If you get to this question before we've discussed the "Birthday Paradox" (a.k.a. the "Birthday Attack" or the "Birthday Bound") in class, take a look at the "Birthday Attack Note" document that we've posted on the class Content page on Brightspace. It describes the formula you need for Q3 and Q4. When we generate nonces randomly, we need to pay attention to the probability that we'll generate the same nonce twice (a "nonce collision"). This depends on the length of the nonce and on how many messages we plan to encrypt. We also need to decide how much risk we're willing to tolerate. For example, a 50% chance of a collision (and therefore a 50% chance of losing all our security) is clearly unacceptable. But what chance is "low enough"? In practice, what we usually say is that a collision probability of 2-64 (remember that's the same as 1/264) is low enough. Given that the secretbox nonce is 24 bytes (192 bits) long, what's the approximate maximum number of messages that we can encrypt with the same key and random nonces, before our probability of a nonce collision rises above 2-64₂ O24 messages O2 messages O2 messages O2 messages
If you get to this question before we've discussed the "Birthday Paradox" (a.k.a. the "Birthday Attack" or the "Birthday Bound") in class, take a look at the "Birthday Attack Note" document that we've posted on the class Content page on Brightspace. It describes the formula you need for Q3 and Q4. When we generate nonces randomly, we need to pay attention to the probability that we'll generate the same nonce twice (a "nonce collision"). This depends on the length of the nonce and on how many messages we plan to encrypt. We also need to decide how much risk we're willing to tolerate. For example, a 50% chance of a collision (and therefore a 50% chance of losing all our security) is clearly unacceptable. But what chance is "low enough"? In practice, what we usually say is that a collision probability of 2-64 (remember that's the same as 1/264) is low enough. Given that the secretbox nonce is 24 bytes (192 bits) long, what's the approximate maximum number of messages that we can encrypt with the same key and random nonces, before our probability of a nonce collision rises above 2-64₂ O24 messages O2 messages O2 messages O2 messages
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Transcribed Image Text:If you get to this question before we've discussed the "Birthday
Paradox" (a.k.a. the "Birthday Attack" or the "Birthday Bound") in
class, take a look at the "Birthday Attack Note" document that we've
posted on the class Content page on Brightspace. It describes the
formula you need for Q3 and Q4.
When we generate nonces randomly, we need to pay attention to the
probability that we'll generate the same nonce twice (a "nonce
collision"). This depends on the length of the nonce and on how many
messages we plan to encrypt. We also need to decide how much risk
we're willing to tolerate. For example, a 50% chance of a collision (and
therefore a 50% chance of losing all our security) is clearly
unacceptable. But what chance is "low enough"?
In practice, what we usually say is that a collision probability of 2-64
(remember that's the same as 1/264) is low enough. Given that the
secretbox nonce is 24 bytes (192 bits) long, what's the approximate
maximum number of messages that we can encrypt with the same key
and random nonces, before our probability of a nonce collision rises
above 2-642
O 254
messages
O 232
messages
O2128 messages
O2¹6 messages
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