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Hi.

There are well-known algorithms for cryptography to compute modular exponentiation $a^b\%c$ (like Right-to-left binary method here : http://en.wikipedia.org/wiki/Modular_exponentiation).

But do algorithms exist to compute modular exponentiation of the form $a^{\left(2^N\right)}\%m$ faster than with "classical" algorithms ?

Thank you very much !

Notes :

1) $m$ has no particular property

2) $N < 2^{32}$

2 removed incorrect tag and fixed typo

Hi.

There are well-known algorithms for cryptography to compute modular exponentiation $a^b\%c$ (like Right-to-left binary method here : http://en.wikipedia.org/wiki/Modular_exponentiation).

But do algorithm algorithms exist to compute modular exponentiation of the form $a^{\left(2^N\right)}\%m$ faster than with "classical" algorithms ?

Thank you very much !

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# Fastest algorithm to compute (a^(2^N))%m?

Hi.

There are well-known algorithms for cryptography to compute modular exponentiation $a^b\%c$ (like Right-to-left binary method here : http://en.wikipedia.org/wiki/Modular_exponentiation).

But do algorithm exist to compute modular exponentiation of the form $a^{\left(2^N\right)}\%m$ faster than with "classical" algorithms ?

Thank you very much !