Z-Sigil public-key cryptosystem secures messages with chained lattice keys
Z-Sigil: A Public-Key Cryptosystem with Chained Selection over a Fiber Bundle of Module-Lattice Keys
Cryptography and SecurityInformation Theory
Summary
Encrypting messages securely is important to keep information private. The authors present Z-Sigil, a way to encrypt messages where each piece of the message chooses the next secret key from a structured family. This approach is based on advanced math with lattices and torsion points but uses classical data formats. They prove it keeps messages confidential under certain mathematical assumptions, even against quantum attackers, but it does not cover all security types like message tampering detection.
What this means in practice
- •For cryptography engineers: Use Z-Sigil’s chained lattice key method to build encryption tools resistant to quantum-aware attackers under Module-LWE assumptions.
- •For security protocol developers: Incorporate Z-Sigil’s structured key chain approach to create secure message encryption schemes with provable confidentiality guarantees.
Authors
Andrea Rondelli
Abstract
Z-Sigil is a public-key cryptosystem in which the plaintext selects successive keys from a fixed module-lattice family. Messages are length-prefixed, zero-padded and divided into 32-byte blocks. Each public vector is a shared public matrix applied to a small secret vector, plus a small error. Key indices label torsion points of a flat Kähler torus; the secret family forms a section of a key bundle over them. A public nonce initializes a hash state that selects each block's key and bit mask. The sender updates the state with the plaintext block; the receiver does so after recovering it. The stream and nonce determine a discrete walk along which decryption reads the secret section. We specify the algorithms, prove correctness under an explicit noise condition and bound decoding failure for messages chosen after the public key. Under stated decisional Module-LWE assumptions, we establish IND-CPA confidentiality for the chain without modelling the state hash as a random oracle. The reduction covers quantum adversaries under quantum hardness assumptions, with classical keys, messages and ciphertexts; no concrete security level is established. With independent uniform selectors, a restricted direct-decryption model quantifies reduced fragment recovery under partial key exposure, without improving full-message recovery probability over an independent-block baseline. Known-plaintext and candidate-message attacks, and parallel candidate-table decryption, delimit this result. Neither a universal sequential lower bound nor authentication or chosen-ciphertext security is established. Replacing an earlier scalar-exposing proposal, we give an augmented-lattice interpretation, integral-transport obstructions and a noise budget for research on curved, nontrivial bundles. A byte-level specification, pseudocode, test vectors and numerical checks support verification.