Download Coding and Cryptography: International Workshop, WCC 2005, by Keisuke Shiromoto (auth.), Øyvind Ytrehus (eds.) PDF

By Keisuke Shiromoto (auth.), Øyvind Ytrehus (eds.)

Thisvolumecontainsrefereedpapersdevotedtocodingandcryptography.These papers arethe complete versionsof a selectionof the easiest prolonged abstractsaccepted for presentation on the foreign Workshop on Coding and Cryptography (WCC 2005) held in Bergen, Norway, March 14–18, 2005. all the 118 - tended abstracts originallysubmitted to the workshop have been reviewed by means of a minimum of individuals of this system Committee. because of this screening procedure, fifty eight papers have been chosen for presentation, of which fifty two have been ultimately awarded on the workshop including 4 invited talks. The authors of the provided papers have been in flip invited to post complete v- sions in their papers to the entire complaints. all of the full-version submissions have been once more completely tested and commented upon via at the least reviewers. This quantity is the outcome of this lengthy approach. i'm thankful to the reviewers who contributed to ensuring the excessive criteria of this quantity, and who're named at the subsequent pages. It used to be a pl- convinced for me to paintings with my software co-chair Pascale Charpin, whose expe- enced suggestion I havefurther bene?ted vastly from throughout the preparationof this ´ quantity. Discussions with Tor Helleseth and Angela Barbero have been additionally worthwhile in placing the amount jointly. ultimately, i want to thank the entire authors and the entire different members of the WCC 2005 for making it in each experience a hugely stress-free event.

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Additional info for Coding and Cryptography: International Workshop, WCC 2005, Bergen, Norway, March 14-18, 2005. Revised Selected Papers

Example text

Iκ , {i1 , . . , iκ } = N (y ( ) ), we denote it in slightly misusing the notation by V N (y( ) ) . Let V −1 be the inverse of N (y ( ) ) V N (y ( ) ) , then we can use the matrix ⎛ −1 ⎞ V N (y(1) ) 0 ... 0 ⎜ ⎟ .. ⎜ ⎟ . 0 V −1 . ⎜ ⎟ (2) ) N (y U =⎜ ⎟ .. ⎜ .. ⎟ . ⎝ ⎠ . 0 −1 0 ... 0 V N (y (l) ) to calculate ⎛ I 0 ... 0 ⎜ ⎜0 0 ... 0 ⎜ ⎜0 I ... 0 ⎜ ˜ =U A =⎜ A ⎜0 0 ... 0 ⎜. . ⎜ . .. . ⎜. ⎜ ⎝0 0 ... I 0 0 ... 0 (1) −W 1 · L (1) −W 2 · L (2) −W 1 · L (2) −W 2 · L .. (l) −W 1 · L (l) −W 2 · L ⎛ (1) T⎞ W 1 · y (1) ⎜ (1) (1) T ⎟ (1) ⎟ ⎜W 2 · y ⎟ ⎟ ⎜ ⎟ (2) ⎟ ⎜ (2) (2) T ⎟ ⎟ W · y ⎜ ⎟ ⎟ ⎜ 1(2) (2) T ⎟ (2) ⎟ ˜ ⎜ ⎟, ⎟ , and b = U b = ⎜W 2 · y ⎟ ⎟ ⎜ ⎟ .

Nk+t−1 )T where the ni are the coefficients of the q-polynomial N . Set ⎛ ⎞⎫ [k+t−1] [t] g1 · · · g1 y1 · · · y1 ⎪ ⎪ ⎬ ⎜ . .. . .. ⎟ ⎟ . S=⎜ . . ⎠⎪ n ⎝ . ⎪ [k+t−1] [t] ⎭ g ··· g y ··· y n n n n Solving (2) is equivalent to solving the system S× N V = 0. (3) In the unknowns N and V. Therefore it costs roughly (k + 2t)3 operations over GF (q). It is far too much to be efficiently implemented, compared to the already existing decoding algorithms. By considering (3), it is clear that a part of the matrix S is independent of the received word, depending only on the parameters of the Gabidulin code.

Ideals over a noncommutative ring and their application in cryptology. In D. W. Davies, editor, Advances in Cryptology – EUROCRYPT’91, volume 547 of LNCS, pages 482–489. Springer-Verlag, 1991. 6. P. Loidreau. Sur la reconstruction des polynˆ omes lin´eaires : un nouvel algorithme de d´ecodage des codes de Gabidulin. Comptes Rendus de l’Acad´ emie des Sciences: S´erie I, 339(10):745–750, 2004. 7. Ø. Ore. On a special class of polynomials. Transactions of the American Mathematical Society, 35:559–584, 1933.

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