Research seriesL3algorithms
Zero-knowledge proves a computation and homomorphic encryption computes on one party's ciphertext; secure multi-party computation lets several distrusting parties jointly compute over their combined private data without any one seeing another's inputs. It is the missing third leg of confidential AI. This series builds MPC from secret sharing and garbled circuits through private set intersection to federated learning with secure aggregation. Grounded in Shamir, Yao, and GMW.
Secure multi-party computation lets several distrusting parties jointly compute a function over their private inputs, learning the result and nothing else. The definition is a comparison to an ideal.
Split a secret into shares so that a threshold of parties can reconstruct it but fewer learn nothing. This one primitive underlies MPC and threshold signing and decryption.
There are two classic ways to securely compute any function: garble the circuit once and evaluate it, or secret-share and evaluate gate by gate. They trade rounds against bandwidth.
Private set intersection lets two parties find their common elements without revealing anything else. With its variants — cardinality, sum, and secure aggregation — it powers real privacy-preserving analytics.
MPC brings machine learning to data that cannot be pooled: federated learning with secure aggregation, and split inference across parties. It completes the confidential-AI trio with zero-knowledge and FHE.