APPLIED CRYPTOGRAPHY, Second Edition
ERRATA
Version 1.2 - 1 February 1996
This errata includes all errors I have found in the book,
including minor spelling and grammatical errors. Please
distribute this errata sheet to anyone else who owns a copy of
the book.
Page 7: In line 31, delete the word "source".
Page 10: The second sentence would be clearer as "Replace the
least significant bit of each byte of the image with the bits of
the message."
Page 11: Line 18, the reference should be "[703]" and not
"[699]".
Page 13: Fifth paragraph, first sentence, should read: "The
original German Enigma had three rotors, chosen from a set of
five,...." This increased to three rotors chosen from eight
during the war, and the Navy started using four rotors chosen
from eight.
Page 14: The last sentence should read: "The smallest
displacement that indicates a multiple of the key length is the
length of the key."
Page 16: Third line from the bottom, "1.44" makes more sense as
"1.544".
Page 18: Table 1.1, second item. 1 in 4,000,000 is 2^22. This
makes the third item equal to 2^55.
Page 53: Second to last sentence about SKEY should read:
"Similarly, the database is not useful to an attacker."
Page 55: William Price's first name is Wyn.
Page 60: In Step (4) of the Kerberos protocol, change "Bob
sends" to "Bob creates".
Page 61: Step (3), the second message should contain A instead
of B.
Page 62: In the third line, there's a comma missing.
Page 63: Second protocol, step (2), the second message should be
"S_T(C,K_C)".
Page 70: In the first step (4), the equation should be "R XOR S
= M". In the second step (2), it should be "to generate U".
Page 77: In step (2), the message is signed with Trent's private
key. And T_n is mistakenly both the time and the timestamp.
Page 80: In line 7, "step (3)" should be "step (5)".
Page 82: Fourth line from the bottom, the correct expression is
"up and died."
Page 99: Tenth line from the bottom, delete the second word:
"will".
Page 104: Graph isomorphism has never been proven to be an NP-
Complete problem. It does seem to be hard, and is probably
useful for cryptography.
Page 105: In Step (2), Peggy gives Victor a copy of H'.
Page 106: In the first line, "step (3)" should be "step (4)".
Page 112: Step (1) should read "Alice takes the document and
multiplies it by a random value."
Page 116: The protocol could be worded better. Step (3) should
begin: "Alice decrypts Bob's key twice, once with each of her
private keys." Step (4) should begin: "Alice encrypts both of
her messages, each with a different one of the DES keys...."
Page 126: The "Voting with Blind Signatures" protocol is a
little more complicated. The voter does not send all the
blinding factors in step (2). The CTF requests 9 of 10 blinding
factors in step (3), and the voter sends only those blinding
factors to the CTF. Additionally, in step three only the one
messages (containing a set of
votes) that has not been unblinded will effectively be signed by
the CTF.
Page 134: Another problem with this protocol is that there are
numerous ways that various participants can cheat and collude to
find out the salary of another participant. These cheaters can
misrepresent their own salaries during their attack.
Page 135: Lines 13-14; technically Alice and Bob get no
additional information about the other's numbers.
Page 136: Lines 14-15; technically Alice and Bob get no
additional information about the other's numbers.
Page 144: Line 27, the odds should be "1 in n". Line 29, "step
(2) should be "step (1)".
Page 146: Fourth line from the bottom, delete the word "that".
Page 161: In the eleventh line from the bottom, "harnesses"
should be "harnessed".
Page 175: Line 8, it's really triple-DES encryption.
Page 181: Line 8 should read "he does not know it" instead of
"he does know it".
Page 195: In line 13, the reference number should be [402].
Page 201: Error Propagation, lines 5-6. The sentence should
read: "In 8-bit CFB mode, 9 bytes of decrypted plaintext are
garbled by a single-bit error in the ciphertext."
Page 202: Third to last line, toggling individual bits does not
affect subsequent bits in a synchronous stream cipher.
