... CDH assumption is converted into q - SDH assumption . It denotes that the q - SDH assumption can also be solved in poly- nomial time . Thus , we can obtain the lemma . = Lemma 1. If the q - SDH + CDH Assumption. 504 J. Zhang , H. Chen , and ...
... CDH-assumption) Voz, Va. 1, . . . , a, er, F, Pr[c/4(g”, , , , , g”) = g”) is negligible. This assumption have been ... Q-CDH-assumption as follows: Definition 13 (m-Q-CDH-assumption) Let Q be a polynomial of F,{X1, . . . . X.n] of ...
... CDH (Shoup's Diffie-Hellman self-corrector [7]). 4. 1poly(n)-CDH ⇔ 1poly(n)-CSE (Maurer and Wolf[5]). 3.2 This Work The following two main theorems of this section state the equivalence of the two assumptions P-CDH and Q-CDH for two ...
... q = “A|S|x", randomly choose ke Z, and compute r = P-k: – If q = “S|A|x ... CDH, G (X"/PW*, Y's PW*)) is in A, (which event is denoted CollH5) ... CDH, G (X*/PW*, Y's PW'”)) is in Aqt, unless one can solve the Diffie-Hellman problem: Pr ...
... q, writing the group action multiplicatively. A bilinear map is a map e : G1 × G1 → G2 satisfying the following ... (CDH) problem)The CDH problem is, given P, Pa, P b ∈ G1 for unknown a,b ∈ Z∗q , to compute P ab. The advantage of any ...
... q CDH + 1 queries to CDH. Definition 3. We say that the OMCDHP is (t ,q CDH ,ε)-hard in G if Pr[A wins] ≤ ε for any A that runs in time t, where q CDH is the total number of queries made to CDH. 3 Formal Definitions of IBI 3.1 ...
... {GapCDH } for defining n,QDdh our ,CorrGapCDH Multi-User n,Q CDH Ddh problems. Multi-User Asymmetric GapCDH With Corruption. This problem is like n-CorrGapCDH, users i ∈ [n 1 where the corruption oracle Corrn1 ]) is restricted to (i ...
... cdh G A ( t , ε ) -CDH ,, G attacker , in a finite cyclic group G of prime order q with g as a generator , is a probabilistic machine △ running in time t such that its success probability Succ ( 4 ) , given random elements go and g3 to ...
... CDH assumption: Let g be a generator of a group G of order q. CDH problem is (t, ε)-hard if for any t-time algorithm A, Pr[gab ← A(ga,gb)] ≤ ε, for the probability going over random a and b in Zq. – (N,Q)-One-More (Non-Adaptive) DH ...
... (q) is at leat e. The (q, t, e) — SDH assumption holds if no adversary A (t,e)— breaks the q— SDH problem. Definition 2 (Computational Diffie-Hellman (CDH) Assumption). . Let Q be a CDH parameter generator. We say an algorithm A has ...