Post-Quantum Cryptography & Electromagnetic Side-Channel Analysis

Last Updated: April 12, 2026

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Overview

The NIST post-quantum cryptography (PQC) standardization process concluded in 2024, selecting four algorithms for standardization. However, unlike traditional cryptographic algorithms designed with side-channel resistance as an afterthought, PQC algorithms introduce new EM leakage characteristics due to their mathematical operations (polynomial arithmetic, lattice operations, Gaussian sampling). This is an active and urgent research area because PQC is being deployed now — before its side-channel resistance is fully understood.

NIST PQC Standardized Algorithms (2024)

Algorithm	Type	Standard	Primary Use	EM-SCA Status
CRYSTALS-Kyber (ML-KEM)	Key Encapsulation	FIPS 203	Key exchange	Vulnerable — multiple published attacks
CRYSTALS-Dilithium (ML-DSA)	Digital Signature	FIPS 204	Signatures	Vulnerable — lattice leakage demonstrated
SPHINCS+ (SLH-DSA)	Digital Signature	FIPS 205	Signatures	Lower risk — hash-based, simpler leakage profile
FALCON (FN-DSA)	Digital Signature	FIPS 206	Signatures	High risk — Gaussian sampling is extremely leaky

CRYSTALS-Kyber (ML-KEM): EM Attack Landscape

Kyber is the sole NIST-standardized KEM (Key Encapsulation Mechanism) and is already being deployed in TLS 1.3, SSH, and hardware security modules. It has received the most side-channel research attention.

Attack Vectors

1. Number Theoretic Transform (NTT) Leakage

Kyber's core operation is polynomial multiplication via NTT (similar to FFT)
NTT operations produce data-dependent switching activity directly proportional to coefficient values
EM leakage from NTT correlates with intermediate polynomial coefficients, leaking the secret key

2. Message Decoding Leakage

The decapsulation routine compares a recomputed ciphertext with the received one
This comparison leaks timing and EM information about the secret key bits
Power/EM traces show distinguishable patterns for 0-bit vs. 1-bit decoding decisions

3. Gaussian/Centered Binomial Sampling Leakage

Kyber uses centered binomial distribution (CBD) for noise generation
CBD sampling involves conditional operations that create EM-distinguishable patterns
This is the same vulnerability vector as FALCON's Gaussian sampler, but milder

Published Attacks (2023–2026)

Hardware Implementation Attacks:

Springer JCEN (2025): "A side-channel attack on a masked hardware implementation of CRYSTALS-Kyber" — demonstrated key recovery against first-order masked implementations using combined power/EM analysis. Required ~50,000 traces.
ASIACCS 2023: First EM attack on hardware Kyber, recovered full secret key with ~10,000 traces on unprotected implementation.

Software Implementation Attacks:

MDPI Cryptography (2024): Analyzed Kyber vulnerabilities, identified CBD sampling and polynomial multiplication as primary EM leakage sources.
IEEE Xplore (2026): "Revisiting the Masking Strategy" — demonstrated attack on first-order masked Kyber by exploiting higher-order leakage from NTT operations.

Novel Framework:

ScienceDirect (2026): PSESV (Physically-Sensed Error Signature Verification) — hybrid framework combining real-time thermal and EM monitoring for both attack detection and side-channel-resistant Kyber implementation.

Attack Complexity vs. Traditional AES

Algorithm	Unprotected (traces)	1st-order masked (traces)	2nd-order masked
AES-128 (SW)	~1,000	~50,000	~5,000,000+
AES-256 (HW)	~10,000	~100,000+	Very difficult
Kyber-512 (HW)	~10,000	~50,000–200,000	Research ongoing
Kyber-768 (HW)	~15,000	~100,000+	Research ongoing

Kyber's attack complexity is comparable to AES at the same protection level — meaning it is not intrinsically more resistant to EM-SCA than traditional crypto.

CRYSTALS-Dilithium (ML-DSA): EM Attack Landscape

Dilithium is a lattice-based signature scheme (CRYSTALS family, same as Kyber). Its signing algorithm leaks differently than Kyber.

Key Leakage Point: Rejection Sampling

Dilithium's signing loop performs rejection sampling: it generates candidate values and discards them if they exceed a threshold
The number of rejected samples (and the sample values themselves) leaks information about the signing key
EM timing and amplitude analysis can detect rejection events, enabling lattice reduction attacks
This is analogous to the nonce reuse vulnerability in ECDSA, but harder to exploit

Published Work

IACR ePrint 2025/1754: "Machine Learning and Side-Channel Attacks on Post-Quantum Cryptography" — systematic study of DL-based attacks on Kyber, Dilithium, and SPHINCS+. Demonstrated that ML significantly reduces trace requirements for all three algorithms.

FALCON (FN-DSA): Highest EM-SCA Risk

FALCON uses discrete Gaussian sampling — generating random values from a Gaussian distribution. This operation is inherently variable in execution time and power, making it the most EM-leaky of the NIST PQC algorithms.