Page 203: Section 9.8, both equations should be "S_i = E_K(S_(i-
1))".
Page 209: Table 9.1. CFB, Security: Bits of the last block can
be changed, not the first. CFB, Efficiency: The speed is the
same as the block cipher only in 64-bit CFB. CFB and OFB,
Efficiency: "Ciphertext is the same size as the plaintext" should
be a plus.
Page 213: In the last line of the third paragraph,
"cryptanalyze" is misspelled.
Page 217: The Table 10.1 headers got garbled. They should be:
"Algorithm", "Confidentiality", "Authentication", "Integrity",
and "Key Management".
Page 246: The last line should be: "#define isEven(x) ((x &
0x01) == 0)".
Page 249: Line 9, "Euclid's generalization" should be "Euler's
generalization".
Page 251: Lines 20-21. The sentence should read: "For example,
there are 11 quadratic residues mod 35: 1, 4, 9, 11, 14, 15, 16,
21, 25, 29, and 30." See page 505 for more details.
Page 258: In line 27, his name is spelled "Chandrasekhar".
Page 259: Lehmann reference "[903]" should be [945]".
Page 275: Figure 12.4; "46-Bit Input" should be "48-Bit Input".
Page 287: In line 13, "first and third" should be "second and
third".
Page 287: In Figure 12.6, there should be no period in X or Y.
Page 288: In figure 12.7, the final output on the right side
should be DELTA=0.
Page 292: Second line, "b_24" should be "b_26". In line 10,
"1/2 - .0061" should be "1/2 + .0061".
Page 295: Fourth line from the bottom, 2^(120/n) should be
(2^120)/n.
Page 300: In the first line, "56" should be "48".
Page 306: The first sentence is wrong. The key is rotated to
the right; the key and data move in opposite directions to
minimize redundant key bit operations. Also, the XOR happens
after the rotation. The third paragraph should be modified to be
the opposite of this. In any case, Madryga is vulnerable to
differential cryptanalysis with about 5000 chosen plaintexts.
Don't use it.
Page 307: Last line, "complementation" is misspelled as
"complemention".
Page 311: Second paragraph, second line should be: "it more
quickly than by brute force..."
Page 316: In Table 13.2, P_2 should be "379", not "279".
Page 319: In line 11, Section "25.13" should be "25.14".
Page 322: Last line, the chip is 107.8 square mm.
Page 325: Last line, "mod 3" should be "mod 4".
Page 338: In Figure 14.3 and in the first line, "f" should be
"F".
Page 340: Second equation should be "mod 256".
Page 341: The current variants of SAFER are SAFER SK-40, SAFER
SK-64, and SAFER SK-128, all with a modified key schedule, in
response to a theoretical attack by Lars Knudsen presented at
Crypto '95.
Page 342: In the description of 3-Way, "K^(n+1)" should be
"K_n".
Page 345: Lines 10 and 11; the + should be a -.
Page 346: The reference number for BaseKing should be [402].
Page 352: In line 8, that second "l" should be an "r".
Page 358: In the decryption equation of Davies-Price mode, the
final D should be an E.
Page 362: In the first equation, P is used to indicate both
padding and plaintext. If P is plaintext and p is padding, then
the equation should be: C = E_K3(p(E_K2(p(E_K1(P))))).
Page 362: Figure 15.2 is wrong. The middle and top rows of
"Encrypt," and the plaintext feeding them, are shifted right by
1/2 block from where they should be.
Page 363: The parenthetical remark would be clearer as:
"encryption with one of n different keys, used cyclically".
Page 363: Second to last line, the equation should have an I_2
in place of the I_1.
Page 367: Second equation, "P XOR K_3" should be "C XOR K_3".
Page 369: A maximal period linear congruential generator as a
period of m, not m-1.
Page 375: Third paragraph should read: "It is easy to turn this
into a maximal period LFSR. The highest exponent is the size of
the register, n. Number the bits from n-1 to 0. The exponents,
including the 0, specify the tap sequence, counting from the
right of the register. The x^n term of the polynomial stands for
the input being fed into the left end." The next paragraph is
wrong, as is the code and the figure.
