Z-Sigil: A Public-Key Cryptosystem with Chained Selection over a Fiber Bundle of Module-Lattice Keys
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.
Related
- Logarithmic upper bounds and axial front selection for spatially periodic lattice Fisher--KPP equations
- A Polynomial-Time Attack on the McEliece Cryptosystem on Elliptic Codes with Arbitrary Divisors
- Exact Chained-Word Threshold and Monotone-Path Structure in the Even Root-of-Unity Kaleidoscope Yang-Baxter Algebra
- Cryptanalysis of Image Cryptosystem via Finite-Time Projective Synchronization in Fractional-Order Inertial Memristive Neural Networks
- Addendum: On generalized canonical bundle formula and boundedness of complements in complex analytic setting
BibTeX
@misc{rondelli2026zsigil,
title = {{Z-Sigil: A Public-Key Cryptosystem with Chained Selection over a Fiber Bundle of Module-Lattice Keys}},
author = {Andrea Rondelli},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.38668},
eprint = {2609.38668},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.38668},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Z-Sigil: A Public-Key Cryptosystem with Chained Selection over a Fiber Bundle of Module-Lattice Keys
AU - Andrea Rondelli
PY - 2026
DA - 2026/09/29
PB - arXiv
DO - 10.48550/arxiv.2609.38668
UR - https://arxiv.org/abs/2609.38668
AB - 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.
ER -