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You can affect the sort behavior by adding optional sort ags. These are stored as static constants in the Array class. To add these options, pass them in separated by bitwise OR (|) operators after your sort function. To learn why you do this, check out 13, Binary Data and Byte Arrays. The following code sorts the elements in the array numerically (rather than using the string equivalent of the date, which is the default) and descending from the highest to lowest year.

bookshelf.sort(byDate, Array.NUMERIC | Array.DESCENDING);



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Brumley and Boneh [22] consider a timing attack against RSA as implemented in OpenSSL. The attack they develop is practical and sufficiently robust that it can recover a private key over a network that includes several routers and switches between the endpoints, which introduces a significant random timing variation. The RSA implementation in OpenSSL is highly optimized, using CRT with repeated squaring, Montgomery multiplication and a sliding window (with a window of size of five for a 1024-bit modulus). In addition, the OpenSSL implementation of RSA employs Karatsuba multiplication to compute the product rcy whenever I(: and y consists of the same number of words, and it uses ordinary long multiplication when IC and y are not of the same word-size. Repeated squaring, CRT, Montgomery multiplication, sliding window and Karatsuba multiplication are all discussed in Section 7.4.1, above. Kocher s original RSA timing attack [85]does not work when CRT is employed, and Schindler s timing attack [129] does not succeed when Karatsuba multiplication is used (below, it will become clear why Schindler s attack fails in this case). Consequently, Brumley and Boneh had to significantly extend Schindler s approach to successfully attack OpenSSL. Their attack is undoubtedly the most advanced practical timing attack developed to date. In the OpenSSL implementation of modular exponentiation, there are two algorithmic issues that create significant timing differences. First, there





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where m is its slope and c is its intercept. Since the slopes and intercepts are sampled sparsely, they may not be as precise as the original straight lines. Moreover, this method cannot generate polylines [3].

"Anathem", Neal Stephenson (2008) "Jonathan Strange & Mr Norrell", Susanna Clarke (2006) "VALIS", Philip K. Dick (1991) "The Crystal World", J.G. Ballard (1966)

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are the extra reductions in the Montgomery algorithm This is precisely the issue that Schindler exploits in his attack [129] Second, the use of Karatsuba and normal multiplication creates significant timing differences However, the timing attack is great,ly complicated by the fact that these two timing effects tend to counteract each other Suppose we want to decrypt C using the OpenSSL implementation of RSA When the Montgomery form of C is close to p , but less than p , then the number of extra reductions will be large--as can be seen from Figure 72% and therefore the decryption time will increase On the other hand, if the Montgomery form of C is slightly larger than p , then the number of extra reductions will be relatively small and the decryption time will decrease (again, see Figure 72).

You can pass ve such optional ags to either sort() or sortOn():

CASEINSENSITIVE Normally, sorting is case-sensitive. Using this ag makes the search ignore the case of letters. You probably want this for most string sorting. DESCENDING Using this causes the array to be sorted from highest to lowest. NUMERIC If you re sorting only numbers, use this ag. Otherwise, numbers are converted

When the Montgomery form of C is slightly less than p , then many of the multiplication operations in (76) will involve numbers that are of about the same magnitude Consequently, Karatsuba multiplication will predominate in this case, which reduces t)he time as compared to normal multiplication On the other hand, when the Montgomery form of C slightly exceeds p , then C is small (due to the mod p reduction) so that more of the multiplication operations in (76) will involve numbers of significantly differing size Consequently, the slower normal multiplication routine will predominate The Brumley-~Bonehattack relies on the fact that these two effects (extra reductions and normal versus Karatsuba multiplication) each dominate during different parts of the attack This implies that Schindler s attack could riot be used to recover those bits where the Karatsuba versus normal multiplication t h i n g effect dominates.

to their string equivalent before sorting occurs. This can be really tricky! For instance, as strings, 2009 is greater than 1000000 because the 2 character is higher than the 1 character. Make sure to enable numeric comparisons to avoid these errors! In this case, writing your own comparison function that explicitly compares years prevents this pitfall.

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