The computational bargain · 1976 → today

Today's crypto: a bet on hard math

Modern web security is a bargain: strangers can talk privately at scale because we bet certain problems stay hard, until machines or math change the calendar. That bargain is real for transport. It is the wrong sole foundation for authorization that must not become a stolen capability.

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~7 min overview · ~5 min formalContinue: Sixth primitive

What the bargain is

The browser padlock promises a secure connection. Underneath is not steel: it is a bet that discrete logs, factoring, or lattice problems stay expensive long enough. Sessions end; harvest-now-decrypt-later clocks keep ticking on whatever an adversary archived.

Call that bet the computational bargain: security that assumes attackers are too slow. One-way functions and Diffie–Hellman-style handshakes buy scalable privacy among strangers. None of that is the same as asking whether an authorization transcript carries secret-relevant information, even against unbounded compute.

The computational bargain: TLS/PKI hardness stack versus Shannon emptiness logistics, two jobs for secrecy — Hardness is a clock · emptiness is a model
Read left as the TLS/PKI hardness stack (a clock that expires with machines) and right as Shannon emptiness logistics (a model, not a race). The bottom strip separates transport secrecy from empty authorization. Takeaway: modern crypto’s bargain is useful for transport; Channel Zero argues a different authorization job.

Why it matters for authorization

Inside the TLS tunnel, bearer tokens still authorize if stolen. Hotel-keycard logic: possession of the card opens the door until the front desk notices. That is why authorization-on-possession remains the breach vector even when the padlock icon is green.

Vs normal crypto: what the bargain purchased

Scale. Strangers without pre-shared one-time pads can negotiate a session. Hybrid TLS stacks handshake hardness with AES for bytes in flight. Perfect forward secrecy shortens damage if long-term keys leak later: valuable mitigation, not Shannon emptiness. Certificates still prove who may speak for a while; that is the part of PKI worth sharpening, not romanticizing: Replaces the part of PKI that keeps breaching you (the credentials that authorize requests).

Transport secrecy versus empty authorization channel
Job	Right tool class
Protect bytes in flight	Computational crypto (TLS / PQ hybrids): keep it
Decide who may act once without ambient secrets	Information-theoretic / Channel Zero-style authorization

If someone records the channel

Under the computational bargain, archives wait for better computers (harvest-now-decrypt-later). Under Channel Zero authorization, the notebook can fill with surface bits while effective mutual information with the secret stays empty, recording without learning. See Recording without learning.

Temporal decay and quantum myths: Quantum myths vs real bounds.

Formal mathematics and notation

Formal framing

Semantic security games ask whether a bounded adversary can distinguish encrypted messages better than chance. Perfect secrecy asks whether the observation updates beliefs at all. Shannon’s classic statement (posterior equals prior) is equivalent to zero mutual information between message and ciphertext. Channel Zero recovers that spirit for authorization transcripts, not OTP logistics for every network byte (notation).

Shannon emptiness (message secrecy)

I(M;C)=0

Read as: The ciphertext carries zero mutual information about the message.

Arguments

$M$: : message or protected value before observation
$C$: : ciphertext in the Shannon secrecy equation

Operators

$I$: : mutual information
$= 0$: : posterior belief does not change after observing ciphertext

Significance: It states the information-theoretic gold standard the computational bargain deliberately relaxed for scalable transport.

Computational contrast: TLS and related stacks replace this emptiness requirement with a hardness-clock game: a bounded adversary should not distinguish ciphertexts better than chance.

References:Perfect secrecy

Authorization emptiness (Channel Zero)

I(X;O\mid C)=0

Read as: Given challenge C, observable transcript O reveals no mutual information about hidden state X.

Arguments

$X$: : hidden state: private map, secret choice, key material, or local ceremony state
$O$: : observable public transcript or archive
$C$: : public challenge or context conditioning the observation

Operators

$I$: : mutual information between hidden state and observation
$\mid$: : conditioning on the public challenge
$= 0$: : zero effective leakage under the stated model

Significance: It relocates Shannon emptiness from message secrecy onto authorization transcripts so stolen archives are not stolen capability under the model.

Computational contrast: The computational bargain is the right tool for bytes in flight; it is the wrong sole foundation for authorization that must not become ambient reusable authority.

References:Channel Zero Information-theoretic authorization

Assumptions: Axioms. Scope: Claims. See also Shannon: Perfect secrecy.

What the bargain is

Why it matters for authorization

Vs normal crypto: what the bargain purchased

If someone records the channel

Formal framing

Shannon emptiness (message secrecy)

Arguments

Operators

Authorization emptiness (Channel Zero)

Arguments

Operators

Bridge to Channel Zero