Power Analysis on NTRU Prime Wei-Lun Huang, Jiun-Peng Chen, Bo-Yin - - PowerPoint PPT Presentation

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Power Analysis on NTRU Prime Wei-Lun Huang, Jiun-Peng Chen, Bo-Yin - - PowerPoint PPT Presentation

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Power Analysis on NTRU Prime Wei-Lun Huang, Jiun-Peng Chen, Bo-Yin Yang Academia Sinica, Taiwan CHES 2020 1 Topics NTRU Prime A Brief Preview Correlation Power Analysis: vertical vs. horizontal in-depth Online Template

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Power Analysis on NTRU Prime

Wei-Lun Huang, Jiun-Peng Chen, Bo-Yin Yang Academia Sinica, Taiwan CHES 2020

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❖ NTRU Prime ❖ A Brief Preview ❖ Correlation Power Analysis: vertical vs. horizontal in-depth ❖ Online Template Attacks ❖ Chosen-Input Simple Power Analysis ❖ Finale

Topics

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❖ NTRU Prime ❖ A Brief Preview ❖ Correlation Power Analysis: vertical vs. horizontal in-depth ❖ Online Template Attacks ❖ Chosen-Input Simple Power Analysis ❖ Finale

Topics

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❖ Shor’s Algorithm

➢ solving integer factorization and discrete logarithms efficiently ➢ Quantum Computers: estimated as arriving in 10~20 years

Post-Quantum Cryptography (PQC)

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  • Peter W. Shor. Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer.
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❖ Shor’s Algorithm

➢ solving integer factorization and discrete logarithms efficiently ➢ Quantum Computers: estimated as arriving in 10~20 years

❖ The NIST PQC Standardization Project

➢ key encapsulation mechanisms (KEM) + digital signatures ➢ lattices / error correction codes / multivariate quadratic equations / ...

Post-Quantum Cryptography (PQC)

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  • Post-Quantum Cryptography | CSRC. https://csrc.nist.gov/Projects/Post-Quantum-Cryptography
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❖ Streamlined NTRU Prime / NTRU LPRime: 653 / 761 / 857

NTRU Prime: lattice-based KEM

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  • Daniel J. Bernstein, Chitchanok Chuengsatiansup, Tanja Lange, and Christine van Vredendaal. NTRU Prime: round 2.
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❖ The Product Scanning Method

➢ Inputs: known c in R/q and secret short f ➢ Ouput: e = (c x f) mod q ➢ Decap / Encap / KeyGen (only ntrulpr*)

Interesting Multiplication in NTRU Prime

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  • Michael Hutter and Erich Wenger. Fast Multi-Precision Multiplication for Public-Key Cryptography on Embedded Microprocessors.
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❖ The Product Scanning Method

➢ Inputs: known c in R/q and secret short f ➢ Ouput: e = (c x f) mod q ➢ Decap / Encap / KeyGen (only ntrulpr*)

Interesting Multiplication in NTRU Prime

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❖ The Product Scanning Method

➢ Inputs: known c in R/q and secret short f ➢ Ouput: e = (c x f) mod q ➢ Decap / Encap / KeyGen (only ntrulpr*)

Interesting Multiplication in NTRU Prime

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❖ The Product Scanning Method

➢ Inputs: known c in R/q and secret short f ➢ Ouput: e = (c x f) mod q ➢ Decap / Encap / KeyGen (only ntrulpr*)

Interesting Multiplication in NTRU Prime

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❖ The Product Scanning Method

➢ Inputs: known c in R/q and secret short f ➢ Ouput: e = (c x f) mod q ➢ Decap / Encap / KeyGen (only ntrulpr*)

Interesting Multiplication in NTRU Prime

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❖ NTRU Prime ❖ A Brief Preview ❖ Correlation Power Analysis: vertical vs. horizontal in-depth ❖ Online Template Attacks ❖ Chosen-Input Simple Power Analysis ❖ Finale

Topics

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❖ sntrup761 Decap on ARM Cortex-M4

➢ p = 761, q = 4591, and w = 286 ➢

  • n STM32F303RCT7 and STM32F415RGT6

Experiment Settings

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  • STMicroelectronics. Datasheet - STM32F303xB STM32F303xC.
  • STMicroelectronics. Datasheet - STM32F415xx STM32F417xx.
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❖ sntrup761 Decap on ARM Cortex-M4

