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RFC 4226, "HOTP: An HMAC-Based One-Time Password Algorithm", December 2005

Source of RFC: IETF - NON WORKING GROUP
Area Assignment: sec

Errata ID: 2405
Status: Held for Document Update
Type: Technical
Publication Format(s) : TEXT
Reported By: Alfred Hoenes
Date Reported: 2006-01-18
Held for Document Update by: Sean Turner
Date Held: 2010-07-30

Section A.4.1 says: 

(6)  [ typos in mathematical text ]

Lemma 1 and its proof in Appendis A.4.1, on page 20, contains
several typos.

In Lemma 1, the line,

          P_{N,m}(z) = Pr [x mod m = z : x randomly pick in Z_{n}]
                                                              ^^^
should read:

          P_{N,m}(z) = Pr [x mod m = z : x randomly pick in Z_{N}]

This corrects the use of an undefined variable, n, by using the
variable N as expected from the LHS term.

In the Proof of Lemma 1, the case distinction for z contains an
improper relational operator at two places.
To adjust to the possible range of values (cf. item (2) above!),
the formula parts:

   P_{N,m}(z)  =  [ ... ]

                = mq/N * 1/m +
                   (N - mq)/N * 1 / (N - mq)     if 0 <= z < N - mq
|                  0                             if N - mq <= z <= m
                                                               ^^^^
                = q/N +
                   r/N * 1 / r                   if 0 <= z < N - mq
|                  0                             if r <= z <= m
                                                          ^^^^
should be modified to read:

   P_{N,m}(z)  =  [ ... ]

                = mq/N * 1/m +
                   (N - mq)/N * 1 / (N - mq)     if 0 <= z < N - mq
|                  0                             if N - mq <= z < m

                = q/N +
                   r/N * 1 / r                   if 0 <= z < N - mq
|                  0                             if r <= z < m

It should say:

see above

Notes:

typos

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