4 Exercise Lists and Challenge Lists 4.1 Elliptic curves over F2m In the following tables, ECC2-k denotes that the exercise or challenge is over a field F2m, and that the parameter n has bitlength k. Furthermore, ECC2K-k denotes that the elliptic curve used is a Koblitz curve (see Section 3.1.3), rather than a randomly generated curve. For a description of the format of the Challenge parameters, see Section 3.1.3. For further details about the challenge, see Section 3.3. The time estimates for each exercise and challenge were derived as in Section 6.2. 4.1.1 Exercises Exercise Field size (in bits) Estimated number of machine days on a Pentium 100 Prize (US$) ECC2-79 79 problem solved Handbook of Applied Cyptography & Maple V software ECC2-89 89 problem solved Handbook of Applied Cyptography & Maple V software ECC2-97 97 2.5 x 105 $ 5,000 ECC2K-95 97 problem solved $ 5,000     4.1.2 Level I Challenges Challenge Field size (in bits) Estimated number of machine days on a Pentium 100 Prize (US$) ECC2-109 109 5.4 x 107 $ 10,000 ECC2K-108 109 1.3 x 106 $ 10,000 ECC2-131 131 3.1 x 1010 $ 20,000 ECC2K-130 131 3.8 x 109 $ 20,000   4.1.3 Level II Challenges Challenge Field size (in bits) Estimated number of machine days on a Pentium 100 Prize (US$) ECC2-163 163 2.9 x 1015 $ 30,000 ECC2K-163 163 4.6 x 1014 $ 30,000 ECC2-191 191 1.4 x 1020 $ 40,000 ECC2-238 239 3.0 x 1027 $ 50,000 ECC2K-238 239 1.3 x 1026 $ 50,000 ECC2-353 359 1.4 x 1045 $ 100,000 ECC2K-358 359 2.8 x 1044 $ 100,000

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