Hi Joy When one uses a subgroup like defined in RFC 5114, q (and (p-1)/2q ) must be chosen carefully.
Precisely: 1. q must be a prime number of 2k or more bits where k is a security parameter. 2. q must be a divisor of ((p - 1) / 2). 3. Every factors of (p - 1) / (2q) must also be primes comparable to or greater than q in size. p corresponding such q is called a "secure prime." X is simply to shift the range of 0 to q-2 to 1 to q-1 to exclude 0 (since g^0 mod p = 1). Kaz > -----Original Message----- > From: ipsec-boun...@ietf.org [mailto:ipsec-boun...@ietf.org] On Behalf Of > Joy Latten > Sent: Saturday, March 27, 2010 6:25 AM > To: mlepin...@bbn.com; k...@bbn.com > Cc: ipsec@ietf.org; avaga...@redhat.com > Subject: [IPsec] Question about RFC 5114 > > Hi, > > I am looking to implement modp groups 22, 23, and 24 into IKE but have a > question. > > RFC 5114 gives the prime, p, the generator, g and a subgroup, q, with a > specific size... > > Because prior rfcs for modp groups did not specify a "q", I was not sure > if this was a new constant or just stating a size requirement? > So I took a look at NIST 800-56A. In particular, > > 5.6.1 Private/Public Key Pair Generation > > 5.6.1.1 FFC Key Pair Generation > For the FFC schemes, each static and ephemeral private key and public > key shall be generated using an Approved method and the selected valid > domain parameters (p, q, g{, SEED,pgenCounter}) (see Appendix B of FIPS > 186-3). > ... > > I then took a look at FIPS 186-3, Appendix B, which documents 2 methods > for finite field cryptography (FFC) key pair generation. > For example, one method is "Key Pair Generation Using Extra Random > Bits". It actually states that "q" is an input and it is used to do an > additional computation to compute "x". > > I am somewhat confused, are the modp groups 22, 23 & 24 suppose to use > one of these new methods and that is why "q" is given in rfc 5114? > Or am I to ignore this and just continue with existing way > where "q" is not used and there aren't any additional computations > to compute x. > > I am not even sure this is correct place to ask, but any advice > would be welcome. > > regards, > Joy > > > (Cut-n-paste from FIPs 186-3 below to show input and process) > > Input: > (p, q, g) The subset of the domain parameters that are used > for this process. p, q and g shall either be > provided as integers during input, or shall be > converted to integers prior to use. > > Process: > 1. N = len(q); L = len(p). Comment: Check that the (L, N) pair > is specified in Section 4.2. > 2. If the (L, N) pair is invalid, then return an ERROR indicator, > Invalid_x, and Invalid_y. > 3. requested_security_strength = the security strength associated > with the (L, N) pair; see SP 800-57. > 4. Obtain a string of N+64 returned_bits from an RBG with a security > strength of requested_security_strength or more. If an ERROR > indication is returned, then return an ERROR indication, > Invalid_x, and Invalid_y. > 5. Convert returned_bits to the (non-negative) integer c (see > Appendix C.2.1). > 6. x = (c mod (q–1)) + 1. Comment: 0 ≤ c mod (q–1) ≤ q–2 and > implies that 1 ≤ x ≤ q–1. > 7. y = gx mod p. > 8. Return SUCCESS, x, and y. > > _______________________________________________ > IPsec mailing list > IPsec@ietf.org > https://www.ietf.org/mailman/listinfo/ipsec _______________________________________________ IPsec mailing list IPsec@ietf.org https://www.ietf.org/mailman/listinfo/ipsec
