Visible to Intel only — GUID: GUID-E0CB0E82-3A21-4515-8884-A87322179164
Visible to Intel only — GUID: GUID-E0CB0E82-3A21-4515-8884-A87322179164
RSA Algorithm Functions (MBX)
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 = xemod n, x and y are plane- and ciphertext correspondingly
RSA private key (1-st representation) operation
x = ydmod n, y and x are cipher- and plaintext correspondingly
RSA private key (2-nd representation) operation or CRT-based RSA private key operation
x1 = ydPmod p
x2 = ydQmod q
t = (x1-x2) * qInv mod p
x = x2 + q*t