➢ p = 761, q = 4591, and w = 286 ➢

  • n STM32F303RCT7 and STM32F415RGT6

❖ ChipWhisperer-Lite Two-Part Version

➢ random input generation + measurement + data collection

❖ Statistical Analysis: in Python 3.6.1 or C++ on a MacBook Air

Experiment Settings

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  • ChipWhisperer-Lite (CW1173) Two-Part Version - NewAE Technology Inc. https://store.newae.com/chipwhisperer-lite-cw1173-two-part-version/
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STM32F415RGT6 + ChipWhisperer-Lite

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Target Board at 7.38MHz Mini-Circuits SLP-10.7+ Coaxial Cable USB to PC Control Board MacBook Air

  • Low Pass Filter - Mini Circuits. https://www.minicircuits.com/pdfs/SLP-10.7+.pdf
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❖ Vertical CPA: robust and fast ❖ Horizontal In-Depth CPA: using one single short trace ❖ Online Template Attacks: fast profiling with few template traces ❖ Chosen-Input SPA: with the naked eye

Power Analysis Methods

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CPA: Correlation Power Analysis SPA: Simple Power Analysis

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❖ NTRU Prime ❖ A Brief Preview ❖ Correlation Power Analysis: vertical vs. horizontal in-depth ❖ Online Template Attacks ❖ Chosen-Input Simple Power Analysis ❖ Finale

Topics

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  • Mun-Kyu Lee et al. Countermeasures against Power Analysis Attacks for the NTRU Public Key Cryptosystem.
  • Aydin Aysu et al. Horizontal Side-Channel Vulnerabilities of Post-Quantum Key Exchange Protocols.
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Vertical CPA

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Vertical CPA

likely to confuse with

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Reveal and at a time.

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Reveal

  • ne by one.

Vertical CPA

likely to confuse with

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Reveal and at a time.

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❖ Vertical CPA: one coefficient at a time with multiple short traces

➢ How to squeeze more information from each short trace?

In-Depth CPA

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❖ Vertical CPA: one coefficient at a time with multiple short traces

➢ How to squeeze more information from each short trace?

❖ In-Depth CPA: multiple coefficients at a time with one short trace

➢ The intermediate state of depends on the current ➢ and all the previous . ➝ Extend-and-Prune

In-Depth CPA

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❖ Block Size m = 67 + Pruning Period n = 6

Candidate Pruning

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❖ Tail Errors: at the end of the block

➢ In the current block recovery, the correlation still looks great. ➢ In the next block recovery, no hypotheses survive.

Tail-Error Removal

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❖ Tail Errors: at the end of the block

➢ In the current block recovery, the correlation still looks great. ➢ In the next block recovery, no hypotheses survive.

❖ Roll Back: by half a block

➢

  • nce no hypotheses survive in the current block recovery.

➢ tail errors in the final block ➝ exhaustive search

Tail-Error Removal

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A Toy Example: m = 5, n = 2, l = 5

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A Toy Example: m = 5, n = 2, l = 5

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❖ In-Depth CPA: inefficient and inaccurate

➢ every m coefficients mapped to only m samples ➢ the lack of data ➝ ineffective candidate pruning

Horizontal In-Depth CPA (HIDCPA)

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❖ In-Depth CPA: inefficient and inaccurate

➢ every m coefficients mapped to only m samples ➢ the lack of data ➝ ineffective candidate pruning

❖ Learn from horizontal attacks!

➢ Observe the calculation of . ➢ For l ≪ p, we have nearly l times as many data.

Horizontal In-Depth CPA (HIDCPA)

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A Real-World Example: m = 67, n = 6, l = 5

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Tail Error The Top

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A Real-World Example: m = 67, n = 6, l = 5

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The Middle

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A Real-World Example: m = 67, n = 6, l = 5

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The Bottom Corrected

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❖ NTRU Prime ❖ A Brief Preview ❖ Correlation Power Analysis: vertical vs. horizontal in-depth ❖ Online Template Attacks ❖ Chosen-Input Simple Power Analysis ❖ Finale

Topics

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  • Lejla Batina, Lukasz Chmielewski, Louiza Papachristodoulou, Peter Schwabe, and Michael Tunstall. Online Template Attacks.
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❖ What if the assumption of simple power models fails?

➢ Classical Correlation Attacks: the Hamming weight/distance models ➢ Classical Template Attacks: multivariate normal distribution

Template Attacks

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❖ What if the assumption of simple power models fails?

