The algebraic decoding of Goppa codes

Abstract

which approaches one uniformly on .H2 as n increases for any a.o. p, since H(Q) 2 2. The same procedure is used for &',, but the sequence is-+ KL.LMhk,). *-+ p(h(j,,j,))p(h(k,,k,)) * *. so that the 2" integers mapped by h" are always drawn from the same distribution (Q, or Q,). Using this encoding on the rows of the array in Fig. I, sending representations of 2" runs of zeros and 2" runs of ones from each row, and using the appropriate marker-moving algorithm gives an a.o. sequence of universal codes for SZZ~, A, and JZ'.

Improved Timing Attacks against the Secret Permutation in the McEliece PKC

“…The Patterson algorithm offers another solution for the syndrome decoding. The decryption described in [12] permits to correct up to t errors by using the syndrome associated to g but not to g 2 .…”

Timing Attacks against the Syndrome Inversion in Code-Based Cryptosystems

“…It makes use of the error correction algorithm, given by the Patterson Algorithm [20], shown in Algorithm 2. In Step 1 of this algorithm, the syndrome vector is computed by multiplying the ciphertext by the parity check matrix, and then turned into the syndrome polynomial S(Y ) by interpreting it as an F t 2 m element and multiplying it with the vector of powers of Y .…”

Note on Modular Reduction in Extended Finite Fields and Polynomial Rings for Simple Hardware

“…This general reduction works for any reduction polynomial, for instance [1][2][3][4][5][6], and thus we can say that it works for random reduction polynomials which can be even secret [7][8][9][10][11]. No special methods are used, and thus no processor is required, just a simple hardware can be used.…”