ZIP: 212 +Title: Allow Recipient to Derive Sapling Ephemeral Secret from Note Plaintext +Owners: Sean Bowe <sean@electriccoin.co> +Status: Proposed +Category: Consensus +Created: 2019-03-31 +License: MIT+
Terminology 
+ The key words "MUST" and "MUST NOT" in this document are to be interpreted as described in RFC 2119.
+The function ToScalar is defined as in Section 4.4.2 of the Zcash Protocol Specification. 1
Abstract
+ This ZIP proposes a new note plaintext format for Sapling Outputs in transactions. The new format allows recipients to check the well-formedness of the emphemeral Diffie-Hellman key in the Output to avoid an assumption on zk-SNARK soundness for preventing diversified address linkability.
+Motivation
+ The Sapling payment protocol contains a feature called "diversified addresses" which allows a single incoming viewing key to receive payments on an enormous number of distinct and unlinkable payment addresses. This feature allows users to maintain many payment addresses without paying additional overhead during blockchain scanning.
+The feature works by allowing payment addresses to become a tuple (pk_d, d) of a public key pk_d and 88-bit diversifier d such that pk_d =
+[ivk] GH(d) for some incoming viewing key ivk. The hash function GH(d) maps from a diversifier to prime order elements of the Jubjub elliptic curve. It is possible for a user to choose many d to create several distinct and unlinkable payment addresses of this form.
In order to make a payment to a Sapling address, an ephemeral secret esk is sampled by the sender and an ephemeral public key epk = [esk] GH(d) is included in the Output description. Then, a shared Diffie-Hellman secret is computed by the sender as [esk] [8] pk_d. The recipient can recover this shared secret without knowledge of the particular d by computing [ivk] [8]
+epk. This shared secret is then used as part of Note decryption.
Naively, the recipient cannot know which (pk_d, d) was used to compute the shared secret, but the sender is asked to include the d within the note plaintext to reconstruct the Note. However, if the recipient has more than one known addresses, an attacker could use a different payment address to perform secret exchange and, by observing the behavior of the recipient, link the two diversified addresses together. (This attacker strategy was discovered by Brian Warner earlier in the design of the Sapling protocol.)
In order to prevent this attack, the protocol currently forces the sender to prove knowledge of the discrete logarithm of epk with respect to the g_d =
+GH(d) included within the Note commitment. This g_d is determined by d and recomputed during Note decryption, and so the recipient will either be unable to decrypt the note or the sender will be unable to perform the attack.
However, this check occurs as part of the zero-knowledge proof statement and so relies on the soundness of the underlying zk-SNARK in Sapling, and therefore it relies on relatively strong cryptographic assumptions and a trusted setup. It would be preferable to force the sender to transfer esk within the Note plaintext so that, during note decryption, the recipient can check that epk =
+[esk] g_d (for the expected g_d) and ignore the payment as invalid otherwise. This forms a line of defense in the case that soundness of the zk-SNARK does not hold.
Merely sending esk to the recipient in the Note plaintext would require us to enlarge the note plaintext, but also would compromise the proof of IND-CCA2 security for in-band secret distribution. We avoid both of these concerns by using a key derivation to obtain both esk and rcm.
Specification
+ Pseudo random functions (PRFs) are defined in section 4.2.1 of the Zcash Protocol Specification. 3 We will be adapting PRF^expand for the purposes of this ZIP. This function is keyed by a 256-bit key sk and takes an arbitrary length byte sequence as input, returning a 64-byte sequence as output.
Changes to Sapling Note plaintexts
+ Note plaintext encodings are specified in section 5.5 of the Zcash Protocol Specification. 4 Currently, the encoding of a Sapling note plaintext requires that the first byte take the form 0x01, indicating the version of the note plaintext. In addition, a 256-bit rcm field exists within the note plaintext and encoding.
Following the activation of this ZIP, the first byte of the encoding MUST take the form 0x02 (representing the new note plaintext version) and the field rcm of the encoding will be renamed to rseed. This field rseed of the Sapling note plaintext will no longer take the type of NoteCommit^Sapling.Trapdoor but will instead be a 32-byte sequence. The requirement that rseed (previously, rcm) be a scalar of the Jubjub elliptic curve, when interpreted as a little endian integer, is removed from the decryption of note plaintexts as described in sections 4.17.2 and 4.17.3 of the Zcash Protocol Specification. 5 6
Changes to the process of sending Sapling notes
+ The process of sending notes in Sapling is described in section 4.6.2 of the Zcash Protocol Specification. 7 During this process, the sender samples rcm^new uniformly at random. In addition, the process of encrypting a note is described in section 4.17.1 of the Zcash Protocol Specification. 2 During this process, the sender also samples the ephemeral private key esk uniformly at random.
