{"product_id":"a-lattice-attack-on-the-zaharina-velikova-9783639055474","title":"A Lattice Attack on the McEliece Public Key Cryptosystem","description":"The McEliece cryptosystem was proposed by R.McEliece in 1978. In its original version it is based on Goppa codes. Given a public key matrix G and a codeword c=mG+e, we reduce the problem of recovering the error vector e to the shortest lattice vector problem. Using Conway and Sloane's \"Construction A\", we construct a basis of a lattice, in which the norm of the shortest vector w.r.t. lp norm is equal to the lp norm of the error vector e for p\u0026gt;log(t), where t is the weight of the error vector e. To find such shortest vector in our lattice we use the LLL and block basis reduction algorithms for the lp norm, which guarantee only an approximation of the length of the shortest lattice vector. Our tests show that this attack method provides no positive results for Goppa codes of length more than 127.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eAuthor:\u003c\/b\u003e Zaharina Velikova\u003cbr\u003e\u003cb\u003eISBN-10:\u003c\/b\u003e 3639055470\u003cbr\u003e\u003cb\u003eISBN-13:\u003c\/b\u003e 9783639055474\u003cbr\u003e\u003cb\u003ePublisher:\u003c\/b\u003e VDM Verlag Dr. Mueller E.K.\u003cbr\u003e\u003cb\u003eLanguage:\u003c\/b\u003e English\u003cbr\u003e\u003cb\u003ePublished:\u003c\/b\u003e 08\/04\/2008\u003cbr\u003e\u003cb\u003ePages:\u003c\/b\u003e 132\u003cbr\u003e\u003cb\u003eFormat:\u003c\/b\u003e Paperback\u003cbr\u003e\u003cb\u003eWeight:\u003c\/b\u003e 0.41lbs\u003cbr\u003e\u003cb\u003eSize:\u003c\/b\u003e 9.00h x 6.00w x 0.28d","brand":"Zaharina Velikova","offers":[{"title":"Paperback","offer_id":47424580714751,"sku":"9783639055474","price":63.72,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0662\/2982\/9887\/files\/img_76815da8-0d67-49da-bfac-45729d1b36d1.jpg?v=1761531176","url":"https:\/\/www.whiterainbookhouse.com\/products\/a-lattice-attack-on-the-zaharina-velikova-9783639055474","provider":"WR Book House","version":"1.0","type":"link"}