1st austria - wordpress.com · kilo mega giga term exa byte 224 see per year 12 see per h. mm....

30
Lower Upper Bounds on inverting functions mm Krzysztof Pietrzak 1ST Austria um

Upload: others

Post on 18-Oct-2020

0 views

Category:

Documents


0 download

TRANSCRIPT

Page 1: 1ST Austria - WordPress.com · kilo mega giga term exa Byte 224 see per year 12 see per h. mm. Inverting Permutations 2 IT NT sCNj GENE xi.it Xo to PO OH I f o of stove Xo Xp Xero

Lower Upper Boundson inverting functions

mm

Krzysztof Pietrzak

1ST Austriaum

Page 2: 1ST Austria - WordPress.com · kilo mega giga term exa Byte 224 see per year 12 see per h. mm. Inverting Permutations 2 IT NT sCNj GENE xi.it Xo to PO OH I f o of stove Xo Xp Xero

AttacksHellman'sTime spaceTrade off

nm

Rainbow tablespassTordslDES

Lower Bounds

Yao90DeTrevisasTulsauilog

Applications Techniques

Proofs ofSpace Compression

SACKPR 17Argument

Page 3: 1ST Austria - WordPress.com · kilo mega giga term exa Byte 224 see per year 12 see per h. mm. Inverting Permutations 2 IT NT sCNj GENE xi.it Xo to PO OH I f o of stove Xo Xp Xero

7Adversaries

mm

RAMmodel

CircuitTuring

Machines

Page 4: 1ST Austria - WordPress.com · kilo mega giga term exa Byte 224 see per year 12 see per h. mm. Inverting Permutations 2 IT NT sCNj GENE xi.it Xo to PO OH I f o of stove Xo Xp Xero

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

Page 5: 1ST Austria - WordPress.com · kilo mega giga term exa Byte 224 see per year 12 see per h. mm. Inverting Permutations 2 IT NT sCNj GENE xi.it Xo to PO OH I f o of stove Xo Xp Xero

N

N 0,1 N 13 0,13mmmm

d TEH FINI INI

ummm

AF E invents f it

PRIAMg x flirtyy c Fan VrICN E

Page 6: 1ST Austria - WordPress.com · kilo mega giga term exa Byte 224 see per year 12 see per h. mm. Inverting Permutations 2 IT NT sCNj GENE xi.it Xo to PO OH I f o of stove Xo Xp Xero

Applications

keg recovery for DESdefine

f 256 s E as

DESCokay

sothen fired

Lt 56

9only use 56 ofthe 64 bit output

Page 7: 1ST Austria - WordPress.com · kilo mega giga term exa Byte 224 see per year 12 see per h. mm. Inverting Permutations 2 IT NT sCNj GENE xi.it Xo to PO OH I f o of stove Xo Xp Xero

Trivial any F N CN

C invented with E N queries

in OTE N time

Page 8: 1ST Austria - WordPress.com · kilo mega giga term exa Byte 224 see per year 12 see per h. mm. Inverting Permutations 2 IT NT sCNj GENE xi.it Xo to PO OH I f o of stove Xo Xp Xero

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

Page 9: 1ST Austria - WordPress.com · kilo mega giga term exa Byte 224 see per year 12 see per h. mm. Inverting Permutations 2 IT NT sCNj GENE xi.it Xo to PO OH I f o of stove Xo Xp Xero

Preprocessing Non Uniformity

What if A has 5 bitsof advice about F

o 5 N logN

Page 10: 1ST Austria - WordPress.com · kilo mega giga term exa Byte 224 see per year 12 see per h. mm. Inverting Permutations 2 IT NT sCNj GENE xi.it Xo to PO OH I f o of stove Xo Xp Xero

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

Page 11: 1ST Austria - WordPress.com · kilo mega giga term exa Byte 224 see per year 12 see per h. mm. Inverting Permutations 2 IT NT sCNj GENE xi.it Xo to PO OH I f o of stove Xo Xp Xero

mm

Page 12: 1ST Austria - WordPress.com · kilo mega giga term exa Byte 224 see per year 12 see per h. mm. Inverting Permutations 2 IT NT sCNj GENE xi.it Xo to PO OH I f o of stove Xo Xp Xero

Inverting Permutations2

IT NT sCNj

GENE xi.itXo

to

PO OH

If o

ofstove Xo Xp XeroOh challenge y apply it

untilsteelvalve is hit

Page 13: 1ST Austria - WordPress.com · kilo mega giga term exa Byte 224 see per year 12 see per h. mm. Inverting Permutations 2 IT NT sCNj GENE xi.it Xo to PO OH I f o of stove Xo Xp Xero

