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diff --git a/design-documents/024-age-restriction.rst b/design-documents/024-age-restriction.rst index c7433f00..5b6e091d 100644 --- a/design-documents/024-age-restriction.rst +++ b/design-documents/024-age-restriction.rst @@ -1,5 +1,5 @@ -DD 024: Anonymous Age Restriction Extension for GNU Taler -######################################################### +DD24: Anonymous Age Restriction Extension for GNU Taler +####################################################### Summary ======= @@ -18,7 +18,7 @@ sensitive private information is disclosed. We want to offer a better mechanism for age-restriction with GNU Taler that * ensures anonymity and unlinkability of purchases -* can be set to particular age groups by parents/wardens at withdrawal +* can be set to particular age groups by parents/wardens at withdrawal * is bound to particular coins/tokens * can be verified by the merchant at purchase time * persists even after refresh @@ -29,8 +29,6 @@ optional feature that can be switched on by the exchange operator. Requirements ============ -TODO - * legal requirements for merchants must allow for this kind of mechanism @@ -55,22 +53,68 @@ protocol, that gives the minor/ward a 1/κ chance to raise the minimum age for the new coin). The proposed solution maintains the guarantees of GNU Taler with respect to -anonymity and unlinkability. (TODO: refer to the paper, once published) +anonymity and unlinkability. We have published a paper +`Zero Knowledge Age Restriction for GNU Taler <https://link.springer.com/chapter/10.1007/978-3-031-17140-6_6>`_ +with the details. ¹) Once the feature is enabled and the age groups are defined, the exchange has to stick to that decision until the support for age restriction is disabled. We might reconsider this design decision at some point. -Building Blocks -^^^^^^^^^^^^^^^ +Main ideas and building blocks +^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ -TODO: Summarize the design based on the five functions ``Commit()``, -``Attest()``, ``Verify()``, ``Derive()``, ``Compare()``. +The main ideas are as follows: + +#. The exchange defines and publishes M+1 different *age groups* of increasing + order: :math:`0 < a_1 < \ldots < a_M` with :math:`a_i \in \mathbb{N}`. The + zeroth age group is :math:`\{0,\ldots,a_1-1\}`. + +#. An **unrestricted age commitment** is defined as a vector of length M of + pairs of Edx25519_ public and private keys on Curve25519. In other words: one + key pair for each age group after the zeroth: :math:`\bigl\langle (q_1, + p_1), \ldots, (q_M, p_M) \bigr\rangle`. Here, :math:`q_i` are the public keys + (mnemonic: **q-mitments**), :math:`p_i` are the private keys. + +#. A **restricted age commitment** *to age group m* is derived from an + unrestricted age commitment by removing all private keys for + indices larger than m: :math:`\bigl\langle (q_1, p_1), \ldots, (q_m, p_m), + \, (q_{m+1}, \perp), \ldots, (q_M, \perp )\bigr\rangle`. F.e. if *none* of + the private keys is provided, the age commitment would be restricted to the + zeroth age group. + +#. The act of restricting an unrestricted age commitment is performed by the + parent/ward. +#. An *age commitment* (without prefix) is just the vector of public keys: + :math:`\vec{Q} := \langle q_1, \ldots, q_M \rangle`. Note that from + just the age commitment one can not deduce if it originated from an + unrestricted or restricted one (and what age). + +#. An *attestation of age group k* is essentially the signature to any message + with the private key for slot k, if the corresponding private key is + available in a restricted age commitment. (Unrestricted age commitments can + attest for any age group). + +#. An age commitment is *bound to a particular coin* by incorporating the + SHA256 hash value of the age commitment (i.e. the M public keys) into the + signature of the coin. So instead of signing :math:`\text{FDH}_N(C_p)` with + the RSA private key of a denomination with support for age restriction, we + sign :math:`\text{FDH}_N(C_p, h_Q)`. Here, :math:`C_p` is the EdDSA public + key of a coin and :math:`h_Q` is the hash of the age commitment :math:`\vec{Q}`. + **Note:** A coin with age restriction can only be validated when both, the + public key of the coin itself **and** the hash of the age commitment, are + present. This needs to be supported in each subsystem: Exchange, Wallet and + Merchant. + + +TODO: Summarize the design based on the five functions ``Commit()``, +``Attest()``, ``Verify()``, ``Derive()``, ``Compare()``, once the paper from +Özgür and Christian is published. -Changes in the Exchange -^^^^^^^^^^^^^^^^^^^^^^^ +Changes in the Exchange API +^^^^^^^^^^^^^^^^^^^^^^^^^^^ The necessary changes in the exchange involve @@ -82,49 +126,84 @@ The necessary changes in the exchange involve Extension for age restriction ----------------------------- +.. note:: + + Registering an extension is defined in + :doc:`design document 006 ― Extensions <006-extensions>`. + + The exchange indicates support for age-restriction in response to ``/keys`` by -registering the extension ``age_restriction.v1`` with a value type +registering the extension ``age_restriction`` with a value type ``ExtensionAgeRestriction``: .. ts:def:: ExtensionAgeRestriction interface ExtensionAgeRestriction { - // The fields ``description``and ``required`` are mandatory for each - // extension. - - // Description will be something like: - // "Support for age restriction version 1 enabled. See - // https://docs.taler.net/design-documents/024-age-restriction.html"; - description: string; - - // Age restriction is not required to be supported by a wallet or - // merchant, so ``required`` will be set to ``false``. - required: boolean; - - // Age restriction specific fields. - - // Representation of the age groups as comma separated edges: Increasing - // from left to right, the values mark the begining of an age group up - // to, but not including the next value. The initial age group starts at - // 0 and is not listed. Example: "8:10:12:14:16:18:21". - // This field is mandatory and binding in the sense that its value is - // taken into consideration when signing the denominations in - // ``ExchangeKeysResponse.age_restricted_denoms``. - age_groups: string; + // The field ``critical`` is mandatory for an extension. + // Age restriction is not required to be understood by an client, so + // ``critical`` will be set to ``false``. + critical: false; + + // The field ``version`` is mandatory for an extension. It is of type + // `LibtoolVersion`. + version: "1"; + + // Age restriction specific configuration + config: ConfigAgeRestriction; } -Registering an extension is defined in -:doc:`design document 006 *Extensions* <006-extensions>`. +.. ts:def:: ConfigAgeRestriction + + interface ConfigAgeRestriction { + // The age groups. This field is mandatory and binding in the sense + // that its value is taken into consideration when signing the + // age restricted denominations in the `ExchangeKeysResponse` + age_groups: AgeGroups; + } + +Age Groups +~~~~~~~~~~ + +Age groups are represented as a finite list of positive, increasing integers +that mark the beginning of the *next* age group. The value 0 is omitted but +implicitly marks the beginning of the *zeroth* age group and the first number +in the list marks the beginning of the *first* age group. Age groups are +encoded as a colon separated string of integer values. They are referred to by +their *slot*, i.e. "age group 3" is the age group that starts with the 3. +integer in the list. + +For example: the string "8:10:12:14:16:18:21" represents the age groups + +0. {0,1,2,3,4,5,6,7} +#. {8,9} +#. {10,11} +#. {12,13} +#. {14,15} +#. {16,17} +#. {18,19,20} +#. {21, ⋯ } + +The field ``age_groups`` of type `AgeGroups` is mandatory and binding in the +sense that