Errata 1 (First printing)

p. xiii line 10 "EEF" should be "EFF"
p. xiii line 15, "mod-2000" should be "mid-2000"
p. xiv line 8 delete both "for"'s
p. xvii line 2 correct doubled "that that" to simply "that"
p. xviii lin -8 change "does easily" to "does not easily"
p. 5 lines 5-6, replace ciphertext by "UIFTF BSF UJNFT UIBU NLBF VT UJSFE"
p. 6 line 4, replace "1.7+3" by "6.2+0"
p. 8 line 15, "r<0" and "r'<0" should be "r<m" and "r'<m"
p. 8 line 19, "q-q" should be "q'-q"
p. 9 line 8, "modulo m" should be "modulo n"
p. 10 line 10, the left-hand side of the equality should be

p. 11 line 6, "not matter" should be "no matter"
p. 13 line -4, "decription" should be "decryption"
p. 16 line -19, "3.x+7" should be "11.x+5"
p. 24, lines 9 and 10, the "10" should be "N"
p. 29, line -1, insert minus sign on right side of inequality
p. 32, second display, replace "character" by "word"
p. 32, line 17, replace "is ciphertext-only" by "in ciphertext-only"
p. 33, in display, replace "e 9.53" by "t 9.53"
p. 33, in display, replace "e 8.22" by "o 8.22"
p. 36, line -2, replace "words" by "characters"
p. 41, line 16, replace "R - 1.7" by "R - 2".
p. 47, line 10, replace "LYICCB" by "ELYICCB"
p. 56, line -1, replace "n by n" by "n by m"
p. 59, in second large display:

p. 62, line 19, replace "3-and-a-third" by "2-and-a-third"
p. 70, line 14, replace "0-10" by "1-10"
p. 70, line 16, delete summand "one-tenth 0-squared" in display
p. 70, line 17, replace "0-10" by "1-10" and "5" by "5.5"
p. 70, line 18, replace "25" by "30.25"
p. 83, line -1, replace "+" by "-", and "k_2-k_0" by "k_2-k_1"
p. 102, line 11, replace two occurrences of "56" by "57"
p. 107, after line 10, insert (in italics) "(Note: in late 2000 Rijndael was chosen as AES.)"
p. 114, line 8, replace "suppose that some integer n>1 did" with "let n be the least integer to"
p. 132, line -3, replace "enought" by "enough"
p. 133, line 8, replace "x'" with "y"
p. 136, line -4, replace "integers" with "candidates"
p. 143, line 9, replace "p superscript 4" with "p superscript 4(e-1)"
p. 143, line 12, delete "p superscript n-squared"
p. 145, line 1, delete "(?)"
p. 145, line 3, replace superscript "1" with superscript "-1"
p. 161, line 24, replace "x-superscript-e % m" by "x-superscript-e % p"
p. 163, line 3, replace "mod 4189" by "mod 4060"
p. 163, line -8, replace "encryption/decryption" by "encryption and decryption"
p. 163, line -8, replace "works" by "work"
p. 164, line 4, replace "we must assume" by "Euler's theorem requires".
p. 164, line 9, at end of paragraph insert "In fact, here Euler's theorem works without assuming gcd(x,n)=1."
p. 165, line -14, replace "p+1" by "p+q"
p. 167, lines -16, -15, replace "8 hours" by "3 days"
p. 172, line 15, replace "that RSA" with "than RSA"
p. 180 last display replace "m" by "x"
p. 183, line 14, replace "convincing" with "plausible"
p. 183, line 14, replace "that seems to break the cipher (and related ciphers)" with "for a class of attacks on this and related ciphers"
p. 186, line -3, replace "the Arithmetica cipher" by "such ciphers"
p. 187, line 7, replace "does not completely break" with "is ineffective against"
p. 203, line -6, replace "12, 5" with "1,2,5"
p. 204, line 11, replace "23, 57" with "2,3,5,7"
p. 204, line -3, replace "7..13" with "7.31"
p. 204, line -1, replace "127" with "17"
p. 205, line 12, replace "7.34=1" with "7.34+1"
p. 205, line 13, replace "23, 57, 1113" with "2,3,5,7,11,13"
p. 205, line 14, replace "8.34=1" with "8.34+1"
p. 205, line 14, replace "9.34=1" with "9.34+1"
p. 209 line -12 replace "10" by "2"
p. 210, line 17, replace "garbage" with "not a square root of the number"
p. 210-11, replace all three-line "congruence" symbols with simple equality signs
p. 211, line 2, replace "if y is a square root" with "if y is a non-zero square root"
p. 211, line -1, replace "(y^r)^n)" by "(y^r)^n" (that is, delete trailing parenthesis)
p. 211, line -1, insert "mod p" at the end of the displayed line
p. 212, line 15, replace "(y^r)^n)" by "(y^r)^n" (that is, delete trailing parenthesis)
p. 212, line 15, replace "x^l (p-1)" with "x-superscript-(l.(p-1))". That is, ell-times-(p-1) is in the exponent
p. 212, line 16, replace "(x^p-1)^n" with "(x^p-1)^ell"
p. 232, lines -1 and -2, insert space between "p" and "if"
p. 246, line -6, replace "(p-1)(q-1)/2" (in the exponent) by "(p-1)(q-1)/4", that is, replacing the denominator "2" by "4"
p. 252, line -2, replace "4 to 2" by "4 to 3"
p. 257, line -8, replace three-line congruence symbol by simple equality sign
p. 259, lines 17-19, replace "note that... 1 mod b" by "recall Fermat's observation that for b>1 gcd(b^m-1,b^n-1) = b^gcd(m,n) - 1. Thus, gcd(b-1,b^n-1)=b-1, and gcd(b-1,(b^n-1)/(b-1))=1."
p. 263, line -9, replace "Euler" with "strong"
p. 263, line -9, replace "pseudoprimes" with "pseudoprime"
p. 264, line 11, replace "b-sub-1" with "b-sub-0"
p. 265, line 11, replace "b-sub-1" with "b-sub-0"
p. 265, line 16, insert "b-sub-1" just before "b-sub-2"
p. 274, line 2, replace "g-superscript-(m+n)" with "g-sup-m . g-sup-n"
p. 274, line 6, replace "smallest exponent" by "smallest positive exponent"
p. 299, line 13, delete "prime or"
p. 299, line 15 replace "prime" by "irreducible"
p. 307, line -5, replace "a function" by "a real-valued function"
p. 317, in the statement of the proposition: The proposition should read "Let f be a polynomial with coefficients in a field k. Let P be a polynomial with coefficients in k. On one hand, if P² divides f, then P divides gcd(f,f'). On the other hand, if the characteristic p of k is positive, if P is irreducible, if every element a in k has a pth root in k, and if P divides gcd(f,f'), then P² divides f. (Note that the latter condition holds, for example, for finite fields Z/p with p prime.)"
p. 318, from the top of the page until the end of the proof, the text should be "Let b_i be a pth root of a_i in k. From above, the latter expression is the pth power of

