Paul.... Here's my list of places where I personally got hung up in MAKING, BREAKING. Some are (I believe) just typos, some are maybe just me, and in some cases I'd love to see more text. Also I should apologise that I didn't make a concerted effort to find these things, I'm just walking thru my copy of the text and looking at marks I made at the time I was reading. Definitely a hit-or-miss operation. p. 8 l. 19. Despite the fix I still find this s. ambiguous. ``If so'' refers to the most recent inequality, but could easily be taken to refer to the first. I'd prefer ``If ..., then necessarily q'-q /= 0, but if q'-q /= 0 then'' p. 51, l -14, ``the number can be as low as eight'' ? (good and bad riffles). p. 62 Theorem statment is ambiguous to a newbie like me. The ``both n and m'' can be taken two ways: you could be describing either numbers of the form kmn or (both) km and kn. Section 4.3. I dunno, one could go on forever about this stuff, but might be worth mentioning that Kasiski can also use digrams and in general the gcd criterion might be too restrictive (typical examples from Gaines for example show generality (and fuzziness) of idea). Ch. 5 Expand? Esp. generating function idea. Not used too much in sequel but also not really self-standing here, I felt. p. 98 l -10, might give page ref to double anagramming definition, (p. 45), or put it in index? p. 109 l. 14. This proof seems a little indirect. Why doesn't one direction follow directly from def. of prime #? (I'm obviously not a mathematician, so take that for what it's worth). P.S. it's a lot of fun to analyze these proofs in terms of contrapositive statements and contradictions. Interesting insight into their structure. In fact I had to do that to see why this proof worked. p. 110, last line, last symbol: final ``n'' should be ``nq'', no? p. 120 l. 18, I'm not sure, but it seems like this display equation should be .... = y'-r' < y' - y'/2 <= y'/2 In my printing ^ ^ these are something else. p. 148 lines -5 and -6 are the same p. 165 line 11, replace n by phi(n)? Here's a Question... Why choose Blum integers (3 mod 4) for your p and q in an RSA modulus? Everybody does it, everybody says they do it, nobody says why. Is it obvious? p. 168 Middle of page. Is it obvious why solving this quadratic helps find primes? I think I found out what's going on somewhere else, but I don't recall.... maybe say more? p. 175 Problem 10.4.03: the "z" is missing from the (y,z) message pair I receive in this problem. So to do this problem the student should make up his own r, compute own z, encrypt and then decrypt some integer or other. Just run thru the whole El-Gamal process on a small integer to prove you get it. p. 177 l. 5 ``In particular,...'' I found this S. misleading, since clearly it's true but it's certainly nowhere good enough. In fact, when I saw it wasn't I went off and (re-? I dunno, maybe I'd seen it) invented superincreasing knapsack problem in search of the true condition for injectivity. What IS the true condition, I wonder. Anyway this sentence could be tweaked, as in ``Clearly, the ai's must all be different but that is also clearly not sufficient''. p. 182 l. 15 Maybe show the meet in middle attack? Nice use of bday paradox. p. 184 l. 14 The Word problem can't be telling if two words are equal: you just eval 'em, no? Maybe the word problem is finding if there is a word that evals to a given value? p. 288 l. -1,-2 replace ``than'' with ``that'' once each line. p. 216 l. -7, It's amazing you made it without eqn numbers, but here maybe should label this in line above ``the single (goofy) congruence'' since you refer to it later that way and several congruences have gone by. Section 18.3 I really got wrapped around the axle here. That was frustrating because I didn't find other technical descriptions of sharing. But I really got confused. In fact I got so confused I don't know yet what happened. line -11, should be a1,..., at ? Line -4 should be n1 not N1? Next page was my big problem. I couldn't straighten out if h or H was largest or smallest, whether the > and < were going the right way, whether it was H or H' (line -8), etc. If you could take another look at this, maybe rethink the notation, make consistent, maybe say more, that'd be good. Just not enough redundancy in treatment to let me straighten out what was going on. p. 301 l. -11 Does this example really work? f(0) seems to be 0+0+0+1 (to me), not 0+0+1+1. p. 340. last 2 lines, 341 first 3 lines. I think you want 1's, not sn's or s_{n-1}'s, or indeed s_{any subscript} in these equations. Those subscripted s's give you LFSRs but don't describe LCGs, I think. Or am I crazy? p. 406 l. 7 N-1 should be K? p. 415 l -3, Should be Fsub2 super t, not super t+1, no? p.416 line 3 display eqn needs 1 more term c sub (t+1) v sub (t+1) = p. 416 line 8 second big PI product should have p sub j, not p sub i p. 416 line -16 in Remark, probably mean Fsub2 super (t+1)? p. 420 halfway down page, Maybe elevate the ``Further, note...'' paragraph to a remark since it's another very useful trick in this quadratic factoring game (I gather). I however got totally confused here, since I didn't see why we were talking about b^2, or a^4, nor did I recognize the Legendre symbol in (n/p)sub2. So this maybe could all be fixed by also working on... 421. Section 25.5, which seems lifted bodily out of the CRC book (p. 97). On P. 95 they seem to use a slightly different form of the formulae that appear on the bottom of p. 417 and top of 418. This formula, for me, made their 1-sentence treatment of the shortcut described in your ``Further, note'' paragraph easy to understand. Anyway, back to 25.5: Unless I'm wrong, you don't actually associate your formula with their notation q(x), so the reference to q(x) on p. 421 comes out of nowhere. So maybe if it were me I'd go the whole way with the CRC treatment, and maybe even go further and show us the sieving at work... it seems nobody else will (even CRC)! Whew. I think that's pretty much all I found, anyway I hope you find it useful. Again, thanks for this book and I hope they let me do this course again next year so I can use it again! Cheers, Chris