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

H - Electricity

04

L

H04L 9/00 (2006.01) H04L 9/14 (2006.01)

Patent

CA 2470422

A method of computing an exponent of a message m in an RSA cryptosystem having a private key d, a public key a 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 r e mod p, combining said exponent r e with the message m to obtain a combined value r e m 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 (r e m) d-s, multiplying the intermediate exponent by a value m s to obtain a resultant value equivalent to r l-es m d and multiplying the resultant value by a value corresponding to r l- es to obtain an exponent corresponding to m d mod p.

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