes . This family includes maximal rank distance (MRD) codes for lengths n>N …
rank product codes . This family includes maximal rank distance (MRD) codes for lengths n>N …
Modeling toroidal networks with the Gaussian integers
…, E Stafford, M Moreto, EM Gabidulin - IEEE Transactions …, 2008 - ieeexplore.ieee.org
In this paper we consider a broad family of toroidal networks, denoted as Gaussian networks,
which include many previously proposed and used topologies. We will define such …
which include many previously proposed and used topologies. We will define such …
A fast matrix decoding algorithm for rank-error-correcting codes
EM Gabidulin - Workshop on Algebraic Coding, 1991 - Springer
The so-called term-rank and rank metrics and appropriate codes were introduced and
investigated in [1 –7]. These metrics and codes can be used for correcting array errors in a set of …
investigated in [1 –7]. These metrics and codes can be used for correcting array errors in a set of …
Error and erasure correcting algorithms for rank codes
EM Gabidulin, NI Pilipchuk - Designs, codes and Cryptography, 2008 - Springer
In this paper, transmitted signals are considered as square matrices of the Maximum rank
distance (MRD) (n, k, d)-codes. A new composed decoding algorithm is proposed to correct …
distance (MRD) (n, k, d)-codes. A new composed decoding algorithm is proposed to correct …
Attacks and counter-attacks on the GPT public key cryptosystem
EM Gabidulin - Designs, Codes and Cryptography, 2008 - Springer
The public key cryptosystem based on rank error correcting codes (the GPT cryptosystem)
was proposed in 1991. Several attacks against this system were published, including Gibson’…
was proposed in 1991. Several attacks against this system were published, including Gibson’…
Linear codes with covering radius 2 and other new covering codes
EM Gabidulin, AA Davydov… - IEEE Transactions on …, 1991 - ieeexplore.ieee.org
Infinite families of linear binary codes with covering radius R=2 and minimum distance d=3
and d=4 are given. Using the constructed codes with d=3, R=2, families of covering codes …
and d=4 are given. Using the constructed codes with d=3, R=2, families of covering codes …
Codes for network coding
EM Gabidulin, M Bossert - 2008 IEEE International Symposium …, 2008 - ieeexplore.ieee.org
… Proof: Represent a m-dimensional subspace by means of a full rank m × 2m basis matrix
of the form [CD], where C and D are square matrices of size m. Choose a non degenerated …
of the form [CD], where C and D are square matrices of size m. Choose a non degenerated …
On improving security of GPT cryptosystems
EM Gabidulin, H Rashwan… - 2009 IEEE International …, 2009 - ieeexplore.ieee.org
The public key cryptosystem based on rank error correcting codes (the GPT cryptosystem)
was proposed in 1991. Use of rank codes in cryptographic applications is advantageous since …
was proposed in 1991. Use of rank codes in cryptographic applications is advantageous since …
Security of the GPT cryptosystem and its applications to cryptography
H Rashwan, EM Gabidulin… - Security and …, 2011 - Wiley Online Library
The public key cryptosystem (PKC) based on rank error correcting codes (the GPT
cryptosystem) was proposed in 1991. Use of rank codes in cryptographic applications is …
cryptosystem) was proposed in 1991. Use of rank codes in cryptographic applications is …