On the Security of IV Dependent Stream Ciphers Côme Berbain and Henri Gilbert France Telecom R&D {
[email protected]} research & development Stream Ciphers IV-less IV-dependent key K key K IV (initial value) number ? generator keystream keystream plaintext ⊕ ciphertext plaintext ⊕ ciphertext e.g. RC4, Shrinking Generator e.g. SNOW, Scream, eSTREAM ciphers well founded theory [S81,Y82,BM84] less unanimously agreed theory practical limitations: prior work [RC94, HN01, Z06] - no reuse of K numerous chosen IV attacks - synchronisation - key and IV setup not well understood IV setup – H. Gilbert (2) research & developement Orange Group Outline security requirements on IV-dependent stream ciphers whole cipher key and IV setup key and IV setup constructions satisfying these requirements blockcipher based tree based application example: QUAD incorporate key and IV setup in QUAD's provable security argument IV setup – H. Gilbert (3) research & developement Orange Group Security in IV-less case: PRNG notion m K∈R{0,1} number truly random VS generator g generator g g(K) ∈{0,1}L L OR Z ∈R{0,1} 1 input A 0 or 1 PRNG A tests number distributions: Adv g (A) = PrK [A(g(K)) = 1] − PrZ [A(Z) = 1] PRNG PRNG Advg (t) = maxA,T(A)≤t (Advg (A)) PRNG 80 g is a secure cipher ⇔ g is a PRNG ⇔ Advg (t < 2 ) <<1 IV setup – H. Gilbert (4) research & developement Orange Group Security in IV-dependent case: PRF notion stream cipher perfect random fct. IV∈ {0,1}n function generator VSOR g* gK G = {gK} gK(IV) q oracle queries • A 0 or 1 PRF gK g* A tests function distributions: Adv G (A) = Pr[A = 1] − Pr[A = 1] PRF PRF Adv G (t, q) = max A (Adv G (A)) PRF 80 40 G is a secure cipher ⇔ G is a PRF ⇔ Adv G (t < 2 ,2 ) << 1 IV setup – H.