Merkle Tree Traversal Techniques - CDC

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To be a little more specific and to investigate the behavior of the four techniques we give some examples on how they would work in real life, using three exemplary trees. These Merkle trees have different heights and give an idea in which particular situation our algorithms may be used. Let T i ( i = 1,2,3) be Merkle trees of height H 1 = 5 , H 2 = 10 and H 3 = 20 . The time requirements for these trees (in number of elementary operations) are given in the following table: Traversal Technique: Classic Merkle Traversal 1979 Logarithmic Traversal 2003 Logarithmic Traversal 2004 Fractal Traversal 2003 Time requirements in number elementary operations: Time Requirements for T 1 10 5 10 4,3068 Time Requirements for 2 T 38 20 10 20 6,0207 Time Requirements for 3 T 40 20 40 9,2552 Now we show the space requirements (in number of saved hash values) for the same Merkle trees. More drastic differences may be seen in the following table: Traversal Technique: Classic Merkle Traversal 1979 Logarithmic Traversal 2003 Logarithmic Traversal 2004 Fractal Traversal 2003 Space requirements in number of saved hash values: Space Requirements for T 1 12,5 15 15 8,0753 Space Requirements for 2 T 50 30 30 22,5774 Space Requirements for 3 T 200 60 60 69,4139
Talking about space requirements we have to notice the fact that the real space requirements of all algorithms depend on the output length of our hash function. The next and last two tables show us the space requirements in bits for hash functions with 160-bit output and with 256-bit output: Traversal Technique: Classic Merkle Traversal 1979 Logarithmic Traversal 2003 Logarithmic Traversal 2004 Fractal Traversal 2003 Traversal Technique: Classic Merkle Traversal 1979 Logarithmic Traversal 2003 Logarithmic Traversal 2004 Fractal Traversal 2003 Space requirements for a 160-bit hash function: Space Requirements for T 1 2000 bits (0,25kB) 2400 bits (0,3kB) 2400 bits (0,3kB) 1292,048 bits (0,1615kB) Space Requirements for 2 T 39 8000 bits (1kB) 4800 bits (0,6kB) 4800 bits (0,6kB) 3612,384 bits (0,4515kB) Space requirements for a 256-bit hash function: Space Requirements for T 1 3200 bits (0,25kB) 3840 bits (0,48kB) 3840 bits (0,48kB) 2067,2768 bits (0,2584kB) Space Requirements for 2 T 12800 bits (1,6kB) 7680 bits (0,96kB) 7680 bits (0,96kB) 5779,8144 bits (0,7225kB) Space Requirements for 3 T 32000 bits (4kB) 9600 bits (1,2kB) 9600 bits (1,2kB) 11106,224 bits (1,3883kB) Space Requirements for 3 T 51200 bits (6,4kB) 15360 bits (1,92kB) 15360 bits (1,92kB) 17769,9584 bits (2,2212kB)
Page 1: Darmstadt University of Technology
Page 4 and 5: 3.5 Logarithmic Merkle Tree Travers
Page 6 and 7: Chapter 1 Introduction Historically
Page 8 and 9: Chapter 2 The Basics In this chapte
Page 10 and 11: mathematical manner we can give the
Page 12 and 13: 2.3.3 Winternitz improvement: One g
Page 14 and 15: Chapter 3 Tree traversal techniques
Page 16 and 17: uns either step 2 or step 3 of the
Page 18 and 19: Algorithm 3.2: Classic Merkle Tree
Page 20 and 21: Step 2: leaf = 1. • ( ) 1 P n wit
Page 22 and 23: P n 03 , because it is the only val
Page 24 and 25: Step 7: leaf = 6 . • ( ) 6 Figure
Page 26 and 27: Figure 3.1: The height of the Merkl
Page 28 and 29: Key Generation and Setup phase: In
Page 30 and 31: Step 1: leaf = 0 . • ( ) 0 Figure
Page 32 and 33: Step 4: leaf = 3. • ( ) 3 Figure
Page 34 and 35: nodes of height smaller than h (the
Page 36 and 37: The bigger the height of the TREEHA
Page 40 and 41: We can easily see the results of ou
Page 42: References [MER79] Ralph Merkle,

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