The **Discrete Logarithm Multiplier** E=DLM_{dlb}(K,C)
allows computation, through a small number of operations, of the
number (E) whose discrete logarithm in a
defined logarithm base (dlb) is equal to the discrete logarithm
of the entry number (C) in the same base, multiplied by a factor
(K) modulo (2^{n}-1).

In other words, E can be found using the following expression :

Note that the discrete algorithm is not known nor computed but, in fact, the final result corresponds effectively to a multiplication of discrete logarithms.

Lets take an example and search vector E with C = 22, dlb = 2,
K = 23. So E = DLM_{2}(23,22)

- DL
_{2}(22) gives 25 (see table for dlb = 2 on page discrete logarithm) - K*25 = 23*25 = 575 or 17 modulo 31
- E can be found by DL
_{2}(E) = 17 - in the table for dlb = 2 we find DL
_{2}(16) = 17 - so E = 16 !

The DLM for dlb = 3, K = 23 and C=16 gives E = DLM_{3}(23,16)

- DL
_{3}(16) gives 13 (see table for dlb = 3 on page discrete logarithm) - K*13 = 23*13 = 299 or 20 modulo 31
- E can be found by DL
_{3}(23) = 20 (see table dlb = 3) - E = 23

Remark : the DLM is a multiplicative group so that it's possible, with the same computing method :

- to compute E knowing C and K and
- to compute C knowing E and K'.