³ò ’K¯Dc@s[dZdZdZddklZdefd„ƒYZdd d„ƒYZed „Z d S( sThis module implements SRP-6a (see http://srp.stanford.edu/design.html). Variable names used here match those used in the description on that page: N a large prime number (N = 2q + 1, where q is prime) g a generator (primitive root) modulo N k a multiplier parameter (k = H(N, g) in SRP-6a) s a random string used as the user's salt I the username p the user's cleartext password H() a one-way hash function u a random scrambling parameter (public) a, b ephemeral private keys, generated randomly and kept secret A, B corresponding ephemeral public keys x a private key derived from p and s v the host's password verifier K the session key The host stores passwords using the following formula: x = H(s, p) (s is chosen randomly) v = g^x (computes password verifier) The host then keeps {I, s, v} in its password database. The authentication protocol itself goes as follows: User -> Host: I, A = g^a (identifies self, a = random number) Host -> User: s, B = kv + g^b (sends salt, b = random number) Both: u = H(A, B) User: x = H(s, p) (user enters password) User: S = (B - kg^x) ^ (a + ux) (computes session key) User: K = H(S) Host: S = (Av^u) ^ b (computes session key) Host: K = H(S) Now the two parties have a shared, strong session key K. To complete authentication, they need to prove to each other that their keys match. One possible way: User -> Host: M = H(H(N) xor H(g), H(I), s, A, B, K) Host -> User: H(A, M, K) The two parties also employ the following safeguards: 1. The user will abort if he receives B == 0 (mod N) or u == 0. 2. The host will abort if it detects that A == 0 (mod N). 3. The user must show his proof of K first. If the server detects that the user's proof is incorrect, it must abort without showing its own proof of K. s Ka-Ping Yees 2006-06-25iÿÿÿÿ(t randrangetSRPErrorcBseZRS((t__name__t __module__(((s,/home/ping/web/passpet/darcs/server/srp6a.pyR;stObjectcBseZd„ZRS(cOs.||_x|D]}||i|is (RRR (((s,/home/ping/web/passpet/darcs/server/srp6a.pyR=scsßd„‰‡‡‡fd†‰‡‡fd†‰ ‡ ‡fd†‰ ˆˆˆƒ‰‡fd†‰d„‰‡‡‡‡ fd†}‡ ‡‡‡‡‡‡‡‡ f d†}‡ ‡‡‡‡‡‡‡‡ f d †}t|||ƒS( NcSs/d}x"|D]}|d>t|ƒ}q W|S(Nll(tord(tstrtvaluetch((s,/home/ping/web/passpet/darcs/server/srp6a.pyR Ds cs&ˆˆditt|ƒƒƒƒˆS(Nt-(tjointmapR (tvalues(thashR tN(s,/home/ping/web/passpet/darcs/server/srp6a.pytHJscsˆ||ˆƒS(N((tbasetexponent(t_powR(s,/home/ping/web/passpet/darcs/server/srp6a.pytpowMscs ˆˆ|ƒS(N((R(Rtg(s,/home/ping/web/passpet/darcs/server/srp6a.pytexpPscs tdˆƒS(Ni(R((R(s,/home/ping/web/passpet/darcs/server/srp6a.pytrandomUscSs|pt|ƒ‚ndS(N(R(t conditiont exception((s,/home/ping/web/passpet/darcs/server/srp6a.pytensureXscs:ˆ|ƒ}ˆƒ}ˆ||ƒ}ˆ|ƒ}||fS(N((tpasswordtptstxtv(RRR R(s,/home/ping/web/passpet/darcs/server/srp6a.pytsetup\s    c3s\ˆ|ƒˆ}ˆ|ƒˆ}g}|iVdVˆƒ}ˆ|ƒ}|VdV|idƒˆ}dV|idƒˆ} ˆ| dƒˆ|| ƒ} ˆ| dƒˆ||ƒ} ˆ| ˆˆ| ƒ|| | ƒ} ˆ| ƒ} ˆˆˆƒˆˆƒAˆ|ƒ||| | ƒ}|VdV|idƒ}ˆ|ˆ||| ƒjdƒ| |_dS(Niisreceived zero for Bsreceived zero for usH(A, M, K) did not match(tappendtNonetpoptkey(tusernameR tRtIR!tqueuetatAR"tBtuR#tStKtMt remote_HAMK( RRRRRtkR RR(s,/home/ping/web/passpet/darcs/server/srp6a.pytloginhs*    % 1c3sdˆ|ƒˆ}|ˆ}|ˆ}g}|iVdV|idƒ}|djoýdV|idƒˆ}ˆ|dƒˆƒ}ˆ|ˆ|ƒˆ} |V| Vˆ|| ƒ} ˆ|ˆ|| ƒ|ƒ} ˆ| ƒ} ˆˆˆƒˆˆƒAˆ|ƒ||| | ƒ} dV|idƒ}ˆ|| jdƒˆ|| | ƒV| |_ntd|ƒ‚dS(Niisreceived zero for AsM did not matchsprotocol %d is unsupported(R&R'R(R)R(R*R"R$R+R,R-tprotocolR/tbR0R1R2R3R4tremote_M( RRRRRR6R RR(s,/home/ping/web/passpet/darcs/server/srp6a.pyt authenticate‚s,      1 (R(RRRRR%R7R;(( RRRRR6RR RRRRs,/home/ping/web/passpet/darcs/server/srp6a.pytSRPCs   ''N(( t__doc__t __author__t__date__RRt ExceptionRRRR<(((s,/home/ping/web/passpet/darcs/server/srp6a.pys4s