Recommended Reading

The following table lists papers relevant for every protocol supported by MP-SPDZ. This is the same as the output when using --papers during compilation. If you prefer a more general yet comprehensive introduction to MPC, we recommend A Pragmatic Introduction to Secure Multi-Party Computation.

Protocol shorthand	Papers
astra	https://eprint.iacr.org/2025/919
atlas	https://eprint.iacr.org/2021/833
brain	https://eprint.iacr.org/2019/164
ccd	https://eprint.iacr.org/2000/037, https://doi.org/10.1145/62212.62214
chaigear	https://eprint.iacr.org/2017/1230, https://eprint.iacr.org/2019/035
cowgear	https://eprint.iacr.org/2017/1230, https://eprint.iacr.org/2019/035
dealer-ring	https://mp-spdz.readthedocs.io/en/latest/readme.html#dealer-model
hemi	https://eprint.iacr.org/2022/933, https://eprint.iacr.org/2017/1230, https://eprint.iacr.org/2014/106
highgear	https://eprint.iacr.org/2017/1230, https://eprint.iacr.org/2019/035, https://eprint.iacr.org/2019/1300
lowgear	https://eprint.iacr.org/2017/1230, https://eprint.iacr.org/2019/035, https://eprint.iacr.org/2019/1300
mal-rep-bmr	https://eprint.iacr.org/2017/981
mal-shamir-bmr	https://eprint.iacr.org/2017/981
mal-ccd	https://eprint.iacr.org/2017/816, https://doi.org/10.1145/62212.62214
mal-rep-bin	https://eprint.iacr.org/2016/944
mal-rep-field	https://eprint.iacr.org/2017/816
mal-rep-ring	https://eprint.iacr.org/2019/164
mal-shamir	https://eprint.iacr.org/2017/816
mama	https://eprint.iacr.org/2016/505
mascot	https://eprint.iacr.org/2016/505
ps-rep-bin	https://doi.org/10.1109/SP.2017.15
ps-rep-field	https://eprint.iacr.org/2017/816
ps-rep-ring	https://eprint.iacr.org/2019/164
real-bmr	https://eprint.iacr.org/2017/981
rep-bmr	https://eprint.iacr.org/2017/981
rep4-ring	https://eprint.iacr.org/2020/1330
replicated	https://eprint.iacr.org/2016/768
rep-field	https://eprint.iacr.org/2016/768
ring	https://eprint.iacr.org/2025/919, https://eprint.iacr.org/2016/768
semi	https://eprint.iacr.org/2016/505, https://eprint.iacr.org/2020/521
semi-bin	https://eprint.iacr.org/2016/505, https://eprint.iacr.org/2020/521
semi-bmr	https://eprint.iacr.org/2017/981
semi2k	https://eprint.iacr.org/2016/505, https://eprint.iacr.org/2020/521
shamir	https://eprint.iacr.org/2000/037
shamir-bmr	https://eprint.iacr.org/2017/981
soho	https://eprint.iacr.org/2017/1230, https://eprint.iacr.org/2020/521
spdz2k	https://eprint.iacr.org/2018/482
sy-rep-field	https://eprint.iacr.org/2018/570
sy-rep-ring	https://eprint.iacr.org/2019/1298
sy-shamir	https://eprint.iacr.org/2018/570
temi	https://eprint.iacr.org/2022/933, https://eprint.iacr.org/2017/1230, https://eprint.iacr.org/2014/106, https://eprint.iacr.org/2000/055
tinier	https://eprint.iacr.org/2015/901
tiny	https://eprint.iacr.org/2018/482, https://eprint.iacr.org/2016/944
trio	https://eprint.iacr.org/2025/919
yao	https://eprint.iacr.org/2014/756, https://eprint.iacr.org/2019/1168

Further recommended reading extracted from the code can be found in the following table. This mostly refers to higher-level protocols based on the arithmetic blackbox provided by the protocols above. You can use --papers when compiling a concrete program to find which papers are relevant for a particular computation.

Keywords	Papers
approximate inverse square root	https://doi.org/10.1145/3411501.3419427
bit decomposition, equality, truncation	https://eprint.iacr.org/2018/403
bit decomposition, fixed-point division, fixed-point numbers, probabilistic truncation	https://www.ifca.ai/pub/fc10/31_47.pdf
client inputs	https://eprint.iacr.org/2015/1006
comparison	https://eprint.iacr.org/2025/919
comparison, modulo, truncation	https://eprint.iacr.org/archive/2019/131/20191015:083051
decision tree learning	https://doi.org/10.56553/popets-2023-0021
deep learning	https://eprint.iacr.org/2022/933
(e)daBits	https://eprint.iacr.org/2020/338
equality, modulo	https://www.researchgate.net/publication/225092133, https://doi.org/10.1007/978-3-642-15317-4_13 (paywall)
exponential, inverse trigonometric functions, logarithm, square root, trigonometric functions	https://eprint.iacr.org/2019/354
floating-point numbers, power of two, secret truncation	https://eprint.iacr.org/2012/405
full bit decomposition	https://doi.org/10.1007/978-3-540-71677-8_23
heap queue, ORAM	https://eprint.iacr.org/2014/137
loop optimization	https://eprint.iacr.org/2024/1990
path oblivious heap	https://eprint.iacr.org/2019/274
probabilistic truncation, secret truncation	https://eprint.iacr.org/2019/131
sorting	https://eprint.iacr.org/2014/121
sorting	https://eprint.iacr.org/2013/143
square-root ORAM	https://doi.org/10.1109/SP.2016.21