Physical security and side channel attacks
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Physical Security and Side-Channel Attacks. Rice ELEC 528/ COMP 538 Farinaz Koushanfar Spring 2009. Outline. Introduction Hardware targets Attack classification Power attacks Timing attacks Electromagnetic attacks Fault injection attacks. Introduction.

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Physical security and side channel attacks

Physical Security and Side-Channel Attacks

Rice ELEC 528/ COMP 538

Farinaz Koushanfar

Spring 2009



  • Introduction

  • Hardware targets

  • Attack classification

  • Power attacks

  • Timing attacks

  • Electromagnetic attacks

  • Fault injection attacks



  • Classic cryptography views the securing problem using mathematical abstractions

  • The classic cryptoanalysis has had a great success and promise

    • Analysis and quantifying crypto algorithms’s resilience against attacks)

  • Recently, many of the security protocols have been attacked using physical attacks

    • Take advantage of the implementation specific to recover the secret parameters

Physical attacks

Physical attacks

  • Traditional cryptography is centered around the concepts of one-way and trapdoor functions

  • A one-way function can be rapidly calculated, but is computationally difficult to invert

  • Polynomial time algorithms rarely find a pre-image of the one-way security functions for a random set of inputs

  • A trapdoor one-way function is a function that is easy to invert if and only if a certain secret (key) is available

  • Physical attacks usually have two phases:

    • Interaction phase: the attacker exploits some physical characteristics of the device

    • Exploitation phase: analyzing the gathered information to recover the secret



  • Consider a device capable of doing cryptographic function

  • The key is usually stored in the device and protected

  • Modern crypto based on Kerckhoff’s assumptions all of the data required to operate a chip is entirely hidden in the secret

  • Attacker only needs to extract the keys

Principle of divide and conquer attack

Principle of divide-and-conquer attack

  • The divide and conquer (D&C) attacks attempt at recovering the key by parts

  • The idea is that an observable characteristic can be correlated with a partial key

    • The partial key should be small enough to enable exhaustive search

  • Once a partial key is validated, the process is repeated for finding other keys

  • D&C attacks may be iterative (some parts of the key dependent on others) or independent



  • Introduction

  • Hardware targets

  • Attack classification

  • Power attacks

  • Timing attacks

  • Electromagnetic attacks

  • Fault injection attacks

Hardware targets

Hardware targets

  • The most common victim of hardware cryptoanalysis are the smart cards (SC)

    • Attacks on SCs are applicable to any general purpose processor with a fixed bus length

    • Attacks on FPGAs are also reported. FPGAs represent application specific devices with parallel computing opportunity

Smart cards

Smart Cards

  • It has a small processor (8bit or 32bit) long with ROM, EEPROM and a small RAM

  • There are eight wires connecting the processor to the outside world

  • Power supply: SCs have no internal batteries, the current provided by the reader

  • Clock: SCs do not have an internal clock

  • SCs are typically equipped with a shield that destroys the chip if a tampering happens



  • The first difference with SCs is in the applications of the two processor.

  • FPGAs and ASICs allow parallel computing

  • Multiple programmable configuration bits



  • Introduction

  • Hardware targets

  • Attack classification

  • Power attacks

  • Timing attacks

  • Electromagnetic attacks

  • Fault injection attacks

Attack classification

Attack classification

  • Many possible attacks, the attacks are often not mutually exclusive

  • Invasive vs. noninvasive attacks

  • Active vs. passive

    • Active attacks tamper with device’s proper functionality, either temporary or permanently

Five major attack groups

Five major attack groups

  • Probing attack (invasive)

  • Fault injection attacks – active attacks , maybe invasive or noninvasive

  • Timing attacks exploit device’s running time

  • Power analysis attack

  • Electromagnetic analysis attacks



  • Introduction

  • Hardware targets

  • Attack classification

  • Power attacks

  • Timing attacks

  • Electromagnetic attacks

  • Fault injection attacks

Power attacks

Power attacks

Measuring phase

Measuring phase

  • This task is usually straightforward

    • Easy for smart cards: the energy is provided by the terminal and the current can be read

