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Classical ISD variants Lee-Brickel (1988) p k w - p n-k e' k Q I n-k = s ⇔ Q + s = e'' wt(Qe'+s) = w-p ● Brute T(n,k,d) force = on Q, Pr[“good” i.e. search randomization] e'= p -1 x with C[Brute wt(Qe'+s) force] = w-p k p n−k w n w− p ● If so, fll up e''= w - p = with remaining w-p x 1's −1 k p IMPROVED INFORMATION SET DECODING ASIACRYPT 2011 | December 2011, Seoul
Classical ISD variants Lee-Brickel (1988) p k w - p n-k e' k Q I n-k = s ⇔ Q + s = e'' wt(Qe'+s) = w-p Complexity ● Brute force (bounded on Q, i.e. search distance e'= decoding) p with wt(Qe'+s) = w-p F(k) ≤ 0.05751 ● If so, fll up e''= w - p with remaining w-p 1's IMPROVED INFORMATION SET DECODING ASIACRYPT 2011 | December 2011, Seoul
Page 1 and 2: Improved Information Set Decoding -
Page 3 and 4: Recap Binary Linear Codes A binary
Page 5 and 6: Scenario (Bounded Distance Decoding
Page 7 and 8: Scenario (Bounded Distance Decoding
Page 9 and 10: Some very basic observations Allowe
Page 15 and 16: Basic Information Set Decoding ''Re
Page 17 and 18: Basic Information Set Decoding Fund
Page 19: Classical ISD variants Lee-Brickel
Page 23 and 24: Classical ISD variants Stern (1989)
Page 29 and 30: Wrapping up so far ● Different me
Page 31 and 32: Wrapping up so far ● Different me
Page 33 and 34: Our New Algorithm IMPROVED INFORMAT
Page 35 and 36: Generalized ISD framework ● Start
Page 37 and 38: Generalized ISD framework ● Major
Page 39 and 40: Our New Algorithm ● Main contribu
Page 41 and 42: How can we proft from representatio
Page 43 and 44: How can we proft from representatio
Page 45 and 46: Summary ● ● ● Asymptotically

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