More and remaining errors in second printing. Sigh.

• Many occurences of "Anshel" were mis-spelled: this should be "Anshel", not "Anschel".

• [page] [line] [original] -> [corrected]

• page x line -4: Roots ---> Roots of Primes
• page xiv line: -17 than here ---> here than
• page xv line 7: possibly ---> possible
• page sv line -15: eveyone ---> everyone
• page xix line -15: occured ---> occurred
• page 5 line -12: arithemetic ---> arithmetic
• page 6 line -8: give ---> gives
• page 8 line 18: q'-q ---> q-q'
• page 8 line -8: q'-q ---> q-q'
• page 19 line -10: subset ---> subsets
• page 28 line 8: Aand B ---> A and B
• page 28 line 12: another another ---> another
• page 40 line 13: the the ---> the
• page 41 lines 15-16: some of the frequencies are messed up, should be: E-11, B-9, J-9, C-7, X-7, G-6, L-4, N-2, S-3, T-3
• page 43 line -18: whatseover ---> whatsoever
• page 44 line 3: n-characer ---> n-character
• page 45 line -13: amgibuities ---> ambiguities
• page 54 line -2: with the other ---> from the other
• page 55 line 4: 3, n+3, 3, ... ---> 3, n+3, ...
• page 55 line 7: shuffle, (or maybe two) ---> shuffle (or maybe two),
• page 55 line 9: 1,2,..., 2n-1 ---> 1,2, ..., 2n-1, 2n
• page 59 line 16: (3m+1)th, ---> (3m+1)th, ...,
• page 59 line 17: m+2th, 2m+2th, 3m+2th ---> (m+2)th, (2m+2)th, (3m+2)th, ...,
• page 61 line 5: m|N and n|N ---> m and n divide N.
• page 68 line 11: 3 of the 6 ---> 2 of the 3
• page 68 line 15: a key ---> this key
• page 68 line 19: 35 ---> 39
• page 73 line -7: ciphertext only ---> ciphertext-only
• page 74 line 22: eight ---> eighth
• page 75 line 10: 0.067 ---> 0.064
• page 75 line -10: 0--25 ---> 0-25
• page 75 line -7: P(y)=p_y0 p_y1 ... p_yN-1 ---> P(y)=(p_y0, p_y1, ..., p_yN-1)
• page 75 line -7: P(y)=p'_y0 p'_y1 ... p'_yN-1 ---> P(y)=(p'_y0, p'_y1, ..., p'_yN-1)
• page 76 line 6: insert 1/N after = sign
• page 76 line 14: insert 1/N after = sign
• page 76 line 15: insert "So E(X)=E(X_i) for all i."
• page 77 line -3: 0.067 ---> 0.064
• page 79 line 10: 0.067 ---> 0.064
• page 79 bottom: Add: "95% of these are between 5% and 8%."
• page 81 line 3: Should screen for I>0.040, not I>0.047
• page 82 line -17: y⁽³⁾ = (y₂,y_3+m,y_3+2m,...) ---> y⁽³⁾ = (y₃,y_3+m,y_3+2m,...)
• page 82 line -16: y⁽⁴⁾ = (y₃,y_4+m,y_4+2m,...) ---> y⁽⁴⁾ = (y₄,y_4+m,y_4+2m,...)
• page 83 line -1: (k₂ - k₀) + (k₁ - k₀) = (k₂ - k₀) ---> (k₂ - k₀) - (k₁ - k₀) = (k₂ - k₀)
• page 84 line -18: (k₃ - k₀) + (k₁ - k₀) = (k₃ - k₀) ---> (k₃ - k₀) - (k₁ - k₀) = (k₃ - k₁)
• page 84 line -8: Add comment "Mildly surprising that correct shift has index only 5.18%."
• page 85 line 4 and following: Should admit that we're now screening just above 5.00%
• page 85 line 22: "all possibilities are excluded except TWO: k₄-k₀=16 and k₄-k₁=15 AND ALSO k₄-k₀=22 and k₄-k₁=21.
