[gnu.emacs.sources] Emacs Cryptographic Library and Tools

burt rosenberg (burt@passaic.cs.miami.edu)
Fri, 22 May 1998 11:34:42 -0400

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> Bruce gives a cite in ACv2:
>
> |> 1596. M.J. Wiener, "Cryptoanalysis of Short RSA Secret Exponents,"
> |>IEEE Transactions on Information Theory, v. 36, n.3, May 1990.
>
> You can get the paper from the OPERA database at www.ieee.org.
>

Or if you want it fast:

knowing x^3 (n_i) for pairwise relatively prime n_i gives, by
the efficiently computed Chinese Remainder Theorem, x^3 (prod_i n_i).
This prod_i n_i is getting big fast (exponential in i), hence soon
x^3 < prod_i n_i. Then the usual cube root is sufficient to extract x.
It's sufficient to take i=3, or for a general "small" exponent d,
let i=d.

-burt

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