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Lower Upper Boundson inverting functions
mm
Krzysztof Pietrzak
1ST Austriaum
AttacksHellman'sTime spaceTrade off
nm
Rainbow tablespassTordslDES
Lower Bounds
Yao90DeTrevisasTulsauilog
Applications Techniques
Proofs ofSpace Compression
SACKPR 17Argument
7Adversaries
mm
RAMmodel
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Machines
Circuit of site C RAM in time
8K usingOC site
data structure
RAM timeTang Circuit ofS sizespace
0C 5 7Model Functions permutations as
black boxes that can be
queried at cost 1
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N 0,1 N 13 0,13mmmm
d TEH FINI INI
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AF E invents f it
PRIAMg x flirtyy c Fan VrICN E
Applications
keg recovery for DESdefine
f 256 s E as
DESCokay
sothen fired
Lt 56
9only use 56 ofthe 64 bit output
Trivial any F N CN
C invented with E N queries
in OTE N time
Lower BoundsThere are f that are
trivial to invent e g constant
o F uniformly randomurn
fNo T query A can
c invent F forC IN L
Preprocessing Non Uniformity
What if A has 5 bitsof advice about F
o 5 N logN
Space Time Complexity ofinventing functions
8exabyte
DES N256
f
s F N
t c
32 GB 6444years
assuming220 DES E
comp per Sec
213 225 233 243 253
kilo mega giga term exa Byte224 see per year 12 see per h
mm
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