  • Relatively inexpensive (<$1000) equipment can digitally sample voltage differences at high rates (1GHz++) with less than 1% error

  • Device’s power consumption depends on many things, including its structure and data

Simple power analysis spa

Simple power analysis (SPA)

  • Monitoring the device’s power consumption to deduce information about data/operation

  • Example: SPA on DES – smart card

    • The internal structure is shown in the next slide

  • Summary DES - a block cipher

    • a product cipher

    • 16 rounds (iterations) on the input bits (of P)

      • substitutions (for confusion) and

      • permutations (for diffusion)

    • Each round with a round key

      • Generated from the user-supplied key

Des basic structure


Input Permutation












Final Permutation


* DES Basic Structure

[Fig. – cf. J. Leiwo]

  • Input: 64 bits (a block)

  • Li/Ri– left/right half of the input block

  • for iteration i (32 bits) – subject to substitution S and permutation P (cf. Fig 2-8– text)

  • K - user-supplied key

  • Ki - round key:

    • 56 bits used +8 unused

    • (unused for E but often used for error checking)

  • Output: 64 bits (a block)

  • Note: Ri becomes L(i+1)

  • All basic op’s are simple logical ops

    • Left shift / XOR

Example 1 spa on des cont d

Example 1 - SPA on DES (cont’d)

  • The upper trace – entire encryption, including the initial phase, 16 DES rounds, and the initial permutation

  • The lower trace – detailed view of the second and third rounds

Spa on des cont d

square and multiply algorithm

SPA on DES (cont’d)

  • The DES structure and 16 rounds are known

  • Instruction flow depends on data  power signature

  • Example: Modular exponentiation in DES is often implemented by square and multiply algorithm

  • Typically the square operation is implemented differently compared with the multiply (for speed purposes)

  • Then, the power trace of the exponentiation can directly yields the corresponding value

  • All programs involving conditional branchingbased on the key values are at risk!

Example 2 spa on rsa

Example 2: SPA on RSA

Spa example cont d

SPA example (cont’d)

Spa example cont d1

SPA example (cont’d)

  • Unprotected modular exponentiation – square and multiply algorithm

  • The pick values reveal the key values

Possible countermeasure randomizing rsa exponentiation

Possible countermeasure – randomizing RSA exponentiation

Differential power analysis dpa

Differential power analysis (DPA)

  • SPA targets variable instruction flow

  • DPA targets data-dependence

  • Difference b/w smart cards (SCs) and FPGAs

  • In SCs, one operation running at a time

    •  Simple power tracing is possible

  • In FPGAs, typically parallel computations prevents visual SPA inspection  DPA

Example dpa on des

Example: DPA on DES

  • Divide-and-conquer strategy, comparing powers for different inputs

  • Record large number of inputs and record the corresponding power consumption

  • We have access to R15, that entered the last round operation, since it is equal to L16

  • Take this output bit (called M’i) at the last round and classify the curves based on the bit

  • 6 specific bits of R15 will be XOR’d with 6 bits of the key, before entering the S-box

  • By guessing the 6-bit key value, we can predict the bit b, or an arbitrary output bit of an arbitrary S-box output

  • Thus, with 26 partitions, one for each possible key, we can break the cipher much faster

A closer look at HW

Implementation Of DES

Dpa cont d

DPA (cont’d)

  • DPA can be performed in any algorithm that has the operation =S(K),

    •  is known and K is the segment key

The waveforms are captured by a scope and

Sent to a computer for analysis

What is available after acquisition

What is available after acquisition?

Dpa cont d1

DPA (cont’d)

The bit will classify the wave wi

  • Hypothesis 1: bit is zero

  • Hypothesis 2: bit is one

  • A differential trace will be calculated for each bit!

