| Internet-Draft | MoLE Cryptography | July 2026 |
| Doe | Expires 7 January 2027 | [Page] |
TODO Abstract¶
This note is to be removed before publishing as an RFC.¶
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TODO¶
The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT", "SHOULD", "SHOULD NOT", "RECOMMENDED", "NOT RECOMMENDED", "MAY", and "OPTIONAL" in this document are to be interpreted as described in BCP 14 [RFC2119] [RFC8174] when, and only when, they appear in all capitals, as shown here.¶
Unless otherwise specified, this document encodes protocol messages in TLS notation (Section 3 of [TLS13]). Moreover, all constants are in network byte order.¶
We define a two round protocol between an Anchor and Client to produce an endorsement, and then a half-round Credential generation step presuming the Client knows the Anchors the Issuer accepts. We let hash2curve be the Hash2Curve function from [Hash2Curve], and H be hash function whose output length is sufficiently long.¶
The Endorsement is a structure with m, Y=Hash2Curve(m), Zhat, Xhat and private data gamma. The Anchor has a public key X and a private key x, and X = xG. The public form of a credential Zhat, Xhat, and a proof that Xhat = vG, Zhat = vY. Xhat = gamma X, and the client will prove it knows gamma such that Xhat is a power of one of the public keys of an Anchor the moderator trusts.¶
Client randomly selects scalars v and gamma, and sends Yprime = v Y to the anchor.¶
The Anchor computes Zprime = x Yprime, selects three random scalars aprime, bprime, and tprime. It computes a commitment. It then computes T1prime = tprime Yprime, T2Prime = tprime G. It then transmits Zprime, Cprime, and T1prime and T2prime to the client.¶
The client now has to compute some proof elements and send a scalar to the server. The client lets Zhat = gamma v^-1 Z. It then picks alpha, a random nonzero scalar, beta, a random scalar, epsilon, a random nonzero scalar, and rho, a random scalar. The client computes C = alpha^-1 C' - beta H, T1 = epsilon ^ -1 v ^ -1 (T1prime - rho Yprime), T2 = epsilon ^ -1 (T2prime - rho G).¶
The client now computes e = H(Y, Zhat, T1, T2, C), and sends eprime = epsilon alpha^{-1} gamma e to the anchor¶
The anchor computes rprime = tprime + eprime aprime x and sends back rprime aprime and bprime.¶
The client then checks Cprime = aprime G + bprime H, that aprime is invertable, and then computes a = alpha ^-1 aprime, b=alpha^-1 bprime - beta, r = epsilon ^ -1 (rprime - rho). The client then verifies Xhat, Zhat, m, e, a, b, r are a valid endorsement as in the section below.¶
A verifier gets Xhat, Zhat, m and e, a, b, r. The verifier computes Y=Hash2Curve(m), and then lets T1 = r Y - e a Zhat, T2 = rG - e a Xhat, C = a G + b H. It checks a is not zero and Y is not the identity and then checks e = H(Y, Zhat, T1, T2, C).¶
In addition to the above endorsement, the client must prove knowledge of a value gamma such that Xhat = gamma Xi for some i, where the Xi is the list of issuers trusted. This is a standard OR sigma proof, and we can use sigma stacking to compact the proof.¶
This document has no IANA actions.¶
TODO acknowledge.¶