Formally verified AES-XTS: The first AES algorithm to join s2n-bignum

Formally verified AES-XTS: The first AES algorithm to join s2n-bignum - Amazon Science

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Automated reasoning

Formally verified AES-XTS: The first AES algorithm to join s2n-bignum

Simplifying and clarifying the assembly code for core operations enabled automated optimization and verification.

By Yan Peng , Nevine Ebeid , June Lee

March 20, 2026

15 min read

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Overview by Amazon Nova

AWS formally verified an optimized Arm64 assembly implementation of AES-XTS decryption, ensuring mathematical correctness and security. The verification process involved simplifying the assembly code, using the HOL Light interactive theorem prover, and integrating formal verification into the continuous-integration workflow. The formally verified AES-XTS implementation provides mathematical guarantees of correctness, enabling performance improvements and maintaining security for AWS's storage encryption algorithm.

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Cryptographic encryption algorithms are mathematical procedures that transform readable data into ciphertext that looks like a stream of random bits. The ciphertext can be decrypted only with the corresponding decryption algorithm and the correct key. For data at rest — information stored on disks or in databases — algorithms like AES-XTS encrypt each block before it’s written to storage, protecting against physical theft or unauthorized access to storage systems. For data in transit — information traveling across networks — protocols like TLS combine multiple algorithms: asymmetric encryption algorithms (RSA or elliptic curves) establish secure connections, while fast symmetric encryption algorithms (like AES-GCM) protect the actual data stream and verify that it hasn't been tampered with. At Amazon Web Services (AWS), we use AES-XTS to protect customer data in services like EBS , Nitro cards , and DynamoDB, while TLS with AES-GCM secures all network communication between services and to customers. We took on the challenge of formally verifying an optimized Arm64 assembly implementation of AES-XTS decryption, where “formal verification” is the process of proving mathematically that an engineered system meets a particular specification . Our work follows the IEEE Standard 1619 for cryptographic protection of block-oriented storage devices and focuses on the AES-256-XTS variant of AES-XTS. The “256” specifies the size of the encryption key. Unlike algorithms that process fixed-size blocks, AES-XTS handles variable-length data from 16 bytes up to 16 megabytes, with special logic for incomplete blocks. The assembly code verified was a 5x-unrolled version, meaning that its loops were executed in parallel across five registers (each containing an input block), and it had been optimized for modern CPU pipelines. It was complex enough that manual review couldn't guarantee correctness yet critical enough that errors could compromise customer data security. As part of Amazon Web Services’ s2n-bignum library of formally verified big-number…