its value is taken into consideration when signing the denominations +in ``ExchangeKeysResponse.age_restricted_denoms``. + +.. ts:def:: AgeGroups + + // Representation of the age groups as colon separated edges: Increasing + // from left to right, the values mark the beginning of an age group up + // to, but not including the next value. The initial age group starts at + // 0 and is not listed. Example: "8:10:12:14:16:18:21". + type AgeGroups = string; + Age restricted denominations ----------------------------- +~~~~~~~~~~~~~~~~~~~~~~~~~~~~ -If age-restriction is registered as an extension under the name -``age_restriction.v1``, as described above, the root-object -``ExchangeKeysResponse`` in response to ``/keys`` MUST be extended by an -additional field ``age_restricted_denoms``. This is an *additional* list of -denominations that must be used for during modified ``refresh`` and ``deposit`` -operations (see below). +If age-restriction is registered as extension ``age_restriction``, as described +above, the root-object ``ExchangeKeysResponse`` in response to ``/keys`` MUST +be extended by an additional field ``age_restricted_denoms``. This is an +*additional* list of denominations that must be used during the modified +``refresh`` and ``deposit`` operations (see below). The data structure for those denominations is the same as for the regular ones in ``ExchangeKeysResponse.denoms``. **However**, the following differences @@ -138,6 +217,11 @@ apply for each denomination in the list: 2. The value of ``TALER_DenominationKeyValidityPS.purpose`` is set to ``TALER_SIGNATURE_MASTER_AGE_RESTRICTED_DENOMINATION_KEY_VALIDITY``. +And similar to ``.denoms``, if the query parameter ``last_issue_date`` was +provided by the client, the exchange will only return the keys that have +changed since the given timestamp. + + .. ts:def:: ExchangeKeysResponse interface ExchangeKeysResponse { @@ -145,60 +229,493 @@ apply for each denomination in the list: // List of denominations that support age-restriction with the age groups // given in age_groups. This is only set **iff** the extension - // ``age_restriction.v1`` is registered under ``entensions`` with type + // ``age_restriction`` is registered under ``entensions`` with type // ``ExtensionAgeRestriction``. // // The data structure for each denomination is the same as for the // denominations in ExchangeKeysResponse.denoms. **However**, the // following differences apply for each denomination in the list: // - // 1. The value of TALER_DenominationKeyValidityPS.denom_hash + // 1. The value of ``TALER_DenominationKeyValidityPS.denom_hash`` // is taken over the public key of the denomination __and__ the // string in ``ExtensionAgeRestriction.age_groups`` from the // corresponding extension object. // - // 2. The value of TALER_DenominationKeyValidityPS.purpose is set to - // TALER_SIGNATURE_MASTER_AGE_RESTRICTED_DENOMINATION_KEY_VALIDITY - age_restricted_denoms: Denoms[]; + // 2. The value of ``TALER_DenominationKeyValidityPS.purpose`` is set to + // ``TALER_SIGNATURE_MASTER_AGE_RESTRICTED_DENOMINATION_KEY_VALIDITY`` + // + // Similar as for ``.denoms``, if the query parameter ``last_issue_date`` + // was provided by the client, the exchange will only return the keys that + // have changed since the given timestamp. + age_restricted_denoms: Denom[]; //... } +SQL schema +----------- + +The exchange has to mark denominations with support for age restriction as such +in the database. Also, during the melting phase of the refresh operation, the +exchange will have to persist the SHA256 hash of the age commitment of the +original coin. + +The schema for the exchange is changed as follows: + +.. sourcecode:: sql + + -- Everything in one big transaction + BEGIN; + -- Check patch versioning is in place. + SELECT _v.register_patch('exchange-TBD', NULL, NULL); + + -- Support for age restriction is marked per denomination. + ALTER TABLE denominations + ADD COLUMN age_restricted BOOLEAN NOT NULL DEFAULT (false); + COMMENT ON COLUMN denominations.age_restriced + IS 'true if this denomination can be used for age restriction'; + + -- During the melting phase of the refresh, the wallet has to present the + -- hash value of the age commitment (only for denominations with support + -- for age restriction). + ALTER TABLE refresh_commitments + ADD COLUMN age_commitment_h BYTEA CHECK (LENGTH(age_commitment_h)=64); + COMMENT ON COLUMN refresh_commitments.age_commitment_h + IS 'SHA256 hash of the age commitment of the old coin, iff the corresponding + denomimination has support for age restriction, NULL otherwise.'; + COMMIT; + +Note the constraint on ``refresh_commitments.age_commitment_h``: It can be +NULL, but only iff the corresponding denomination (indirectly referenced via +table ``known_coins``) has ``.age_restricted`` set to true. This constraint +can not be expressed reliably with SQL. + + +Protocol changes +---------------- + +Withdraw +~~~~~~~~ + +The withdraw protocol is affected in the following situations: + +- A wire transfer to the exchange (to fill a reserve) was marked by the + originating bank as coming from a bank account of a minor, belonging to a of + a specific age group, or by other means. +- A Peer-to-Peer transaction was performed between customers. The receiving + customer's KYC result tells the exchange that the customer belongs to a + specific age group. + +In these cases, the wallet will have to perform a zero-knowledge protocol with +exchange as part of the the withdraw protocol, which we sketch here. Let + +- :math:`\kappa` be the same cut-and-choose parameter for the refresh-protocol. +- :math:`\Omega \in E` be a published, nothing-up-my-sleeve, constant + group-element on the elliptic curve. +- :math:`a \in \{1,\ldots,M\}` be the maximum age (group) for which the wallet + has to prove its commitment. + +The values :math:`\kappa`, :math:`\Omega` and :math:`a` are known to the +Exchange and the Wallet. Then, Wallet and Exchange run the following protocol +for the withdrawal of one coin: + +- *Wallet* + 1. creates planchets :math:`C_i` for :math:`i \in \{1,\ldots,\kappa\}` as candidates for *one* coin. + #. creates age-commitments :math:`\vec{Q}^i` for :math:`i \in \{1,\ldots,\kappa\}` as follows: + + a) creates :math:`a`-many Edx25519-keypairs :math:`(p^i_j, q^i_j)` + randomly for :math:`j \in \{1,\ldots,a\}` (with public keys :math:`q^i_j`), + #) chooses randomly :math:`(M - a)`-many scalars :math:`s^i_j` for :math:`j \in \{a+1,\ldots,M\}`, + #) calculates :math:`\omega^i_j = s^i_j*\Omega` for :math:`j \in \{a+1,\ldots,M \}`, + #) sets :math:`\vec{Q}^i := (q^i_1,\ldots,q^i_a,\omega^i_{a+1},\ldots,\omega^i_M)` + + #. calculates :math:`f_i := \text{FDH}(C_i, H(\vec{Q}^i))` for :math:`i \in \{ 1,\ldots,\kappa \}`. + #. chooses random blindings :math:`\beta_i(.)` for :math:`i \in \{1,\ldots,\kappa\}`. The blinding functions depend on the cipher (RSA, CS). + #. calculates :math:`F := \text{H}(\beta_1(f_1)||\ldots||\beta_\kappa(f_\kappa))` + #. sends :math:`F` to the Exchange + +- *Exchange* + 7. receives and stores :math:`F` + #. chooses randomly :math:`\gamma \in \{1,\ldots,\kappa\}` and + #. sends :math:`\gamma` to the Wallet. + +- *Wallet* + 10. receives :math:`\gamma` + #. sends to the Exchange the tuple :math:`\left(r_\gamma, \vec{\beta}, \vec{\vec{Q}}, \vec{\vec{S}}\right)` with + + - :math:`r_\gamma := \beta_\gamma(f_\gamma)` + - :math:`\vec{\beta} := (\beta^1,\ldots,\beta^{\gamma-1},\bot,\beta^{\gamma+1},\ldots,\beta^\kappa)` + - :math:`\vec{\vec{Q}} := (\vec{Q}^1,\ldots,\vec{Q}^{\gamma-1},\bot,\vec{Q}^{\gamma+1},\ldots,\vec{Q}^\kappa)` + - :math:`\vec{\vec{S}} := (\vec{S}^1,\ldots,\vec{S}^{\gamma-1},\bot,\vec{S}^{\gamma+1},\ldots,\vec{S}^\kappa)` + with :math:`\vec{S}^i := (s^i_j)` + +- *Exchange* + 12. receives :math:`\left(r, (\beta^i), (\vec{Q}^i), (\vec{B}^i) \right)` + #. calculates :math:`g_i := \beta_i\left(\text{FDH}(\vec{Q}^i)\right)` for :math:`i \neq \gamma` + #. compares :math:`F \overset{?