CVE-2026-84308: phpseclib — non-constant-time X25519 scalar multiplication permits full private-key recovery

The pure-PHP X25519 scalar multiplication in phpseclib is not constant-time. Field addition and subtraction each perform a data-dependent conditional modular reduction, so the cost of each Montgomery-ladder step is a linear function of that step’s reduction count which is a quantity determined by the secret scalar’s prefix.

An observer with per-ladder-step resolution recovers the 251-bit clamped private scalar. This is a per-step leak, not an aggregate one: an instrumented code proof-of-concept recovers 20/20 test keys from 32 observed operations, and an observer that counts libgmp calls instead of timing them recovers a key from a single operation.

This is not a low-order-input issue. Recovery works with the RFC 7748 base point u = 9, with no attacker-chosen input at all. Rejecting low-order public values does not close it.