b_pmxⁿ + b_p(m-1)x^m-1 + b_p(m-2)x^m-2 + ... + b_2px² + b_px+b₀

R=0

P²

p. 320 line 1 change "m=n" to "m and n"
p. 335, line -4, insert ellipsis+comma "...m" before "s-sub-n"
p. 335, line -1, replace "s-sub-(n-3)" by "s-sub-(n-N+1)"
p. 337, line -11, replace "a-sub-1" by "s-sub-1"
p. 366, line 14, replace "cyclid" by "cyclic"
p. 374, line -10, replace "then for 2" by "then 2"
p. 393, line 1, replace "which" by "such that p-1"
p. 393, line 20, replace "1=g" by "g=1"
p. 393, line -7, delete "B-smooth" and replace "of n" with "of n such that p-1 is B-smooth"
p. 394, lines 6, 9, 13, replace "b^T" by "b^T - 1". That is, the exponent is T, and there should be a subtraction of 1, _not_ in the exponent: (b^T)-1
p. 395, line 12, replace "2604247" by "2604247-1"
p. 415, line -4, replace "redn" by "% n"
p. 417 lines -1 replace "b-sub-i" by simply "b"
p. 417, line -1, replace 3 times "a" by "a-sub-i"
p. 418, lines 2,3 replace 3 times "a" by "a-sub-i"
p. 418 line 10, replace "14" by "12"
p. 429, lines 13 and 22, replace "bold-F2" by "bold-F-sub-2"
p. 433, line 7, replace "b-sup-minus-1" by "b-sup-minus-m"
p. 434, line 13, should be "log_2 3 = 9.7 + 6 = ..."
p. 435, line 19 (middle line in display), replace "x^2" by "X^2", that is, lowercase "x" by uppercase "X"
p. 435, line -6, replace "=e" by "=X-sub-o"
p. 435, line -5, replace "f(f(Y))" by "f(f(Y_i))"
p. 437, line -11, replace "square mod 59" by "squares mod 59"
p. 437, line -6, replace "log_b 9" by "log_4 9"
p. 452, line 2, replace "which are" by "which is"
p. 466, lines 1-2, replace

p. 501, line -8, replace "ln 1 + ln 1" by "ln 1 + ln 2"
p. 516, solution to 1.01.08 should be "These are the times that make us tired"
p. 516, solution to 1.03.02 should be "VHDSJKBTV"
p. 517, solution 10.02.05, replace "9854" by "9611"