}{=} \text{H}(g_1||\ldots||g_{\gamma - 1}||r||g_{\gamma+1}||\ldots||g_\kappa)` and bails out on inequality + #. for each :math:`\vec{B}^i, i \neq \gamma` + + i. calculates :math:`\tilde{\omega}^i_j := b^i_j * \Omega` for :math:`j \in \{a+1,\ldots,M\}` + #. compares each :math:`\tilde{\omega}^i_j` to :math:`q^i_j` from :math:`\vec{Q}^i = (q^i_1, \ldots, q^i_M)` and bails out on inequality + #. signs :math:`r` + #. sends (blinded) signature :math:`\sigma_r` to Wallet + +- *Wallet* + 18. receives :math:`\sigma_r` + #. calculates (unblinded) signature :math:`\sigma_\gamma := \beta^{-1}_\gamma(\sigma_r)` for coin :math:`C_\gamma`. + + +Note that the batch version of withdraw allows the withdrawal of *multiple* +coins at once. For that scenario the protocol sketched above is adapted to +accomodate for handling multiple coins at once -- thus multiplying the amount +of data by the amount of coins in question--, but all with the same value of +:math:`\gamma`. + +The *actual* implementation of the protocol above will have a major optimization +to keep the bandwidth usage to a minimum. Instead of generating and sending +the age commitment (array of public keys) and blindings for each coin, the +wallet *MUST* derive the corresponding blindings and the age commitments from +the coin's private key itself as follows: + +Let + +- :math:`c_s` be the private key of the coin, +- :math:`m \in \{1,\ldots,M\}` be the maximum age (according to the reserve) + that a wallet can commit to during the withdrawal. +- :math:`P` be a published constant Edx25519-public-key to which the private + key is not known to any client. + + +Then calculate the blinding :math:`\beta` for the coin as + +.. math:: + \beta &:= \text{HKDF}(c_s, \text{"blinding"}) + +If the denomination is using Clause-Schnorr signatures, calculate the nonce +:math:`n` for the coin as + +.. math:: + n &:= \text{HKDF}(c_s, \text{"cs-nonce"}) + + + +For the age commitment, calculate: + +1. For age group :math:`a \in \{1,\ldots,m\}`, set + +.. math:: + s_a &:= \text{HDKF}(c_s, \text{"age-commitment"}, a) \\ + p_a &:= \text{Edx25519\_generate\_private}(s_a) \\ + q_a &:= \text{Edx25519\_public\_from\_private}(p_a) + +2. For age group :math:`a \in \{m,\ldots,M\}`, set + +.. math:: + f_a &:= \text{HDKF}(c_s, \text{"age-factor"}, a) \\ + q_a &:= \text{Edx25519\_derive\_public}(P, f_a). + +Then the vector :math:`\vec{q} = \{q_1,\ldots,q_M\}` is then the age commitment +associated to the coin's private key :math:`c_s`. For the non-disclosed coins, +the wallet can use the vector :math:`(p_1,\ldots,p_m,\bot,\ldots,\bot)` of +private keys for the attestation. + +Provided with the private key :math:`c_s`, the exchange can therefore calculate +the blinding :math:`\beta`, the nonce :math:`n` (if needed) and the age +commitment :math:`\vec{q}` itself, along with the coin's public key :math:`C_p` +and use the value of + +.. math:: + + \text{TALER\_CoinPubHashP}(C_p, \text{age\_commitment\_hash}(\vec{q})) + +during the verification of the original age-withdraw-commitment. + + +For the withdrawal with age restriction, a sketch of the corresponding database +schema in the exchange is given here: + +.. graphviz:: + + digraph deposit_policies { + rankdir = LR; + splines = true; + fontname="monospace" + node [ + fontname="monospace" + shape=record + ] + + subgraph cluster_commitments { + label=<<B>withdraw_age_commitments</B>> + margin=20 + commitments [ + label="<id>withdraw_age_commitments_id\l|h_commitment\l|amount_with_fee_val\l|amount_with_fee_frac\l|noreveal_index\l|max_age_group\l|<res>reserve_pub\l|reserve_sig\l|timestamp\l" + ] + } + + subgraph cluster_reveals { + label=<<B>withdraw_age_reveals</B>> + margin=20 + reveals [ + label="freshcoin_index\l|<comm>withdraw_age_commitments_id\l|<denom>denominations_serial\l|h_coin_ev\l" + ] + } + + commitments:res->reserves:id [ label="n:1"; fontname="monospace"]; + reveals:comm -> commitments:id [ label="n:1"; fontname="monospace" ]; + reveals:denom -> denominations:id [ label="n:1"; fontname="monospace"] ; + + } + + +Refresh - melting phase +~~~~~~~~~~~~~~~~~~~~~~~ + +During the melting phase of the refresh, the wallet has to present the hash +value of the age commitment (for denominations with support for age +restriction). Therefore, in the ``/coins/$COIN_PUB/melt`` POST request, the +``MeltRequest`` object is extended with an optional field +``age_commitment_hash``: + +.. ts:def:: MeltRequest + + interface MeltRequest { + ... + + // SHA256 hash of the age commitment of the coin, IFF the denomination + // has age restriction support. MUST be omitted otherwise. + age_commitment_hash?: AgeCommitmentHash; + + ... + } + +.. ts:def:: AgeCommitmentHash + + type AgeCommitmentHash = SHA256HashCode; + +The responses to the POST request remain the same. + +For normal denominations *without* support for age restriction, the calculation +for the signature check is as before (borrowing notation from +`Florian's thesis <https://taler.net/papers/thesis-dold-phd-2019.pdf>`_): + +.. math:: + \text{FDH}_N(C_p)\; \stackrel{?}{=}\; \left(\sigma_C\right)^{e} \;\;\text{mod}\,N + +Here, :math:`C_p` is the EdDSA public key of a coin, :math:`\sigma_C` is its +signature and :math:`\langle e, N \rangle` is the RSA public key of the +denomination. + +For denominations *with* support for age restriction, the exchange takes the +hash value ``age_commitment_hash`` (abbreviated as :math:`h_a`) into account +when verifying the coin's signature: + +.. math:: + \text{FDH}_N(C_p, h_a)\; \stackrel{?}{=}\; \left(\sigma_C\right)^{e} \;\;\text{mod}N + + + + +Refresh - reveal phase +~~~~~~~~~~~~~~~~~~~~~~ + +During the reveal phase -- that is upon POST to ``/refreshes/$RCH/reveal`` -- +the client has to provide the original age commitment of the old coin (i.e. the +vector of public keys), iff the corresponding denomination had support for age +restriction. The size of the vector is defined by the Exchange implicetly as +the amount of age groups defined in the field ``.age_groups`` of the +``ExtensionAgeRestriction``. + +.. ts:def:: RevealRequest + + interface RevealRequest { + ... + + // Iff the corresponding denomination has support for age restriction, + // the client MUST provide the original age commitment, i.e. the vector + // of public keys. + // The size of the vector is defined by the Exchange implicetly as the + // amount of age groups defined in the field ``.age_groups`` of the + // ``ExtensionAgeRestriction``. + old_age_commitment?: Edx25519PublicKey[]; + + + ... + } + + +The exchange can now check if the provided public keys ``.old_age_commitment`` +have the same SHA256 hash value when hashed in sequence as the +``age_commitment_hash`` of the original coin from the call to melt. + +The existing `cut&choose protocol during the reveal phase +</core/api-exchange.html#post--refreshes-$RCH-reveal>`__ is extended to perform +the following additional computation and checks: -Refresh -------- +Using the κ-1 transfer secrets :math:`\tau_i` from the reveal request, the +exchange derives κ-1 age commitments from the ``old_age_commitment`` by calling +``Edx25519_derive_public()`` on each `Edx25519PublicKey`, with :math:`\tau_i` +as the seed, and then calculates the corresponding κ-1 hash values :math:`h_i` +of those age commitments. -TODO: Extension of the cut'n-choose-protocol. +It then calculates the κ-1 blinded hashes +:math:`m_i = r^{e_i}\text{FDH}_N(C^{(i)}_p, h_i)` (using the notation from Florian's +thesis) of the disclosed coins and together with the :math:`m_\gamma` of the +undisclosed coin, calculates the hash +:math:`h'_m = H(m_1,\cdots,m_\gamma,\cdots,m_\kappa)` which is then used in the +final verification step of the cut&choose protocol. Deposit -------- +~~~~~~~ -TODO: Add opaque hash value of the commitments to the protocol +As always, the merchant has to provide the public key of a coin during a POST +to ``/coins/$COIN_PUB/deposit``. However, for coins with age restriction, the +signature check requires the hash of the age commitment. Therefore the request +object ``DepositRequest`` is extended by an optional field +``age_commitment_hash`` which MUST be set (with the SHA256 hash of the age +commitment), iff the corresponding denomination had support for age restriction +enabled. The merchant has received this value prior from the customer during +purchase. -Changes in the Merchant -^^^^^^^^^^^^^^^^^^^^^^^ +.. ts:def:: DepositRequest -TODO: Spending protocol + interface DepositRequest { + ... + // Iff the corresponding denomination had support for age restriction + // enabled, this field MUST contain the SHA256 value of the age commitment that + // was provided during the purchase. + age_commitment_hash?: AgeCommitmentHash; -Changes in the Wallet -^^^^^^^^^^^^^^^^^^^^^ + ... + } + +Again, the exchange can now check the validity of the coin with age restriction +by evaluating + +.. math:: + \text{FDH}_N(C_p, h_a)\; \stackrel{?}{=}\; \left(\sigma_C\right)^{e} \;\;\text{mod}N + +Also again, :math:`C_p` is the EdDSA public key of a coin, :math:`\sigma_C` is +its signature, :math:`\langle e, N \rangle` is the RSA public key of the +denomination and :math:`h_a` is the value from ``age_commitment_hash``. + + + +Changes in the Merchant API +^^^^^^^^^^^^^^^^^^^^^^^^^^^ + + +Claiming the order +------------------ + +If an order requires a minimum age, the merchant MUST express that required +minimum age in response to order claim by the wallet, that is, a POST to +``[/instances/$INSTANCE]/orders/$ORDER_ID/claim``. + +The object ``ContractTerms`` is extended by an optional field +``minimum_age`` that can be any integer greater than 0. In reality +this value will not be smaller than, say, 8, and not larger than, say, 21. + +.. ts:def:: ContractTerms + + interface ContractTerms { + ... + + // If the order requires a minimum age greater than 0, this field is set + // to the integer value of that age. In reality this value will not be + // smaller than, say, 8, and not larger than, say, 21. + minimum_age?: Integer; + + ... + } + +By sending the contract term with the field ``minimum_age`` set to an +non-zero integer value, the merchant implicetly signals that it understands the +extension ``age_restriction`` for age restriction from the exchange. + + +Making the payment +------------------ + +If the ``ContractTerms`` had a non-zero value in field +``minimum_age``, the wallet has to provide evidence of that minimum +age by + +#. *either* using coins which are of denominations that had *no* age support + enabled, + +#. *or* using coins which are of denominations that have support for age + restriction enabled -TODO. + * and then ―for each such coin― it has the right private key of the + restricted age commitment to the age group into which the required minimum + age falls (i.e. a non-empty entry at the right index in vector of Edx25519 + keys, see above). -* choosing age-restriction during withdrawal coins from denominations with - support for age restriction. -* Define protocol to pass denominations to child/ward. + * and signs the required minimum age with each coin's private key + corresponding to the age group, + * and sends ―for each coin― the complete age commitment and the signature to + the merchant. + +The object ``CoinPaySig`` used within a ``PayRequest`` during a POST to +``[/instances/$INSTANCE]/orders/$ORDER_ID/pay`` is extended as follows: + +.. ts:def:: CoinPaySig + + export interface CoinPaySig { + ... + + // If a minimum age was required by the order and the wallet had coins that + // are at least committed to the corresponding age group, this is the + // signature of the minimum age as a string, using the private key to the + // corresponding age group. + minimum_age_sig?: Edx25519Signature; + + // If a minimum age was required by the order, this is age commitment bound + // to the coin, i.e. the complete vector of Edx25519_ public keys, one for each + // age group (as defined by the exchange). + age_commitment?: Edx25519PublicKey[]; + + } + + +The merchant can now verify + +#. the validity of each (age restricted) coin by evaluating + + .. math:: \text{FDH}_N(C_p, h_a)\; \stackrel{?