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Therefore, 324 = 37 (mod 101) and we have solved this particular discrete log problem. In general, for the giant-step phase, we compute about fi values and store these in our table. Then in the baby-step phase, after trying about J r/2 choices for we expect to have found a solution. Assuming the table lookups do not carry any cost (the table could be sorted or a hash table used), this algorithm requires about 1.5J r niultiplications and it also requires storage (or space) of about &. Assuming the storage requirement is feasible, this is A significant improvement over the nai've method of trial multiplication, but still an cxponential work factor.

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This expression nds what it is that someone likes to do. It uses a group to allow for several subjects. However, the rst group is noncapturing, so it does not interfere with the verb, which is captured in the rst position.

Beyond noncapturing groups, there are also zero-width groups: groups that try to match the source string without moving ahead in the pattern. ActionScript 3.0 regular expressions have a positive lookahead group, or a zero-width positive lookahead assertion. When you use the syntax

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As above, we are given the generator 9.a prime p , and x = ga (mod p ) , and we want to find a. Analogous to Dixon's factoring algorithm, we first select a bound B and a factor base of primes less than B . Then we pre-compute the discrete logarithms to the base y of the elements in the factor base and we save the logarithms of these elements. These logarithms of the factor base can he found efficiently by solving a system of linear equations; see Problem 11. Once the logarithms of the elements in the factor base are known, the attack is straightforward. We have 11: = g" (mod p ) , and we want to find a. Let { p ~ . p l ,. .. ,p,-l} be the set of primes in the factor base. We randomly select k E ( 0 , l . 2 , . . . , p - 2 } and compute y = J:. gk (mod p ) until we find a y that factors completely over the factor base. Given such a y we have

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you ensure that the pattern represented by the ellipsis would match, if you tried to. However, it doesn t perform the match, so that after the lookahead group, you re still talking about the same location in the source text as before it. This is unlike most metasequences you ve seen so far, which match and then continue through the source text. Recall that anchors such as ^ and \b are also zero-width.

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var re:RegExp = /\b ( :\w{3}) \b ( = .* \b \1 \b) \s* (\w+) /x; var testString:String = "far, farther fetched free fun fetched fun free"; trace(testString.match(re)); //fun fetched,fetched

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