Merkle trees. Alice can use a binary Merkle tree to commit to a set of elements...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
Merkle trees. Alice can use a binary Merkle tree to commit to a set of elements S = T,..., Tn, so that later she can prove to Bob that some T is in S using a proof containing at most log n hash values. The binding commitment to the entire S is a single hash value. This question explores generalization to k-ary tree, that is, where every nonleaf node has up to k children. 1. Suppose S Ti,T9. Explain how Alice computes a commitment to S using a ternary Merkle tree (i.e. k= 3). Specify exactly how hash function is applied to what arguments. How can Alice later prove to Bob that T4 is in S? = 2. Suppose S contains n elements. Let the length of the hash function output be X. What is the exact length of the proof that proves that some Ti is in S, as a function of n, k, X? 3. What is the storage requirements for the k-ary tree of n leaves each of size s (and where x is the security parameter)? Discuss storage/proof size trade offs in choosing the arity (i.e. number of children per node) for Merkle trees. 4. If you are given n = 1000 Merkle trees of possibly different sizes and arity, how can you quickly (i.e. in work linear in n) combine them into a single Merkle tree and still be able to prove membership? Merkle trees. Alice can use a binary Merkle tree to commit to a set of elements S = T,..., Tn, so that later she can prove to Bob that some T is in S using a proof containing at most log n hash values. The binding commitment to the entire S is a single hash value. This question explores generalization to k-ary tree, that is, where every nonleaf node has up to k children. 1. Suppose S Ti,T9. Explain how Alice computes a commitment to S using a ternary Merkle tree (i.e. k= 3). Specify exactly how hash function is applied to what arguments. How can Alice later prove to Bob that T4 is in S? = 2. Suppose S contains n elements. Let the length of the hash function output be X. What is the exact length of the proof that proves that some Ti is in S, as a function of n, k, X? 3. What is the storage requirements for the k-ary tree of n leaves each of size s (and where x is the security parameter)? Discuss storage/proof size trade offs in choosing the arity (i.e. number of children per node) for Merkle trees. 4. If you are given n = 1000 Merkle trees of possibly different sizes and arity, how can you quickly (i.e. in work linear in n) combine them into a single Merkle tree and still be able to prove membership?
Expert Answer:
Answer rating: 100% (QA)
1 Suppose ST1ldots T9 To compute a commitment to S using a ternary Merkle tree k3 Alice would follow these steps a Compute the hash of each leaf node ... View the full answer
Related Book For
Introduction to Algorithms
ISBN: 978-0262033848
3rd edition
Authors: Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest
Posted Date:
Students also viewed these operating system questions
-
Let A, B be sets. Define: (a) the Cartesian product (A B) (b) the set of relations R between A and B (c) the identity relation A on the set A [3 marks] Suppose S, T are relations between A and B, and...
-
Portray in words what transforms you would have to make to your execution to some degree (a) to accomplish this and remark on the benefits and detriments of this thought.You are approached to compose...
-
Example Problem for Declining Balance Depreciation Methods Historical cost of equipment A: $120,000, purchased on January 1, 2014. Estimated salvage value: $20,000; Estimated useful life: 5 years....
-
Several people have written that Twitter is one of the most creative developments in the history of business and the world in general. What is your opinion about Twitter as a powerfully creative...
-
The net price of a snow shovel is $20.40 after discounts of 20% and 15%. What is the list price?
-
Smith et al. [1992] discuss a study of the ozone layer over the Antarctic. These scientists developed a measure of the degree to which oceanic phytoplankton production is inhibited by exposure to...
-
Multiple Choice Questions 1. The moving average inventory cost flow method is applicable to which of the following inventory systems? Periodic Perpetual a. Yes..... Yes b. Yes..... No c. No..... No...
-
In the accompanying diagram, PA is tangent to circle O at A. If CB = 21 and PB = 4, what is the length of PA? 0. A P B C
-
There are N houses (numbered from 0 to N-1) along a street. In each of them, recyclable trash (plastic, glass, metal) is collected into separate bags. There are three trucks that collect the trash....
-
Plainbank has $29 million in cash and equivalents, $41 million in loans, and $35 million in core deposits. A. Calculate the financing gap. (Enter your answer in millions.) Funding deficit million $...
-
2 5 = 32 Change each exponential expression to an equivalent expression involving a logarithm.
-
Assume that you are manufacturing aspirin tablets that are supposed to contain 325 mg of aspirin. If the standard deviation of the amounts of aspirin is calculated, which value would you prefer: a...
-
The percentage of heights between 159 centimeters and 165 centimeters
-
The first class in a frequency table of incomes shows a frequency of 24 corresponding to the range of values from \($0\) to \($999.\) Using only this information about the frequency table, is it...
-
The percentage of heights greater than 179 centimeters
-
Read the case from Contemporary Strategy Analysis,. ISBN: 978-1-119-12083-4: Bank of Americas Acquisition of Merrill Lynch. Use the case analysis format provided below to address to identify the...
-
Use translations to graph f. f(x) = x-/2 +1
-
Show that if L 2, then every binary tree with L leaves contains a subtree having between L/3 and 2L/3 leaves, inclusive.
-
Demonstrate what happens when we insert the keys 5, 28, 19, 15, 20, 33, 12, 17, 10 into a hash table with collisions resolved by chaining. Let the table have 9 slots, and let the hash function be...
-
Modify the proto-vEB structure to support keys that have associated satellite data.
-
Define internal combustion engine and explain how it is different from external combustion engines?
-
In an air standard Otto cycle, the pressure and temperature at the start of compression stroke are 1 bar and \(30^{\circ} \mathrm{C}\), respectively. The temperature at the end of compression is...
-
In I.C. engines, power developed inside the cylinder is known as: (a) Brake horse power (b) Indicated horse power (c) Pumping power (d) None of the above
Study smarter with the SolutionInn App