# P. Grabner, C. Heuberger, H. Prodinger, and J. Thuswaldner --- Analysis of linear combination algorithms in cryptography --- Online Resources

## Joint Non-Adjacent-Form

For *d*=1,2,3,4,5, the file Joint-NAF-results.m contains
the generating function `GF[d]`

, the expected value E(W_{n,w}) `Expectation[d]`

and the variance V(W_{n,w}) `Var[d]`

.
The expected value and the variance are correct up to an error term of *o*(1).

## Simple Joint Sparse Form

For *d*=1,...,20, the file SJSF-NAF-results.m contains
the generating function `GF[d]`

, the expected value E(W_{n,w}) `Expectation[d]`

and the variance V(W_{n,w}) `Var[d]`

.
The expected value and the variance are correct up to an error term of *o*(1).

*Note:* Both files are suitable to be read with Mathematica® using `<<Joint-NAF-results.m`

,
but they are just plain text.
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Last modified on August 26, 2004 by Clemens Heuberger

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