References & Further Reading

References

A. Shamir, How to Share a Secret, 1979
The foundational paper introducing polynomial-based secret sharing. Remarkably short and readable — still the clearest introduction to the subject 45 years later.
G. R. Blakley, Safeguarding Cryptographic Keys, 1979
Independent, near-simultaneous introduction of secret sharing using hyperplane geometry. Worth reading alongside Shamir to appreciate both perspectives on the same information-theoretic problem.
E. D. Karnin, J. W. Greene, and M. E. Hellman, On Secret Sharing Systems, 1983
Systematizes the information-theoretic framework for secret sharing, including the share-size lower bound proved in Section 3.1. Essential reference for the converse analysis.
G. R. Blakley and C. Meadows, Security of Ramp Schemes, 1985
First formal treatment of ramp secret sharing. Introduces the threshold / ramp-width trade-off and proves the basic security properties.
H. Yamamoto, Secret Sharing System Using $(k, L, n)$ Threshold Scheme, 1986
The information-theoretic characterization of ramp secret sharing, including the linear leakage formula used in Section 3.4.
C. Asmuth and J. Bloom, A Modular Approach to Key Safeguarding, 1983
Chinese Remainder Theorem–based threshold scheme. Useful when the secret is naturally an integer and when the arithmetic primitives align with existing cryptographic systems (e.g., threshold RSA).
R. J. McEliece and D. V. Sarwate, On Sharing Secrets and Reed-Solomon Codes, 1981
Identifies the equivalence between Shamir secret sharing and Reed-Solomon coding. Important perspective for Chapter 11, where we combine secret sharing with error correction.
R. Cramer, I. B. Damgård, and J. B. Nielsen, Secure Multiparty Computation and Secret Sharing, Cambridge University Press, 2015
The definitive modern textbook on secret sharing and its role in secure multi-party computation. Chapters 3–6 cover the constructions of this chapter in full generality.
W.-T. Chang and R. Tandon, On the Upload versus Download Cost for Secure and Private Matrix Multiplication, 2018
A modern reference for secure coded matrix multiplication — the composition of Shamir with polynomial codes. Anticipates the protocol developed in Chapter 5.
K. Bonawitz, V. Ivanov, B. Kreuter, A. Marcedone, H. B. McMahan, S. Patel, D. Ramage, A. Segal, and K. Seth, Practical Secure Aggregation for Privacy-Preserving Machine Learning, 2017
The protocol that brought additive secret sharing into federated-learning production. Uses exactly the $(n, n)$-scheme of Section 3.1 with Diffie–Hellman–seeded masks.
H. Sun and S. A. Jafar, The Capacity of Private Information Retrieval, 2017
Derivation of the classical PIR capacity $C_{\\text{PIR}} = (1 + 1/N + \\cdots + 1/N^{K-1})^{-1}$. Uses linear secret sharing as the privacy primitive.
K. Wan, D. Tuninetti, and G. Caire, Fundamental Limits of Caching for Demand Privacy against Colluding Users, 2021
Representative CommIT-group contribution building on secret sharing. Tagged in Chapter 7 as the primary commit_contribution block for coded data shuffling with demand-privacy constraints.
T. Jahani-Nezhad, M. A. Maddah-Ali, and G. Caire, Byzantine-Resilient Secure Aggregation for Federated Learning Based on Ramp Sharing, 2023
The ByzSecAgg paper — one of the CommIT group's signature contributions to this book. Combines ramp secret sharing, coded outlier detection, and vector commitments. Tagged in Chapter 11 as the primary commit_contribution block.