Deterministic CSIDH variants enable full key recovery with ≤297 faults

The five-minute version

Deterministic CSIDH and OSIDH-LD are vulnerable to a simple fault that flips the secret-dependent conditional mask, turning it into a key-recovery oracle; a binary search recovers the full private key in at most 222 queries for CSIDH (n=74, B=5) and 297 queries for OSIDH-LD, and the required fault can be induced reliably on a ChipWhisperer-Lite board (p ≥ 0.94). The paper demonstrates the attack in software simulation and on real hardware, and proposes randomization countermeasures that raise the fault cost dramatically.

What they found 4

• Binary-search key recovery needs at most 222 queries for deterministic CSIDH (n=74, B=5).

  “A binary search per secret component recovers the key in at most n⌈log2(B + 1)⌉queries: 222 for deterministic CSIDH (n = 74, B = 5).”

• Full-key recovery succeeds in software fault simulation of OSIDH-LD.

  “We recover full keys in a software fault simulation of the OSIDH-LD reference implementation [22].”

• Clock-glitch fault succeeds in 50/50 attempts on ChipWhisperer-Lite (p ≥ 0.94).

  “On a ChipWhisperer-Lite, a clock glitch aligned to the isolated mask computation skips the instruction in 50 of 50 attempts (p ≥0.94 at 95% confidence).”

• For OSIDH-LD, shuffling plus an extra all-zero iteration makes every effective fault abort and hide the targeted prime.

  “For OSIDH-LD, shuffling plus one extra all-zero iteration turns every effective fault into an abort that hides the targeted prime, provided the lane check is enforced.”

What undercuts it the paper’s own results

• The empirical fault success rate for deterministic CSIDH is low (3 successful instruction skips out of 1281 executions, ≈2.34 × 10−3), which may make the attack impractical without highly precise glitching.

Stated limits 2

• Scope and limitations. Both hardware campaigns fault only steps whose honest mask is all-ones (t > s).
• As for deterministic CSIDH, we fault an isolated control site behind a dedicated trigger, not a full on-device group action.

What’s new here 4

• First fault attack targeting deterministic, dummy-free CSIDH/OSIDH-LD implementations.
• Shows that determinism makes the secret-dependent lane-selection mask a reproducible fault target.
• Provides a hardware demonstration of the mask-flip fault on a commodity microcontroller using clock-glitching.
• Analyzes countermeasures (prime order shuffling, outer-loop randomization) and quantifies their impact on fault complexity.

Artifacts & methods 7

• deterministic CSIDH (Houben)system
• OSIDH-LDsystem
• ChipWhisperer-Lite clock-glitch fault injection
• software fault simulation (eval_action_faulty)
• binary-search key recovery
• prime-order randomization countermeasure
• outer-loop randomization countermeasure

Topics