Method and apparatus for exponentiation in an RSA cryptosystem

Details Method and apparatus for exponentiation in an RSA cryptosystem Method and apparatus for exponentiation in an RSA cryptosystem

2007-02-13

2007-02-13

Jung, David (Department: 2134)

Cryptography

Particular algorithmic function encoding

C380S030000, C380S277000

Reexamination Certificate

active

10863162

ABSTRACT:
A method of computing an exponent of a message m in an RSA cryptosystem having a private key d, a public key e and system parameters p, q where p and q are primes and ed=1 mod (p−1) (q−1). The method comprises the steps of obtaining a value r, and exponentiating the value r to the power e to obtain an exponent remod p, combining said exponent rewith the message m to obtain a combined value rem and mod p; selecting a value s and obtaining a difference (d−s), exponentiating the combined value with said difference to obtain an intermediate exponent (rem)d−s, multiplying the intermediate exponent by a value msto obtain a resultant value equivalent to r1−esmdand multiplying the resultant value by a value corresponding to r1−esto obtain an exponent corresponding to mdmod p.

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