A high performance ROM-based structure for modular exponentiation

Modular processing of large numbers requires high speed computing resources. In particular an operation slowing the whole computing process heavily is modular exponentiation.A previous method reduces the computation of |xe|m|xe|m to n   simpler modular exponentiations |xiηi|mi at most, where mimi is an element of the factorization of m  , xi=|x|mixi=|x|mi and ηi

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► Modular exponentiation heavily affects the speed of modular arithmetic computation.
► Generally, high speed can be obtained using tables, but they may result too large.
► By defining an extended discrete logarithm, table size can be reduced.
► Modular exponentiation needing tables with address up to 56-bit can be performed using tables with halved address.