Abstract: Methods and apparatus for generating a private-public key pair, for encrypting a message for transmission through an unsecure communication medium (30), and for decrypting the message are disclosed. The methods are based on the well-known McEliece cryptosystem or on its Niederreiter variant. More general transformation matrices Q are used in place of permutation matrices, possibly together with an appropriate selection of the intentional error vectors. The transformation matrices Q are non-singular n×n matrices having the form Q=R+T, where the matrix R is a rank-z matrix and the matrix T is some other matrix rendering Q non-singular. The new Q matrices, though at least potentially being dense, have a limited propagation effect on the intentional error vectors for the authorized receiver. The use of this kind of matrices allows to better disguise the private key into the public one, without yielding any further error propagation effect.

Abstract: Methods and apparatus for generating a private-public key pair, for encrypting a message for transmission through an unsecure communication medium (30), and for decrypting the message are disclosed. The methods are based on the well-known McEliece cryptosystem or on its Niederreiter variant. More general transformation matrices Q are used in place of permutation matrices, possibly together with an appropriate selection of the intentional error vectors. The transformation matrices Q are non-singular n×n matrices having the form Q=R+T, where the matrix R is a rank-z matrix and the matrix T is some other matrix rendering Q non-singular. The new Q matrices, though at least potentially being dense, have a limited propagation effect on the intentional error vectors for the authorized receiver. The use of this kind of matrices allows to better disguise the private key into the public one, without yielding any further error propagation effect.

Abstract: An apparatus and method are disclosed for evaluating an input polynomial (p(x)) in a (possibly trivial) extension of the finite field of its coefficients, which are useful in applications such as syndrome evaluation in the decoding of cyclic codes. The apparatus comprises a decomposition/evaluation module (110) configured to iteratively decompose the input polynomial into sums of powers of the variable x, multiplied by powers of transformed polynomials, wherein each transformed polynomial has a reduced degree as compared to the input polynomial, and to evaluate the decomposed input polynomial. In another aspect, an apparatus and method of identifying errors in a data string based in a cyclic code are disclosed, which employ the Cantor-Zassenhaus algorithm for finding the roots of the error-locator polynomial, and which employ Shank's algorithm for computing the error locations from these roots.