Contents

# RSA Algorithm Functions

## RSA Notation

The following description uses PKCS #1 v2.1: RSA Cryptography Standard conventions:
• n
- RSA modulus
• e
- RSA public exponent
• d
- RSA private exponent,
e*d = mod lambda(n), lambda(n) = LCM
• (n, e)
- RSA public key
• a pair
(n, d)
- so-called 1-st representation of the RSA private key
• p, q
- two prime factors of the RSA modulus
n, n = p*q
• dP
- the
p
's CRT exponent,
e*dP = 1 mod(p-1)
• dQ
- the
q
's CRT exponent,
e*dQ = 1 mod(q-1)
• qInv
- the CRT coefficient,
q*qInv = 1 mod(p)
• a quintuple
(p, q, dP, dQ, qInv)
- so-called 2-nd representation of the RSA private key
All the numbers above are positive integers.
Keep in mind the following assumptions:
• Current implementation supports RSA-1024, RSA-2048, RSA-3072 and RSA-4096 (the number denotes size of RSA modulus in bits)
• Public exponent is fixed, e=65537
• No specific assumption relatively "
d
", except bitsize(d) ~ bitsize(n) and
d<n
• Size of
p
and
q
in bits is approximately the same and equals bitsize(n)/2

## RSA public key operation

y = x
e
mod n, x
and
y
are plane- and ciphertext correspondingly

## RSA private key (1-st representation) operation

x = y
d
mod n, y
and
x
are cipher- and plaintext correspondingly

## RSA private key (2-nd representation) operation or CRT-based RSA private key operation

x1 = y
dP
mod p
x2 = y
dQ
mod q
t = (x1-x2) * qInv mod p
x = x2 + q*t

#### Product and Performance Information

1

Performance varies by use, configuration and other factors. Learn more at www.Intel.com/PerformanceIndex.