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Method of authentication using a decoding of an error correcting code on the basis of a public matrix



Statut des brevets

French patent application FR0704518 filed on June22, 2007 and entitled “Procédé d’authentification utilisant un décodage de code correcteur d’erreurs a partir d’une matrice publique”


Philippe GABORIT

Statut commercial

Research agreement, exclusive or non exclusive licenses


Laboratory XLIM (UMR6172), Limoges, France,



The process cryptographic authentication is the most common being based on the RSA algorithm.

However, in the RSA algorithm, it is necessary to calculate on very large integers, including calculations of discrete exponentials. Such calculations can be slo


The method involves decoding of error correcting code from a public matrix (H) e.g. quasi-cyclic matrix, where the public matrix includes K row and 2 K columns and is a juxtaposition of a size identity block Kx K, and of a size circulating block Kx K. A circulating square block is defined by a vector of random size K, where the circulating block is composed of binary data and the number K is equal to 317. The quasi-cyclic matrix is used in a Stern protocol or Veron protocol.


The method can be implemented easily in the cryptographic device at low cost with limited capacities of calculation and/or storage. The method reduces the quantity of public data to be stored in the method using decoding of the error correcting code from the public matrix, and utilizes the random matrices for fast calculations in the cryptographic device. The method provides the public matrix compatible with the protocol decoded by Stern syndrome, and dual protocol decoded by Stern syndrome.


This cryptographic authentication method can be used in a cryptographic device of a smart card.

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