implementation of the rsa algorithm on a dataflow architecture
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Implementation of the RSA Algorithm on a Dataflow Architecture . Nikola Be ž ani ć [email protected] Advisors: Veljko Milutinovi ć , Jelena Popovi ć -Bo ž ovi ć, and Ivan Popović. Introduction. Case study area: Public key cryptography acceleration

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implementation of the rsa algorithm on a dataflow architecture

Implementation of the RSA Algorithm on a Dataflow Architecture

Nikola Bežanić

[email protected]

Advisors:VeljkoMilutinović, JelenaPopović-Božović, and Ivan Popović

School of Electrical Engineering, University of Belgrade, 2013.

introduction
Introduction
  • Case study area: Public key cryptography acceleration
  • Problem: RSA implementation on Maxeler
  • Existing problem solutions: None
  • Summary: Under review (IPSI)
  • Approach:
    • Accelerate multiplications
    • Analyze usability
  • Conclusions:
    • Multiplication speedup: 70% (28% total)
    • Usability: Picture encryption

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slide3
RSA
  • Montgomery method: n -> r
  • r=2sw -> power of 2
  • Montgomery product (MonPro): modulo r arithmetic

------------------------------------

ms-1

. . .

m1

m0

bits

ek-1

. . .

e1

e0

1 bit

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montgomery product
Montgomery product
  • a and b are big numbers
  • Breaking them to digits:
    • bs-1…b1b0
    • as-1…a1a0
  • Processing on a word basis

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montgomery product step 1
Montgomery product: Step 1

a[j]

b[i]

X

CPU

Product:

hi

low

32 bits

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dataflow multiplier
Dataflow multiplier

a[j]

b[i]

X

CPU

Product:

hi

low

32 bits

Stream a

Constant b0

Dataflow engine (DFE)

X

Stream y

Stream x

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dataflow multiplier pipeline problem
Dataflow multiplier: Pipeline problem
  • Next iteration (next constant b1) => new DFE run
  • New DFE run => new pipeline fill-up overhead
  • 1024-bits key requires only 32 digits (32 bits each)
  • Not enough to fill-up the pipeline
  • Result: CPU time < DFE time !
  • Solution:
    • Work on blocks of data
    • Do not use constants, rather use a stream
    • Stream has redundant values: acts as a const.

b0

b1

a0

a1

a2

a3

a0

a1

a2

a3

X

Stream y

Stream x

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dataflow multiplier blocks of data
Dataflow multiplier: Blocks of data

b0 x a < = >

Block 0

Block 1

Big streams for each run

Block z-1

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results
Results
  • Using blocks pipeline is full
  • Using one multiplier speed up is 10% for RSA
  • Speedup is 70% for multiplication using 4 multiplers
  • It leads to 28% for complete RSA (Amdahl’s law)
  • Future work
    • Deal with carry at DFE or
    • Overlap carry propagation at CPU and multiplication at DFE

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the end
The End

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