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