40 November/December 2021

COURTESY IBM

D e e p M a t h

9

// B Y A D R I E N N E B E R N H A R D //

Quantum

Cyberattacks

Are Coming.

This Math Can

Stop Them

E

NCRYPTION—THE PROCESS OF SENDING

a scrambled message that only the

intended recipient’s device can decode—

allows private and public sectors alike

to safeguard information. Traditional

encryption uses schemes based on com-

plex mathematics such as factoring

(breaking an integer down to its prime factors)

or discrete logarithm. Classical computers would

require billions of years to crack these codes.

Quantum computers, however, won’t be stumped

by such hard problems; their exponential leaps

in processing power will render classical cyphers

obsolete, potentially exposing troves of sensitive

data across commercial entities, healthcare pro-

viders, government institutions, and billions of

individual users.

Experts are working to devise cryptographic

schemes that can run on today’s computers, but

that can also be used in ciphers to protect data

against quantum attackers.

Quantum computers can perform certain

functions that ordinary computers simply can’t;

in part, this is because qubits (the way informa-

tion is encoded on quantum computers) adopt the

properties of quantum mechanics, using individ-

ual atoms, ions, photons, or electrons to take on a

combination of various states at once. This gives

quantum computers—once little more than a labo-

ratory curiosity—access to a larger space of values

than conventional computers, with their binary

0’s and 1’s. Someday, quantum computers will

be able to perform a vast number of calculations

almost instantaneously, breaking the ciphers that

protect personal data.

“We need to identify alternative problems we

can use as the foundation for quantum-secure

cryptosystems,” says Chris Peikert, professor of

computer science and engineering at the Univer-

sit y of Michigan. “What hard problem are we going

to use? How do we use that problem to encr y pt mes-

sages securely?”

Enter lattices. Abstract algebraic structures,

lattices are enormous grids with many individual

points across two, three, or potentially hundreds

of dimensions. In a high enough dimension, for

instance, a bounded distance decoding prob-

lem—a type of lattice-based conundrum—should

be able to flummox these machines (see side-

bar). “The best algorithms we come up with still

IBM says that a

quantum system

with just 50 qubits

might overpower

today’s top

supercomputers.