After the activation of this ZIP, the sender will sample a uniformly random 32-byte sequence rseed. The note plaintext will take rseed in place of rcm^new.
rcm^new is then computed by the sender as the output of ToScalar(PRF^expand_rseed([4])).
esk is also computed by the sender as the output of ToScalar(PRF^expand_rseed([5])).
Changes to the process of receiving Sapling notes
+ The process of receiving notes in Sapling is described in sections 4.17.2 and 4.17.3 of the Zcash Protocol Specification. 5 6
+After the activation of this ZIP, the note plaintext contains a field rseed that is a 32-byte sequence rather than a scalar value rcm. The recipient, during decryption and in any later contexts, will interpret the value rcm as the output of ToScalar(PRF^expand_rseed([4])). Further, the recipient MUST compute esk as ToScalar(PRF^expand_rseed([5])) and check that epk =
+[esk] g_d and fail decryption if this check is not satisfied.
Rationale
+ The attack that this prevents is an interactive attack that requires an adversary to be able to break critical soundness properties of the zk-SNARKs underlying Sapling. It is potentially valid to assume that this cannot occur, due to other damaging effects on the system such as undetectable counterfeiting. However, we have attempted to avoid any instance in the protocol where privacy (even against interactive attacks) depended on strong cryptographic assumptions. Acting differently here would be confusing for users that have previously been told that "privacy does not depend on zk-SNARK soundness" or similar claims.
+It is possible for us to infringe on the length of the memo field and ask the sender to provide esk within the existing note plaintext without modifying the transaction format, but this would harm users that have come to expect a 512-byte memo field to be available to them. Changes to the memo field length should be considered in a broader context than changes made for cryptographic purposes.
It is possible to transmit a signature of knowledge of a correct esk rather than esk itself, but this appears to be an unnecessary complication and is likely slower than just supplying esk.
Security and Privacy Considerations
+ The changes made in this proposal prevent an interactive attack that could link together diversified addresses by only breaking the knowledge soundness assumption of the zk-SNARK. It is already assumed that the adversary cannot defeat the EC-DDH assumption of the Jubjub elliptic curve, for it could perform a linkability attack trivially in that case.
+In the naive case where the protocol is modified so that esk is supplied directly to the recipient (rather than derived through rseed) this would lead to an instance of key-dependent encryption, which is difficult or perhaps impossible to prove secure using existing security notions. Our approach of using a key derivation, which ultimately queries an oracle, allows a proof for IND-CCA2 security to be written by reprogramming the oracle to return bogus keys when necessary.
Reference Implementation
+ TBD
+Acknowledgements
+ The discovery that diversified address unlinkability depended on the zk-SNARK knowledge assumption was made by Sean Bowe and Zooko Wilcox.
+References
+ | 1 | +Zcash Protocol Specification, Version 2020.1.4 [Overwinter+Sapling+Blossom+Heartwood] or later | +
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| 2 | +Section 4.17.1: Encryption (Sapling). Zcash Protocol Specification, Version 2020.1.4 [Overwinter+Sapling+Blossom+Heartwood] or later | +
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| 3 | +Section 4.1.2: Pseudo Random Functions. Zcash Protocol Specification, Version 2020.1.4 [Overwinter+Sapling+Blossom+Heartwood] or later | +
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| 4 | +Section 5.5: Encodings of Note Plaintexts and Memo Fields. Zcash Protocol Specification, Version 2020.1.4 [Overwinter+Sapling+Blossom+Heartwood] or later | +
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| 5 | +Section 4.17.2: Decryption using an Incoming Viewing Key (Sapling). Zcash Protocol Specification, Version 2020.1.4 [Overwinter+Sapling+Blossom+Heartwood] or later | +
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| 6 | +Section 4.17.3: Decryption using a Full Viewing Key (Sapling). Zcash Protocol Specification, Version 2020.1.4 [Overwinter+Sapling+Blossom+Heartwood] or later | +
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| 7 | +Section 4.6.2: Sending Notes (Sapling). Zcash Protocol Specification, Version 2020.1.4 [Overwinter+Sapling+Blossom+Heartwood] or later | +
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