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Session 1. Analytic Number Theory
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\((d, B)\) - exceptional numbers with applications to cryptology |
Jacek Pomykała, Warsaw University, Poland
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In the lecture we define \((d, \zeta^i, B)\)-exceptional primes
\(p\). We prove the upper bound for the corresponding primes when
\(i=0\). The possible extensions will be announced. As an
application the lower bound for the number of large prime
\(q\)-orders (\(q|d\)) of elements generated by small intervals
\([1,B] \mod p\) is established. In this connection the
computational efficiency of cryptographic systems designs will be
underlined.
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