Why FALCON is Especially Vulnerable

Variable loop iterations: Gaussian sampling uses rejection sampling with variable number of iterations
Branch-dependent operations: Conditional acceptance/rejection creates EM-distinguishable traces
Floating-point arithmetic: FALCON uses floating-point NTT, which leaks differently than integer NTT (Kyber/Dilithium)
Fast Fourier Sampling: The core signing operation involves a tree structure that produces highly structured, recoverable EM patterns

Current Status

FALCON hardware implementations without countermeasures are considered straightforwardly attackable by any researcher with research-grade EM-SCA equipment (HackRF + Langer probes)
Several labs have demonstrated full signing key recovery; research into countermeasures is active but no fully side-channel-resistant FALCON implementation has been standardized

SPHINCS+ (SLH-DSA): Lower Risk Profile

SPHINCS+ is a hash-based signature scheme. Its side-channel profile is more similar to SHA-2/SHA-3 than to lattice operations.

Why It's More Resistant

Hash function evaluations produce relatively uniform EM profiles (constant-time implementations are straightforward)
No polynomial arithmetic or Gaussian sampling
The "few times" signing property (stateless, no reuse vulnerabilities) eliminates certain attack classes

Remaining Risks

EM leakage from the Winternitz OTS (one-time signature) chains can still reveal key material
Large signature size makes it impractical for constrained IoT devices where EM-SCA risk is highest

Countermeasures for PQC Implementations

1. Masking (Most Deployed)

Split secret polynomial coefficients into multiple shares. An attacker must exploit all shares simultaneously (higher-order attack), exponentially increasing trace requirements.

1st-order masking: ~10× increase in required traces
2nd-order masking: ~1,000× increase
Challenge: Masking of NTT is costly — 3–5× performance overhead; masking of Gaussian sampling (FALCON) is exceptionally complex

2. Multiplicative Masking (Novel, 2025)

Telecom Paris / HAL research (2025): Proposed multiplicative masking as a countermeasure specifically for Kyber — previously overlooked because additive masking was standard. Multiplicative masking provides better protection for polynomial coefficient operations.

3. PSESV Framework (2026)

ScienceDirect (2026): Physically-Sensed Error Signature Verification — combines:

Real-time EM monitoring as a detection layer
Side-channel-resistant implementation as the defense layer
Error signature verification to detect tampering

Claims to provide dual-layer protection: both resistance to SCA and active detection of ongoing attacks.

4. Algorithmic Countermeasures

Shuffling: Randomize operation order in NTT butterfly stages
Noise injection: Add fake operations to obscure real ones
Constant-time CBD sampling: Remove data-dependent branches in noise generation

5. Hardware Countermeasures

Dedicated co-processors with built-in masking (e.g., ARM TrustZone, RISC-V with security extensions)
Shielding at IC package level (same as for AES — see Practical Guide §4)
Active monitoring circuits (see Practical Guide §4.3)

Implications for EM-SCA Practitioners

Testing PQC Implementations

The same equipment used for AES EM-SCA is applicable to PQC:

Entry-level RTL-SDR + DIY probes: sufficient for unprotected Kyber/Dilithium
HackRF + Langer probes: sufficient for first-order masked implementations
Professional USRP + calibrated probes: required for second-order masked implementations

See Equipment Tier Guide for equipment selection.

Key Differences from AES Analysis

Longer operations: PQC signing/encapsulation involves more operations than one AES block → longer traces, larger files
Different frequency profile: Lattice operations may have different dominant frequencies than AES S-box operations — calibration required
Algorithm-specific leakage models: The Hamming weight model used for AES must be adapted (lattice coefficient values, CBD distribution shapes)
NTT alignment challenges: NTT operations are iterative; trace alignment requires detecting the NTT butterfly structure

Testing Checklist for PQC Devices

Identify PQC algorithm(s) implemented (Kyber, Dilithium, FALCON, SPHINCS+)
Determine implementation type: software, hardware, or hybrid
Check for masking: unprotected, 1st-order, 2nd-order
Measure leakage during: key generation, encapsulation/signing, decapsulation/verification
Apply leakage models specific to NTT operations
Test for rejection sampling timing leakage (Dilithium, FALCON)
Verify constant-time implementation of CBD/Gaussian sampling

Regulatory & Certification Implications

FIPS 203/204/205/206 and Side-Channel

The NIST PQC FIPs standards specify the algorithms but do not yet include SCA resistance requirements. This is expected to be addressed in future revisions and in the CMVP (Cryptographic Module Validation Program) testing requirements. As of 2026:

FIPS 140-3 testing labs are beginning to develop PQC-specific SCA test vectors
No certified PQC hardware module with formal SCA resistance validation exists yet
The field is in the same state as AES SCA testing was in ~2000: known vulnerabilities, no standardized test methodology

Market Opportunity

The gap between PQC deployment and PQC SCA resistance validation represents a significant market opportunity for testing labs and tool providers (see Market Analysis §Growth Catalysts and Key Players §FortifyIQ).