• page 90 5.1.02 [duplicates 22.1.07]
• page 90 5.1.03 [duplicates 5.1.02]
• page 93 line -7 : sigma² = ---> sigma² >=
• page 94 line -2: sqrt(p(1-p))/n ---> p(1-p)/epsilon²n
• page 98 line -5: while th eeach ---> while each
• page 99 line 21: Kerckhoff's ---> Kerckhoffs'
• page 100 line 6: Kerckhoff's ---> Kerckhoffs'
• page 100 line -10: eigth ---> eighth
• page 101 line 12: round is ---> round is a
• page 105 line 15: permutation ---> permutations
• page 109 line 8: A positive integer ---> An integer greater than 1
• page 109 line 14: A positive integer ---> An integer greater than 1
• page 109 line -10: equal n ---> equal to n
• page 110 line -1: (-y₀) . n ---> (-qy₀) . n
• page 113 line 1: integer ---> non-zero integer
• page 113 line 12: n = ---> N =
• page 113: n and N used interchangeably/inconsistently
• page 115: n and N used interchangeably/inconsistently
• page 116 line -21: other than 5 ---> not divisible by 5
• page 118 lines 10-12: Add "For 2^m+1 to be prime requires that m=2ⁿ for some n, but this is not a sufficient condition. No Fermat prime is known beyond the case of 2²⁴+1."
• page 120 line 7: x > y ---> x and y such that |x| > |y|
• page 120 line 18: = y' - r' < r'-y'/2 = y'/2 ---> =< y' - r' < y'-y'/2 = y'/2 [equality becomes less-or-equal]
• page 130 line 11: 18-3 ---> 3-18
• page 131 line -12: overline(10) ---> overline(9)
• page 133 line 9: is a ---> are
• page 133 line 10: 0 =< r < |m| and an integer q so that ---> integers r and q with 0 =< r < |m| and
• page 135 7.7.15 three ---> four
• page 135 7.7.20 a_=< ---> a₀ [twice]
• page 136 line -17: m ---> n
• page 136 line -16: m ---> n
• page 136 line -15: m ---> n
• page 137 line 3: m ---> n
• pages 136-137 The m's and n's should be the same thing!
• page 137 7.8.04 2 is ---> 2 is not, but 3 is,
• page 138 7.8.12 log_r2 = log_rs . log_s2 ---> log_{r line}2 = log_rs . log_s2 mod 16
• page 138 7.8.13 log_rx = log_rs . log_sx ---> log_{r line}2 = log_rs . log_s2 mod phi(m)
• page 143 and to end of section: "k" ---> "K"
• page 146 line 6: [missing equality sign between second and third matrices in middle of equality]
• page 148 line -6: O(k) ---> O(h)
• page 148 line -6: O(hk) ---> O(h²)
• page 149 line 3: |f(x|) ---> |f(x)|
• page 150 line -12: equal ---> equal to
• page 152 line 7: (log₁₀2)^l ---> (log₁₀2)^-l
• page 154 line 17: to to ---> to
• page 154 line -9: 2^log₂N/2 ---> 2^(log₂N)/2
• page 157 line -5: s₃, s_N-1 ---> s₃, ..., s_N-1
• page 157 line -3: s_n-3 ---> s_n-N+1
• page 158 line 4: s₃, s_N-1 ---> s₃, ..., s_N-1
• page 161 line 23: m ---> p
• page 165 line 11: n ---> phi(n)
• page 165 line -10: -n(-phi(n)+1) ---> n-phi(n)+1
• page 166 line -5: there ---> the
• page 169 line -1: exponentiations ---> multiplications
• page 170 line 9: equal ---> equal to
• page 170 line 15: help: ---> help.
• page 170 line -14: occuring ---> occurring
• page 175 line 20: add "These special primes are Sophie Germain primes."
• page 178 line -16: b_i ---> c_i
• page 179 line -22: be be ---> be
• page 180 line 9: a_lb_k ---> a_ib_j
• page 181 line 1: may may ---> may
• page 181 line 7: x ---> m
• page 181 line -2: h ---> m
• page 185 line -13: a₂^ba^-1 ---> ab₂a^-1
• page 185 line -5: e_i1 ---> k_i1
• page 185 line -2: a_iN^e_i1 ---> a_i1^k_i1
• page 185 line -1: e_i1 ---> k_i1
• page 187 line 13: effect ---> effects
• page 192 line -14: surely not ---> surely is not
• page 195 line 2: theta(2^e) = 2^e+1 ln 2 ---> theta(2^e) =< 2^e+1 ln 2
• page 196 line 5: Stieljes ---> Stieltjes
• page 196 line 8: [inside integral] theta(x) ---> theta(t)
• page 196 line 9: theta(x)=O(x) ---> theta(t) = O(t)
• page 196 line 10: [inside integral] O(x) ---> O(t)
• page 197 line 15: G. Riemann ---> B. Riemann
• page 202 line 5: +1 ---> +1)
• page 205 line 15: 19.34 ---> 10.34
• page 205 line 19: 725, ---> 725.
