A Method for Rapid RSA Key Generation

Abstract

Systems Development Laboratory, H i t a c h i , L t d . , Kawasaki, Japan 215 SUMMARY The RSA p u b l i c key cryptosystem i s one of t h e cryptosystems which can be a p p l i e d n o t only t o t h e s e c u r i t y p r o t e c t i o n b u t a l s o t o t h e v e r i f i c a t i o n s of o t h e r u s e r s and messages. It i s one of t h e most important techniques i n ensuring t h e s e c u r i t y of information.To c o n s t r u c t a secure RSA p u b l i c key cryptosystem, t h e key must be generated usi n g primes which are r o b u s t a g a i n s t a " ( p + 1) f a c t o r i z i n g a t t a c k . " For t h i s purpose, Gordon proposed a method of g e n e r a t i n g t h e key by s i e v i n g using known primes less than 8 b i t and by employing t h e higher-order exponential c a l c u l a t i o n . This paper i s an extension of Gordon's approach.The range of known primes i s defined optimally through an e v a l u a t i o n f o r t h e s i e v i n g primes less than 32 b i t . The expon e