Dpa cont d2

DPA (cont’d)

Dpa cont d3

DPA (cont’d)

Dpa testing

DPA -- testing

Dpa testing1

DPA -- testing

Dpa the wrong guess

DPA – the wrong guess

Dpa cont d4

DPA (cont’d)

  • The DPA waveform with the highest peak will validate the hypothesis

Dpa curve example

DPA curve example

Dpa by correlations

DPA by correlations

Attacking a secret key algorithm

Attacking a secret key algorithm

Typical dpa target

Typical DPA Target

Example dpa

Example -- DPA

Example hypothesis testing

Example – hypothesis testing

Dpa on des algorithm

DPA on DES algorithm

Dpa on other algorithms

DPA on other algorithms

Dpa cont d5

DPA (Cont’d)

Improvements over dpa

Improvements over DPA

  • Correlation power analysis (CPA) - attacker steps

    • Predict the power usage of the device at one specific instant, as a function of certain key bits

      • E.g., for DES, it is assumed to be function of the Hamming weight of the data

    • Prediction matrix stores the predicted values

    • Consumption vector Stores the measured power

    • The attacker compared the actual and the predicted values, using correlation coefficient

    • E.g., correlation b/w all the columns of the prediction vector and the consumption matrix

Modeling the power consumption

Modeling the power consumption

  • Hamming weight model

    • Typically measured on a bus, Y=aH(X)+b

    • Y: power consumption; X: data value; H: Hamming weight

  • The Hamming distance model

    • Y=aH(PX)+b

    • Accounting for the previous value on the bus (P)

Correlation power analysis cpa

Correlation power analysis (CPA)

  • The equation for generating differential waveforms replaced with correlations

  • Rather than attacking one bit, the attacker tries prediction of the Hamming weight of a word (H)

  • The correlation is computed by:

More about pa cont d

More about PA (cont’d)

  • Data-dependent attacks require power consumption model

    • Can be measured and learned

  • Synchronization of the measurements needs to be addressed

  • The attack is affected by parallel computing which lowers observability

  • The described attack is not the best achieved to date, e.g., techniques based on maximum likelihood often offer better results

Statistical pa countermeasures

Statistical PA -- countermeasures

Anti dpa countermeasures

Anti-DPA countermeasures

Anti dpa


  • Internal clock phase shift

Further readings

Further Readings

  • Differential power analysis, by kocher, Jaffe, and Jun

  • Power analysis tutorial, by Aigner and Oswald

  • A tutorial on physical security and side-channel attacks, by Koeune and Standaert

  • Michael Tunstall has some good material – a few of the charts are his courtesy

  • Side channel attacks: countermeasures, by Verbauwhede



  • Introduction

  • Hardware targets

  • Attack classification

  • Power attacks

  • Timing attacks

  • Electromagnetic attacks

  • Fault injection attacks

Timing attacks

Timing attacks

  • Running time of a crypto processor can be used as an information channel

  • The idea was proposed by Kocher, Crypto’96

Physical security and side channel attacks

Timing attacks (cont’d)

Rsa cryptosystem

RSA Cryptosystem

  • Key generation:

    • Generate large (say, 2048-bit) primes p, q

    • Compute n=pq and (n)=(p-1)(q-1)

    • Choose small e, relatively prime to (n)

      • Typically, e=3 (may be vulnerable) or e=216+1=65537 (why?)

    • Compute unique d such that ed = 1 mod (n)

    • Public key = (e,n); private key = d

      • Security relies on the assumption that it is difficult to factor n into p and q

  • Encryption of m: c = me mod n

  • Decryption of c: cd mod n = (me)d mod n = m

How does rsa decryption work

How Does RSA Decryption Work?