• page 205 line -5: 19*58 ---> 19.58
• page 208 line -2: n ---> m
• page 213 line -2: the the ---> the
• page 216 line 2: f₂ compose f₁ ---> f₁ compose f₂
• page 216 line -6: solutions) as ---> solutions as)
• page 218 line 10: b₂ ---> b₃
• page 219 line -8: 17 ---> 17,
• page 219 line -8: 13 ---> 29
• page 220 line -10: [delete dot before rightmost "4"]
• page 221 line -1: 21y ---> 42y
• page 223 line 6: f' circ g . g ---> f' circ g . g'
• page 224 line 8: f'(x_n)^-1 ---> f'(x_n)^-1)
• page 224 line -16: f(x_n).tp ---> -f(x_n).tp
• page 226 line -1: 1/(1-x) ---> 1/(1-x) - 1
• page 227 line 1: 1/(1-x) ---> (1/(1-x) - 1)
• page 227 line 5: 1 = 107 ---> q = 107
• page 230 line 3: not ---> no
• page 230 line 14: mod n ---> mod n.
• page 231 line 2: a efficient ---> an efficient
• page 246 line 7: [second quadratic symbol a mod n should be b mod n]
• page 247 line -5: 319 ---> quadratic symbol 3 over 19
• page 250 line -10: [in exponent] (n²-1)8 ---> (n²-1)/8
• page 250 line -4: [missing '+' between two fractions with denominators 8]
• page 257 line -18: p ---> n
• page 257 line -16: p ---> n
• page 267 line -11: form ---> forms
• page 267 17.1.02 integer n ---> integer n,
• page 277 line 2: that that ---> that
• page 282 line -7: should define n_i=(1/M) % m_i
• page 282 line -4: N_i ---> n_i
• page 283 in the Theorem h_k ---> h_k-1
• page 283 line 13: h_k ---> h_k-1
• page 283 line -13: a_i ---> m_i
• page 283 line -3: a_i ---> m_i
• page 301 line -13: x³+x²+x+1 ---> x²+x
• page 301 line -11: 0 + 0 + 1 + 1 ---> 0 + 0
• page 301 line -9: 1 + 1 + 1 + 1 ---> 1 + 1
• page 302 problem 19.3.06: a ---> 1
• page 302 line -9: = x-1 ---> = -x+1
• page 302 line -8: x-1 ---> -x+1
• page 303 line 2: [delete "at each step"]
• page 315 line -7: fg ---> (fg)'
• page 321 line 12: phi₍d) ---> phi(d)
• page 336 line -17: occuring ---> occurring
• page 340 line -1: [first] s_n ---> 1
• page 340 line -1: s_n-1 ---> 1
• page 341 line 2: s_n+k-1 ---> 1
• page 341 line 2: s_n-1 ---> 1
• page 341 line 5: numbers ---> nonzero numbers
• page 343 line -6: if if ---> if
• page 345 line 10: [italicize left parenthesis by "Proof"]
• page 346 line 3: special, case ---> special case
• page 347 line -6: ['F' in F_p^N should be bold]
• page 347 line -5: ['F' in F_p^N should be bold]
• page 347 line -4: ['F' in F_p^N should be bold]
• page 351 line 1: it i ---> it is
• page 352 line 5: an polynomial ---> a polynomial
• page 353 line 7: x⁷3 ---> x⁷³
• page 356 line -10: is the image of an inverse ---> is the inverse of the image
• page 358 22.1.10 [duplicates 22.1.07]
• page 359 22.1.14 [duplicates proof on page 356]
• page 360 line 10: that that ---> that
• page 361 line -14: (g^k)^q ---> (g^k)^-q
• page 362 line 10: alright ---> all right
• page 362 line -16: homorphism ---> homomorphism
• page 362 22.2.02 Z/13 ---> Z/13^x
• page 362 22.2.04 g²⁴ g²⁸ ---> g²⁴, g²⁸
• page 363 line 10: g^-1e=g⁰ ---> g^-1, e=g⁰
• page 366 line -4: N|l m ---> N|lm [remove space]
• page 367 line -19: version ---> version of
• page 367 line -8: odd. Let ... Let ---> odd. Let
• page 368 lines 6, 9, 13, 13: b ---> y
• page 368 line 19: 235 ---> 253
• page 375 : delete proposition, proven earlier (p. 261)
• page 377 line -15: [second quadratic symbol should be y mod n]
• page 377 line -13: [second quadratic symbol should be y mod n]