➢ Classical Correlation Attacks: the Hamming weight/distance models ➢ Classical Template Attacks: multivariate normal distribution

❖ The Profiling Stage

➢ numerous template traces + heavy computational power

Template Attacks

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Can we mount template attacks with few template traces?

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Online Template Attacks (OTA)

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Can we mount template attacks with fewer executions? Step: 1 2, 4, 6, ... 3, 5, 7, ...

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❖ Chosen-Input:

➢ enhancing the reusability of template traces

The Chosen-Input Offline Variant

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❖ Illegitimate Private Key: f* on the template generator

➢ generating all the required template traces within four executions ➢ and expressed as

The Chosen-Input Offline Variant

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❖ NTRU Prime ❖ A Brief Preview ❖ Correlation Power Analysis: vertical vs. horizontal in-depth ❖ Online Template Attacks ❖ Chosen-Input Simple Power Analysis ❖ Finale

Topics

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  • Paul C. Kocher, Joshua Jaffe, and Benjamin Jun. Differential Power Analysis.
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Not Countermeasures

❖ Apply a random mask to each output coefficient.

➢ integer offsets added at the beginning and removed at the end

❖ Shuffle multiply-and-accumulates for each output coefficient.

➢ input-coefficient pairs accessed in a random order

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  • Mun-Kyu Lee et al. Countermeasures against Power Analysis Attacks for the NTRU Public Key Cryptosystem.
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Not Countermeasures

❖ Apply a random mask to each output coefficient.

➢ integer offsets added at the beginning and removed at the end

❖ Shuffle multiply-and-accumulates for each output coefficient.

➢ input-coefficient pairs accessed in a random order

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subject to chosen-input SPA (CISPA) subject to chosen-input SPA (CISPA)

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CISPA on Countermeasure 2

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❖ Two Stages: nonzero identification + clustering ❖ The First Stage: continuous? discontinuous?

➢ similar to CISPA on Countermeasure 2 ➢ Zero or Nonzero: output coefficient ➝ private-key coefficient

CISPA on Countermeasure 1

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❖ The Second Stage:

➢ knowing + observing the calculation

CISPA on Countermeasure 1

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❖ NTRU Prime ❖ A Brief Preview ❖ Correlation Power Analysis: vertical vs. horizontal in-depth ❖ Online Template Attacks ❖ Chosen-Input Simple Power Analysis ❖ Finale

Topics

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❖ Optimized Product Scanning

➢ Modular Reduction: per multiply-and-accumulate ➝ per calculation ➢ SMLABB ➝ SMLADX: two multiply-and-accumulates per instruction ➢ 4.4x faster / immune to OTA / still subject to HIDCPA and CISPA

Two Optimizations and One Countermeasure

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  • Cortex-M4 Devices Generic User Guide. http://infocenter.arm.com/help/topic/com.arm.doc.dui0553b/DUI0553.pdf
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❖ Optimized Product Scanning

➢ Modular Reduction: per multiply-and-accumulate ➝ per calculation ➢ SMLABB ➝ SMLADX: two multiply-and-accumulates per instruction ➢ 4.4x faster / immune to OTA / still subject to HIDCPA and CISPA

❖ First-Order Masking: both inputs masked

➢ If the ciphertext not masked: horizontal CPA ➢ If the private key not masked: SPA or profiling attacks (potentially)

Two Optimizations and One Countermeasure

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  • Stefan Mangard, Elisabeth Oswald, and Thomas Popp. Power Analysis Attacks - Revealing the Secrets of Smart Cards.
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❖ Single-Trace Power Analysis on the Product Scanning Method

➢ applicable to NTRU Prime Decap/Encap/KeyGen ➢ targeting the reference/protected/optimized implementations ➢ with short observation span, few template traces, or the naked eye

Conclusion

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❖ Single-Trace Power Analysis on the Product Scanning Method

➢ applicable to NTRU Prime Decap/Encap/KeyGen ➢ targeting the reference/protected/optimized implementations ➢ with short observation span, few template traces, or the naked eye

❖ Potential Applications

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  • ther ideal-lattice-based cryptosystems with

➢ private/session-key coefficients from a small set of possibilities ➢ multi-level Karatsuba ending with the product scanning method

Conclusion

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  • Anatolii Karatsuba. Multiplication of Multidigit Numbers on Automata.
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Q & A

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