Fingerprinting Codes - Encryption for Digital Content - page 28

Choosing `,Z to be the smallest value allowed by the above constraints, we
can set

` = 3· (1−3wβ) −1 · 1

· log( 1

α + w )

(1.27)

β

Instantiating the construction. We find t,α,β,`,Z that satisfy the bounds
given in ( 1.18 ) ,( 1.20 ) , ( 1.21 ) , ( 1.23 ) and ( 1.26 ) . Below for illustration purposes
we provide a possible choice:

1
12w 2 6w t = 1

1

α = β =

300w
Which allows determining the basic parameters as follows:
Z = 24·w· log( 1

)
` = 108·w 2 · log( 1

)
We note finally that the analysis of framing an innocent user was performed
for a single user and thus in order to accommodate a number of n users as
well as the two error summants in the bound calculation, the error parameter
in the above expressions can be set to log(2n/). This completes the proof of
theorem 1.21 .

1.4.5 Code Concatenation

As illustrated in the results of this section the challenge in the design of fin-
gerprinting codes is to support many reasonably long codewords while main-
taining a small alphabet size. Code concatenation is a technique utilized ex-
tensively in coding theory and is proven effective in reducing alphabet size
in code designs. The technique is also useful in the context of fingerprinting
codes yielding valuable trade-offs in the e ciency parameters of a fingerprint-
ing code. We investigate this further in this section.
Code concatenation entails the composition of two codes: an “inner” code
with an “outer” code. The composition is feasible as long as the codes adhere
to a suitable structural characteristic. The end effect is that the codewords
of the inner code substitute the alphabet symbols of the outer code. In more
details we have the following.
Code Generation for a q-ary Concatenated Code. Given the number
of users n, an intermediate value n 1 is chosen as a function of q and n. The
technique, then, employs two fingerprinting codes as follows:
• An inner q-ary fingerprinting code (Codegen in ,Identify in ) over an al-
phabet Q in . This inner fingerprinting code is chosen to be collusion resis-
tant against any traitor coalition size, with possibly some failure proba-
bility; the code generation will be executed on input 1 n 1 , i.e., produce n 1
codewords.