Protocol Interactive Message Authentication Auth Sample Clauses

Protocol Interactive Message Authentication Auth string (i.e., a string with the same number of zeros and ones), by encoding, for example, a 0 as 01 and a 1 as a 10. This doubles the length of M .3 | | We note that [RW03] present a technique that can be used even if M is unknown (namely, encoding M as a string that becomes balanced only at the end), but we will not need it here.

Protocol Interactive Message Authentication Auth. The [RW03] authentication protocol allows two parties who share the same string R to authenticate a message M , even if R has very little entropy. ≥ We generalize this protocol slightly (to use general extractors instead of the specific polynomial authentication function) and present it in Figure 1. We as- sume that Ext is an average-case extractor that takes seeds of length q, and outputs L + 1-bit strings that are 2−L−1-close to uniform as long as the input has sufficient entropy h (in particular, h 3L+1 suffices if one is using universal hashing as the extractor). For our purposes, it suffices to assume that the length | | of M and the number of ones in it (i.e., its Hamming weight wt(M )) are known to Bob. If M is known but wt(M ) is not, M can be first encoded as a balanced string (i.e., a string with the same number of zeros and ones), by encoding, for example, a 0 as 01 and a 1 as a 10. This doubles the length of M .3 | | We note that [RW03] present a technique that can be used even if M is unknown (namely, encoding M as a string that becomes balanced only at the end), but we will not need it here. ˜ Each round of the protocol reveals L + 1 bits of information correlated to R if Mi = 0, and 2L + 1 bits of information of information correlated to R if Mi = 1. Hence, by Xxxxx 2, the adversary’s uncertainty about R will be sufficient for the extractor to work until the last round as long as H∞(R|E) ≥ 3L + 1 + (L + 1)(λM + wt(M )), and by Lemma 1 the ai and bi values will have entropy L from the adversary’s point of view. The intuition for the security of this protocol is that Xxx cannot answer a random query xi or yi with probability greater than 2−L because of the entropy of the answers, and hence can neither remove zero bits (because challenges to Bob keep him synchronized) nor insert one bits (because Xxxxx is required to answer a challenge for each one). She can insert zero bits and change zeros to ones, but that is taken care of by the assumption that Bob knows λM and wt(M ). ƒ We do not formally define or prove security of this protocol, as the proof is essentially the same as in [RW03]. The probability that Xxx succeeds in trans- mitting M j = M to Bob and Bob does not reject (or Xxxxx rejects and Bob accepts) is at most 2−L. ƒ We note the following security property observed in [RW04]. Consider a setting where, because of Xxx’s malicious interference, Bob does not have the same R as Xxxxx does, but instead some (possibly correlated) Rj. The pro...