Page 379: Second line of code has an extra close parentheses.
Page 380: The fourth line should begin: "On the other hand, an
astonishingly...."
Page 382: In paragraph 4, "LFSR" would be more clear if it were
labeled "LFSR-2". Similarly, in the first sentence of paragraph
5 "LFSR" would be more clear if it were labeled "LFSR-3".
Page 384: Bilateral Stop-and-Go Generator: To agree with Figure
16.11, reverse "LFSR-1" and "LFSR-2".
Page 389: Some more details on the GSM algorithms. A3 is the
authentication algorithm in the smart card. A8 is just a bit
shuffling process that takes part of the output of A3 and turns
it into a session key for A5. A5 is the privacy algorithm.
There are two algorithms used in GSM: A5/1 and A5/2. A5/1 can be
used by only certain countries; A5/2 can be used by all
countries.
Page 391: In the 11th line under Fish, it should be "D_j"
instead of "D_i".
Page 393: In Figure 16.17, there should be an arrow from the
fourth byte to the Output Function.
Page 393: Second sentence should be: "It's a method for
combining multiple pseudo-random streams that increases their
security."
Page 398: In the third line of the section on SEAL, "kilobytes"
is misspelled as "kiloytes".
Page 411: Another option for an alternating stop-and-go
generator would be to use a LFSR in Register-2, a FCSR in
Register-3, and either in Register-1. This may have advantages
over either of the three constructions listed.
Page 420: Table 17.3, the speed should be in kilobytes/second.
Page 429: The second sentence should be: "It returns a fixed-
length hash value, h."
Page 431: In step (2), "prepend" instead of "append".
Page 440: In item 3, there is an "AND" missing in the equation.
Page 441: The compression function of MD2 is confusing without
the indentations. The two for-loops are nested; the inner loop
includes the next two statements; and the other loop the
statement after that.
Page 443: Last paragraph, the operation number runs from 0 to
79.
Page 444: In figure 18.7, the a, b, c, d, and e variables are
backwards.
Page 445: Line 14, SHA should be compared to MD4.
Page 447: Lines 3-4 should read: "...CFB in [1145], CBC in
[55,56,54]...."
Page 449: Figure 18.9, M_i and H_i-1 in the upper-left diagram
should be reversed.
Page 454: Seventh and sixth lines from the bottom, Z is the sum
of the message blocks as if they were 256-bit integers.
Page 456: Table 18.2. It's "Hash Speeds", not "Encryption
Speeds", and it is measured in "kilobytes/second". "SNEERU"
should be "SNEFRU".
Page 465: In the third line of text, the number should be n^-1.
Page 469: Table 19.3, the "Clock Cycles" entry for the Siemens
chip should be ".3M".
Page 470: Sixth line from the bottom, the n' should be an m'.
Page 470: The second to last line is missing an "is".
Page 471: In the sixth line from the bottom, "n'^d mod n" should
be "m'^d mod n".
Page 480: An additional reference for elliptic-curve
cryptosystems is N. Koblitz, A Course in Number Theory and
Cryptography, Second Edition, Springer-Verlag, 1994. This is an
excellent book, and omitting it was an oversight.
Page 481: Second-to-last line, delete the word "a".
Page 487: In two places the second to last paragraph,
"recompute" should be "precompute".
Page 489: Caption to Table 20.3 should specify an "80386 33 MHz
personal computer".
Page 495: In Step (8), the constant should be "0x7fffffff".
Page 497: Delete the fourth equation in the list of verification
equations.
Page 499: ESIGN, seventh line: "m-1 should be "n-1".
Page 505: In step 3, the third sentence should be: "If Victor's
first bit is a 1, then s_1 is part of the product...."
Page 514: In step (1), Alice must send X to Bob. In step (9)
"X'^y" should be "X'^z".
Page 515: In line 1, "commutative" is misspelled as
"communitive".
