Checkpoint the party/runtime stack before share-program and malicious-mode work.
Ship the TLS mesh, composer, Beaver/Yao/leaf MPC, prep/online paths, apps, and docs so the tree is pushable before elevating share_expr, security_mode, and prep resume. Co-authored-by: Cursor <cursoragent@cursor.com>
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# Point-programmable vector commitments {#ppvc_manual}
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<div class="eli5"><b>ELI5.</b> The vector is bound before the coordinate is chosen. Each coordinate is a pair of 1-bit DPF roots, and both roots are committed with a Naor string. Opening one side of each pair writes the hidden coordinate, or the sum, onto a public index.</div>
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\endhtmlonly
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A point-programmable vector commitment binds a vector
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`x` in `(Z/2^s Z)^n` and still lets one hidden coordinate be chosen
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after the commitment is published.
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## What an opening proves {#ppvc_verify}
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<div class="eli5"><b>ELI5.</b> verify recomputes the Naor string on each opened root and compares it to the commitment. A root that was not the committed one fails. The check does not reveal the other coordinates.</div>
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\endhtmlonly
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`verify` checks each opened root against its Naor string.
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`accept` also checks the programmed statement: the rotated coordinate
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when `mu` is 0, the column sum when `mu` is 1.
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Naor's string commitment is Moni Naor, [Bit Commitment Using Pseudorandomness](@ref bib_naor), Journal of Cryptology 1991.
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The point keys are the Boyle–Gilboa–Ishai construction named in
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[DPF basics](@ref point_functions).
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\htmlonly
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<div class="tldr"><b>TL;DR.</b> Commit binds the vector before the coordinate is chosen, by committing both DPF roots. Open writes one coordinate or the sum onto a public index. verify checks those roots against the Naor strings.</div>
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\endhtmlonly
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