De nition 2 Sample Clauses

De nition 2. If a message Ci is secret (by the protocol speci cation), Xxx learns nothing about it except that it exists2. However, she may replace such a message by a di erent message. If a message Ci is authenticated (by the protocol speci ca- tion), then the receiver will always (with probability 1) detect any modi cation to the message due to Xxx, but Xxx sees the message. Considering a passive adversary is equivalent to assuming the entire com- munication to be authenticated. The above de nition can be made information- theoretically precise. If two parties share a secret key, they can use the one-time pad encryption to transmit a message in perfect secrecy over a completely insecure channel. They can also use part of the secret key for authenticating messages (see Section 2.2). 1 The initialization phase summarizes the parties' entire initial information, for in- stance the history of previous executions of protocols, the information resulting from quantum transmissions (like in quantum cryptography [2]), or information received from other sources like a satellite broadcasting random bits (see Section 4.3) or the signal of a deep-space radio source. When the initialization phase is missing, this means that Xxxxx's and Bob's complete knowledge at the beginning of the protocol is assumed to be statistically independent.

De nition 2. The secret key rate of X and Y with respect to Z, denoted S(X; Y jjZ), is the maximum rate at which Xxxxx and Xxx can agree on a secret key S while keeping the rate at which Xxx obtains information arbitrarily small, i.e., it is the maximal R such that for every > 0 there exists a protocol for su ciently large N satisfying (4)-(8) with X and Y replaced by XN and Y N , respectively, satisfying 1 I(S; CtZN ) ; N and achieving

De nition 2. 1. De ne a functor F from the category of Noetherian FP schemes to the category of sets as follows: for an FP scheme S, de ne F pSq to be the set of isomorphism classes of 4 tuples pA, i, θ, αq, where