# Reducible rank codes and their applications to cryptography

##### Citations

150 citations

### Cites background from "Reducible rank codes and their appl..."

...[27], [ 26 ], [28], [70] and [35]) in order to reduce the public key size....

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...8. Reducible Codes [ 26 ]: Choose some matrices Y ∈ F k×n and S ∈ F l×k with l ≤ k. Then take the code generated by % SG 0...

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149 citations

### Cites background from "Reducible rank codes and their appl..."

...In [9], the authors proposed to substitute the underlying code by a reducible rank code:...

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...In the examples from [9] the authors propose to take two Gabidulin codes G1 and G2 over Fqm (with length ni and dimension ki , i = 1,2) and a random matrix Y = Y21 ∈ Fk2×n1 qm to build a reducible rank code G....

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...Using this construction, the authors of [9] propose that the...

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...The authors of [9] considered every parameter set with mi ≥ 24 and r ≥ 4 to provide sufficient security, even if X1 and X2 are zero matrices....

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102 citations

93 citations

92 citations

##### References

9,334 citations

9,262 citations

### "Reducible rank codes and their appl..." refers background in this paper

...1An algorithm to find the greatest common divisor for two linearized polynomials of degree from the ring of linearized polynomials with complexity ( log ) can be elaborated on the basis of the algorithm for finding gcd for two ordinary polynomials described in [8]....

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265 citations

### "Reducible rank codes and their appl..." refers background in this paper

...Originally, codes in rank metric were proposed for cryptographic applications in the GPT public-key cryptosystem [3]....

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...The Gabidulin–Paramonov–Tretjakov (GPT) public-key cryptosystem (PKC) (see [3]) is built on linear MRD codes....

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122 citations

### "Reducible rank codes and their appl..." refers background in this paper

...It is well known that the use of a parity-check matrix in systematic form is as secure as the use of any parity-check matrix: this will halve the size of the key (see further [11])....

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