  • RSA decryption: compute yx mod n

    • This is a modular exponentiation operation

  • Naïve algorithm: square and multiply

Kocher s observation

Kocher’s Observation

Whether iteration takes a long time

depends on the kth bit of secret exponent

This takes a while

to compute

This is instantaneous

Outline of kocher s attack

Outline of Kocher’s Attack

  • Idea: guess some bits of the exponent and predict how long decryption will take

  • If guess is correct, will observe correlation; if incorrect, then prediction will look random

    • This is a signal detection problem, where signal is timing variation due to guessed exponent bits

    • The more bits you already know, the stronger the signal, thus easier to detect (error-correction property)

  • Start by guessing a few top bits, look at correlations for each guess, pick the most promising candidate and continue

Rsa in openssl

RSA in OpenSSL

  • OpenSSL is a popular open-source toolkit

    • mod_SSL (in Apache = 28% of HTTPS market)

    • stunnel (secure TCP/IP servers)

    • sNFS (secure NFS)

    • Many more applications

  • Kocher’s attack doesn’t work against OpenSSL

    • Instead of square-and-multiply, OpenSSL uses CRT, sliding windows and two different multiplication algorithms for modular exponentiation

      • CRT = Chinese Remainder Theorem

      • Secret exponent is processed in chunks, not bit-by-bit

Chinese remainder theorem

Chinese Remainder Theorem

  • n = n1n2…nk

    where gcd(ni,nj)=1 when i  j

  • The system of congruences

    x = x1 mod n1 = … = xk mod nk

    • Has a simultaneous solution x to all congruences

    • There exists exactly one solution x between 0 and n-1

  • For RSA modulus n=pq, to compute x mod n it’s enough to know x mod p and x mod q

Rsa decryption with crt

Attack this computation in order to learn q.

This is enough to learn private key (why?)

RSA Decryption With CRT

  • To decrypt c, need to computem=cd mod n

  • Use Chinese Remainder Theorem (why?)

    • d1 = d mod (p-1)

    • d2 = d mod (q-1)

    • qinv = (1/q) mod p

    • Compute m1 = cd1 mod p; m2 = cd2 mod q

    • Compute m = m2+(qinv*(m1-m2) mod p)*q

these are precomputed

Rsa decryption with crt1

Attack this computation in order to learn q.

This is enough to learn private key (why?)

RSA Decryption With CRT

  • To decrypt c, need to computem=cd mod n

  • Use Chinese Remainder Theorem (why?)

    • d1 = d mod (p-1)

    • d2 = d mod (q-1)

    • qinv = (1/q) mod p

    • Compute m1 = cd1 mod p; m2 = cd2 mod q

    • Compute m = m2+(qinv*(m1-m2) mod p)*q

these are precomputed

Operations involved in decryption

Operations Involved in Decryption

What is needed to compute cd mod q and xy mod q?

  • Exponentiation

    • Sliding windows

  • Multiplication routines

    • Normal (when operands have unequal length)

    • Karatsuba (when operands have equal length): faster

  • Modular reduction

    • Montgomery reduction

Montgomery reduction

Montgomery Reduction

  • Decryption requires computing m2 = cd2 mod q

  • This is done by repeated multiplication

    • Simple: square and multiply (process d2 1 bit at a time)

    • More clever: sliding windows (process d2 in 5-bit blocks)

  • In either case, many multiplications modulo q

  • Multiplications use Montgomery reduction

    • Pick some R = 2k

    • To compute x*y mod q, convert x and y into their Montgomery form xR mod q and yR mod q

    • Compute (xR * yR) * R-1 = zR mod q

      • Multiplication by R-1 can be done very efficiently

Schindler s observation

Schindler’s Observation

  • At the end of Montgomery reduction, if zR > q, then need to subtract q

    • Probability of this extra step is proportional to c mod q

  • If c is close to q, a lot of subtractions will be done

  • If c mod q = 0, very few subtractions

    • Decryption will take longer as c gets closer to q, then become fast as c passes a multiple of q

  • By playing with different values of c and observing how long decryption takes, attacker can guess q!

