Arcane Rituals for Cryptography Performance Optimization

The Council of ShadowsBrown University

Presented by Edward Tremel, Computational Archaeologist

A Mysterious Disappearance

Setting: Providence, two years ago

CS research group vanishes without trace

Mysterious events surround disappearance Rain of blood Unexplainable

earthquake

Investigation Leads to Puzzling DiscoveryDocument Fell Behind File Cabinet in Disused CIT Basement

The Ill-Fated Group’s Results?

Brown faculty deny existence of Council of Shadows

No such project ever funded

Results appear publishable

Search For Lost Archive Leads To Long-Abandoned Tunnel

Reached Beneath Basement of University Hall

A Discovery of Ill Portent

Bricked up within building’s walls

Bound in human skin Aura of corruption Obscure and

forbidding runes

The Problem With Cryptography

Must sacrifice efficiency for security

Often does not scale Fundamental

operations involve difficult computation

Optimizing math libraries a thankless task

512 1024 2048 409602468

101214

RSA Signature Cost

RSA Modulus Size (bits)

Tim

e t

o S

ign (

ms)

0

2000

4000

6000

8000

10000

12000SNARK Verification Time

Input Size (KB)

Tim

e t

o V

eri

fy (

ms)

Black Magic: The Solution?

Instead, sacrifice the blood of the innocent for both efficiency and security

Often suggested in theory, but impossible in practice until book’s discovery Detailed

instructions for rituals

Gathering the Materials

3 human hearts 2 pounds flesh Extract of

Nightshade Aura of Pestilence Stone carved with

Elder Sign Defiled altar of the

Elder Gods 1 goat

The Horrifying Experiment

Unsuccessful attempts Required additional

grave robbing Accidentally

summoned disgusting tentacle monster

Some incantations granted power, but too unstable to use

Exploiting the Dark Arts

Success: opened stable portal to plane of Elder Gods

Black magic used to solve modular exponentiation

Arcane forces allowed impossibly fast computation

Corruption-Based Computation

Low-level math library constructed with diabolical forces

ModExp, Group ops, Field ops, Elliptic Curve pairings

Channel to Abyss used for source of true randomness

Chaos of the Abyss

Impossibly optimized assembly arithmetic

Group/Field operations

Elliptic Curve

operations

Source of True Rando

m

RSA encrypt & decrypt

Promising Results

RSA Sign RSA Verify Group multiply Group pairing0

2

4

6

8

10

12

Cryptography operations

Best current implementationPrototype CBC implementation

Tota

l ti

me (

ms)

But At What Cost?

Channel to Abyss may not be as stable as originally thought

Chaos leaking into mortal plane

Increased incidence of unholy monstrosities in Providence area

He comes, oh god, he comes