This paper presents results on formal verification of high-speed cryptographic software. We consider speed-record-setting hand-optimized assembly software for Curve25519 elliptic-curve key exchange presented by Bernstein et al. at CHES 2011. Two versions for different micro-architectures are available. We successfully verify the core part of the computation, and reproduce detection of a bug in a previously published edition. An SMT solver supporting array and bit-vector theories is used to establish almost all properties. Remaining properties are verified in a proof assistant with simple rewrite tactics. We also exploit the compositional of Hoare logic to address the scalability issue. Essential differences between both versions of the software are discussed from a formal-verification perspective.