    • Doesn’t work directly against OpenSSL because of sliding windows and two multiplication algorithms

Reduction timing dependency

Reduction Timing Dependency

Decryption time




Value of ciphertext c

Summary of time dependencies

Summary of Time Dependencies

Attack is binary search

Decryption time

#ReductionsMult routine

0-1 Gap


Value of ciphertext

Attack Is Binary Search

Attack overview

Attack Overview

  • Initial guess g for q between 2512 and 2511 (why?)

  • Try all possible guesses for the top few bits

  • Suppose we know i-1 top bits of q. Goal: ith bit

    • Set g =…known i-1 bits of q…000000

    • Set ghi=…known i-1 bits of q…100000 (note: g<ghi)

      • If g<q<ghi then the ith bit of q is 0

      • If g<ghi<q then the ith bit of q is 1

  • Goal: decide whether g<q<ghi or g<ghi<q

Two possibilities for g hi

Decryption time

#ReductionsMult routine





Value of ciphertext

Two Possibilities for ghi

Difference in decryption times

between g and ghi will be small

Difference in decryption times

between g and ghi will be large

Timing attack details

Timing Attack Details

  • What is “large” and “small”?

    • Know from attacking previous bits

  • Decrypting just g does not work because of sliding windows

    • Decrypt a neighborhood of values near g

    • Will increase difference between large and small values, resulting in larger 0-1 gap

  • Attack requires only 2 hours, about 1.4 million queries to recover the private key

    • Only need to recover most significant half bits of q

The 0 1 gap

The 0-1 Gap

Zero-one gap

Extracting rsa private key

Extracting RSA Private Key

Montgomery reductiondominates

zero-one gap

Multiplication routine dominates



  • Introduction

  • Hardware targets

  • Attack classification

  • Power attacks

  • Timing attacks

  • Electromagnetic attacks

  • Fault injection attacks

Electromagnetic power analysis

Electromagnetic power analysis

Ema probe design

EMA – probe design

Ema signal

EMA signal

Spatial positioning

Spatial positioning

Spatial positioning1

Spatial positioning

Example sema on rsa

Example: SEMA on RSA

Ema cont d

EMA (cont’d)

Counter measures

Counter measures



  • Introduction

  • Hardware targets

  • Attack classification

  • Power attacks

  • Timing attacks

  • Electromagnetic attacks

  • Fault injection attacks

Fault injection attacks

Fault injection attacks

Fault attacks

Fault attacks

Fault injection techniques

Fault injection techniques

  • Transient (provisional) and permanent (destructive) faults

    • Variations to supply voltage

    • Variations in the external clock

    • Temperature

    • White light

    • Laser light

    • X-rays and ion beams

    • Electromagnetic flux

Need some maybe expensive equipment eg laser

Need some (maybe expensive equipment) – eg, laser

Fault injection steps

Fault injection steps

Provisional faults

Provisional faults

  • Single event upsets

    • Temporary flips in a cell’s logical state to a complementary state

  • Multiple event faults

    • Several simultaneous SEUs

  • Dose rate faults

    • The individual effects are negligible, but cumulative effect causes fault

  • Provisional faults are used more in fault injection

Permanent faults

Permanent faults

  • Single-event burnout faults

    • Caused by a parasitic thyristor being formed in the MOS power transistors

  • Single-event snap back faults

    • Caused by self-sustained current by parasitic bipolar transistors in MOS

  • Single-event latch-up faults

    • Creates a self sustained current in parasitics

  • Total dose rate faults

    • Progressive degradation of the electronic circuit

Fault impacts model

Fault impacts (model)

  • Resetting data

  • Data randomization – could be misleading, no control over!

  • Modifying op-code – implementation dependent

Example fault attack on des

Example – fault attack on DES

15 th round dpa

15-th round DPA

15 th round dpa1

15-th round DPA

15 th round des

15-th round DES

Fault attacks counter measures

Fault attacks – counter measures

Fault attacks counter measures1

Fault attacks – counter measures

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