• page 377 line -11: [second quadratic symbol should be y mod n]
• page 379 line -1: ord_p = ---> ord_pk =
• page 380 line 9: ord_p = ---> ord_pk =
• page 382 line -13: a^n-1 ---> g^n-1
• page 382 line -10: a^l ---> g^l
• page 392 line -2: equal B ---> equal to B
• page 392 line -1: equal B ---> equal to B
• page 393 second bullet: rewrite as "replace b by b^r, where r=p_i ^ell
• page 394 line 1: equal e_i ---> equal to e_i
• page 396 in exercises 1-4 delete words "factor base"
• page 398 line -15: k=1 ---> u=1
• page 406 line 7: N-1 ---> K
• page 406 line 9: difficult ---> difficult condition
• page 409 line -2: n ---> N
• page 410 line -3: division ---> divisions
• page 413 line -16: operations ---> operations,
• page 413 line -10: m ---> n
• page 414 line -9: Yet these ---> Yet
• page 415 line 4: b mod n, ---> b mod n;
• page 415 line -4: a_i² mod n ---> a_i² % n
• page 415 line -1: e_it ---> e_i,t+1
• page 416 line 2: c_t ---> c_t+1
• page 416 line 3: c_tv_t ---> c_t+1v_t+1
• page 416 line 8: p_i ---> p_j
• page 416 line -16: F₂^t ---> F₂^t+1
• page 416 line -3: satisying ---> satisfying
• page 417 line -1: b_i ---> b
• page 418 line 2: b_i ---> b
• page 419 line 11: 14 ---> 12
• page 421 line 10: q(x) ---> q(x) = (x+m)² - n
• page 421 line 13: [insert] (We will take a_i = x+m .)
• page 424 line 14: upon upon ---> upon
• page 426 line -18: I ---> the ideal generated by x²+1
• page 427 problems 26.2.01 and 26.2.02 are incorrect: there are no cube roots as indicated. In fact, the interested reader can prove that the only way to acquire a cube root of 2 in a finite field, if there isn't one to begin with, is by taking a cubic extension of the field.
• page 433 line 3: (0,b⁰%p) ---> (0,b⁰%p), (1,b¹%p)
• page 433 line -15: (0,b⁰) ---> (0,b⁰%29)
• page 433 line -5: (0,b⁰) ---> (0,b⁰%101)
• page 434 line 11: (2^-9)⁷) ---> (2^-9)⁷
• page 436 line -5: ['Z' should be boldfaced, twice]
• page 437 line -11: square ---> squares
• page 438 line 4: pair ---> pairs
• page 438 line -14: pair ---> pairs
• page 439 line 8: divisionx ---> divisions
• page 439 line 10: P) ---> P
• page 439 line -12: either of in ---> in either of
• page 439 [Example is incorrect: 1+x lies in the intersection...]
• page 440 [Example is incorrect: 1+x lies in the intersection...]
• page 440 line 15: either of in ---> in either of
• page 442 line -10: unsuccesful ---> unsuccessful
• page 448 line 12: possible ---> possibly
• page 449 line -14: intersect ---> intersects
• p 452, (1/3)^2 - 2 is not 6^2 - 2 :)
• page 487 line 6: will try ---> will not try
• page 488 line 7: 1 ---> id_B
• page 489 line 11: an an ---> an
• page 491 line 13: length L₁ + length L₁ ---> length L₁ + length L₂
• page 491 line 18: length L₁ + length L₁ ---> length L₁ + length L₂
• page 493 line -12: (x₁,x₂)to ---> (x₁,x₂) to [add space]
• page 493 line -9: (x₁,x₂,x₃)to ---> (x₁,x₂,x₃) to [add space]
• page 498 line -22: it's ---> its
• page 509 line 1: 2, 3, 5, 7 ---> 3, 5, 7
• page 511 line [in: header] Roots ---> Roots of Primes
• page 511 line 1: Roots ---> Roots of Primes
• page 516 3.3.05 [lower line of permutation] 5 1 7 2 7 6 3 ---> 5 1 4 2 7 6 3
• page 517 7.8.03 2⁹%11=3 ---> 2⁸%11=3, 2⁹%11=6
• page 517 12.1.06 3 ---> 1
• page 517 12.4.03 500, 111 ---> 500111
• page 517 12.4.03 14, 197 ---> 14197