Page 515: Hughes. Step (2): In order for step (4) to work, y
must be relatively prime to n-1 else the inverse function in step
(4) won't work. If n is a strong prime such that (n-1)/2 is also
prime, then y can be any odd random large integer except for
(n-1)/2. In step (4), Bob computes: z=y^-1 mod (n-1).
Page 516: In the Station-to-Station protocol, the exponentiation
is missing. In step (1), Alice sends Bob g^x mod n. In step
(2), Bob computes the shared key based on g^x mod n and y. He
signs g^x mod n and g^y mod n, and encrypts the signature using
k. He sends that, along with g^y mod n, to Alice. In step (3),
Alice sends a signed message consisting of g^x mod n and g^y mod
n, encrypted in their shared key.
Page 517: In the fifth equation, every "M" should be a "P".
Page 521: In the equations of Steps (1) and (2), the lowercase
"r" should be uppercase. And in the equation of Step (2), "r^a"
should be "R^b".
Page 522: Fortified Key Negotiation: "k" is the password;
H(k,x) can be a normal hash function on k concatenated with x.
In the fifth line from the bottom, "H * (P,K2)" is supposed to be
H'(P,K2).
Page 529: Line 13 should be a polynomial of degree 5, not 6;
also, the entire polynomial is mod p.
Page 535: The technique wherein Mallory leaks 10 bits of DSA
secret per signature, can be sped up by a factor of 16 or so.
Instead of choosing a 4-bit block randomly and then searching for
a k that leaks
the correct 14 bits, he can just use the low 4 bits of r to
select the block of the signature to leak (no need to have an
opaque subliminal channel) and he only has to check an average of
1024 k values until the bits sent out over the 10 subliminal
channels match the 10 bits of the secret selected by r = (g^k mod
p) mod q.
Page 568: In the Kerberos Version 5 Messages, step 3, the final
"s" should be deleted.
Page 586: Figure 24.7, in the key the arrow should point from y
to x.
Page 586: Seventh line, "revokation" should be spelled
"revocation".
Page 589: Section 24.15, fourth line: "Nambia" should be
"Namibia".
Page 592: The equation is wrong. The structure of the LEAF is
"E_KF(U,E_KU(K_S),C)", where U is the 32-bit unit ID, K_S is the
80-bit session key, and C is a 16-bit checksum of K_S and the IV
(and possibly other material) used by the receiving chip to
ensure that it has a valid LEAF.
Page 592: In the third paragraph, the reference to section 3.5
should be 3.6.
Page 600: The area code for the NSA is 410, not 301.
Page 604: Fourth line from the bottom should read: "to U.S.
patent law."
Page 604: In Table 25.3, the issue data for patent #4,200,770 is
4/29/80.
Page 605: In the fourth paragraph, the date when the
Diffie-Hellman key exchange will enter the
public domain is April 29, 1997.
Page 606: In lines 12 and 13, the cross-references to sections
in chapter 14 are to chapter 18.
Page 607: In Table 25.4, the column headers are reversed.
Page 609: Second to last line, the "Census Office" should be the
"Patent Office".
Page 610: Sixth line should read "it is filed", not "it is
filled".
Page 676: In reference 19, the author is "Rumeley".
Page 680: In reference 140, the author is "Berlekamp".
Page 683: In reference 210, the title of the paper is "A
Comparison of Three Modular Reduction Functions".
Page 697: In reference 550, the second author should be "M.Y.
Liberman".
Page 704: In reference 703, it should be "Communications of the
ACM".
Page 705: In reference 727, subscript should be a superscript.
Page 718: In reference 1067, the year should be "1988".
Page 735: In reference 1505, the second author should be "V.G.
Gligor".
This errata is updated periodically. For a current errata sheet,
send a self-addressed stamped envelope to: Bruce Schneier,
Counterpane Systems, 101 East Minnehaha Parkway, Minneapolis, MN
55419; or send electronic mail to: schneier@counterpane.com.