Inverting random functions2

f CNI IN

Page 14: 1ST Austria - WordPress.com · kilo mega giga term exa Byte 224 see per year 12 see per h. mm. Inverting Permutations 2 IT NT sCNj GENE xi.it Xo to PO OH I f o of stove Xo Xp Xero

a

o pick m starting pointsKi t k h

nocompute ki e ft Kia ic.cm

o store 7 kin Kiit ie Cud

i

Page 15: 1ST Austria - WordPress.com · kilo mega giga term exa Byte 224 see per year 12 see per h. mm. Inverting Permutations 2 IT NT sCNj GENE xi.it Xo to PO OH I f o of stove Xo Xp Xero

sorted bymum

inverting

given g f find x

Page 16: 1ST Austria - WordPress.com · kilo mega giga term exa Byte 224 see per year 12 see per h. mm. Inverting Permutations 2 IT NT sCNj GENE xi.it Xo to PO OH I f o of stove Xo Xp Xero

m E N m Ek y

C TNif m.EEN

Page 17: 1ST Austria - WordPress.com · kilo mega giga term exa Byte 224 see per year 12 see per h. mm. Inverting Permutations 2 IT NT sCNj GENE xi.it Xo to PO OH I f o of stove Xo Xp Xero

Aable m

if m.EENPeaslee t

eg in E E eNwhat itIffeyed

f NI sous

pen gCNI CNT

flirtyf fl GH y pas

fait y

Page 18: 1ST Austria - WordPress.com · kilo mega giga term exa Byte 224 see per year 12 see per h. mm. Inverting Permutations 2 IT NT sCNj GENE xi.it Xo to PO OH I f o of stove Xo Xp Xero

Boo

Page 19: 1ST Austria - WordPress.com · kilo mega giga term exa Byte 224 see per year 12 see per h. mm. Inverting Permutations 2 IT NT sCNj GENE xi.it Xo to PO OH I f o of stove Xo Xp Xero

I m

Nit week N

S e m T E E

C nm eles T E.N

Page 20: 1ST Austria - WordPress.com · kilo mega giga term exa Byte 224 see per year 12 see per h. mm. Inverting Permutations 2 IT NT sCNj GENE xi.it Xo to PO OH I f o of stove Xo Xp Xero

breaking Windows passwords237 complexity

Page 21: 1ST Austria - WordPress.com · kilo mega giga term exa Byte 224 see per year 12 see per h. mm. Inverting Permutations 2 IT NT sCNj GENE xi.it Xo to PO OH I f o of stove Xo Xp Xero

Rainbow tablesmm

L

in i

Y'T

Page 22: 1ST Austria - WordPress.com · kilo mega giga term exa Byte 224 see per year 12 see per h. mm. Inverting Permutations 2 IT NT sCNj GENE xi.it Xo to PO OH I f o of stove Xo Xp Xero

fr

sikn to tookNiko

O

on

coe

sikn u

so so

Page 23: 1ST Austria - WordPress.com · kilo mega giga term exa Byte 224 see per year 12 see per h. mm. Inverting Permutations 2 IT NT sCNj GENE xi.it Xo to PO OH I f o of stove Xo Xp Xero

O

o

I

o

outoui si

kn

Page 24: 1ST Austria - WordPress.com · kilo mega giga term exa Byte 224 see per year 12 see per h. mm. Inverting Permutations 2 IT NT sCNj GENE xi.it Xo to PO OH I f o of stove Xo Xp Xero
Page 25: 1ST Austria - WordPress.com · kilo mega giga term exa Byte 224 see per year 12 see per h. mm. Inverting Permutations 2 IT NT sCNj GENE xi.it Xo to PO OH I f o of stove Xo Xp Xero

What if f is not

uniformly randommm

Page 26: 1ST Austria - WordPress.com · kilo mega giga term exa Byte 224 see per year 12 see per h. mm. Inverting Permutations 2 IT NT sCNj GENE xi.it Xo to PO OH I f o of stove Xo Xp Xero

one

ogrand

3 GIFT t N

W m

T S T S N g

Page 27: 1ST Austria - WordPress.com · kilo mega giga term exa Byte 224 see per year 12 see per h. mm. Inverting Permutations 2 IT NT sCNj GENE xi.it Xo to PO OH I f o of stove Xo Xp Xero

TT 091

Rainbow

1

Page 28: 1ST Austria - WordPress.com · kilo mega giga term exa Byte 224 see per year 12 see per h. mm. Inverting Permutations 2 IT NT sCNj GENE xi.it Xo to PO OH I f o of stove Xo Xp Xero
Page 29: 1ST Austria - WordPress.com · kilo mega giga term exa Byte 224 see per year 12 see per h. mm. Inverting Permutations 2 IT NT sCNj GENE xi.it Xo to PO OH I f o of stove Xo Xp Xero

TT 09

e

i

Page 30: 1ST Austria - WordPress.com · kilo mega giga term exa Byte 224 see per year 12 see per h. mm. Inverting Permutations 2 IT NT sCNj GENE xi.it Xo to PO OH I f o of stove Xo Xp Xero