}{=}\; \left(\sigma_C\right)^{e} \;\;\text{mod}N + + Again, :math:`C_p` is the EdDSA public key of a coin, :math:`\sigma_C` is + its signature, :math:`\langle e, N \rangle` is the RSA public key of the + denomination and :math:`h_a` is the SHA256 hash value of the vector in + ``age_commitment``. + +#. the minimum age requirement by checking the signature in ``minimum_age_sig`` + against the public key ``age_commitment[k]`` of the corresponding age group, + say, ``k``. (The minimum age must fall into the age group at index ``k`` as + defined by the exchange). + +**Note**: This applies only to coins for denominations that have support for +age restriction. Denominations *without* support for age restriction *always* +satisfy any minimum age requirement. + + + +Changes in the Wallet +^^^^^^^^^^^^^^^^^^^^^ + +A wallet implementation SHOULD support denominations with age restriction. In +that case it SHOULD allow to select an age group as upper bound during +withdraw. Alternatives ============ -TODO. - * ID-based systems * credit/debit card based systems @@ -206,12 +723,10 @@ TODO. Drawbacks ========= -TODO. - * age groups, once defined, are set permanently -* age restricted coins are basically shared between ward and warden. Also discuss: + * storage overhead * computational overhead * bandwidth overhead @@ -220,19 +735,115 @@ Also discuss: Discussion / Q&A ================ -We had some very engaged discussions on the GNU Taler mailing list -`<mailto:taler@gnu.org>`: +We had some very engaged discussions on the GNU Taler `mailing list <taler@gnu.org>`__: + +* `Money with capabilities <https://lists.gnu.org/archive/html/taler/2021-08/msg00005.html>`_ + +* `On age-restriction (was: online games in China) <https://lists.gnu.org/archive/html/taler/2021-09/msg00006.html>`__ + +* `Age-restriction is about coins, not currencies <https://lists.gnu.org/archive/html/taler/2021-09/msg00021.html>`__ + +* The published paper: `Zero Knowledge Age Restriction for GNU Taler <https://link.springer.com/chapter/10.1007/978-3-031-17140-6_6>`_ + + +.. _Edx25519: + +Edx25519 +======== + +Edx25519 is a variant of EdDSA on curve25519 which allows for repeated +derivation of private and public keys, independently. It is implemented in +`GNUNET with commit ce38d1f6c9bd7857a1c3bc2094a0ee9752b86c32. +<https://git.gnunet.org/gnunet.git/commit/?id=ce38d1f6c9bd7857a1c3bc2094a0ee9752b86c32>`__ + +The private keys in Edx25519 initially correspond to the data after expansion +and clamping in EdDSA. However, this correspondence is lost after deriving +further keys from existing ones. The public keys and signature verification +are compatible with EdDSA. + +The scheme is as follows: + +:: + + /* Private keys in Edx25519 are pairs (a, b) of 32 byte each. + * Initially they correspond to the result of the expansion + * and clamping in EdDSA. + */ + + Edx25519_generate_private(seed) { + /* EdDSA expand and clamp */ + dh := SHA-512(seed) + a := dh[0..31] + b := dh[32..64] + a[0] &= 0b11111000 + a[31] &= 0b01111111 + a[31] |= 0b01000000 + + return (a, b) + } + + Edx25519_public_from_private(private) { + /* Public keys are the same as in EdDSA */ + (a, _) := private + return [a] * G + } + + Edx25519_blinding_factor(P, seed) { + /* This is a helper function used in the derivation of + * private/public keys from existing ones. */ + h1 := HKDF_32(P, seed) + + /* Ensure that h == h % L */ + h := h1 % L + + /* Optionally: Make sure that we don't create weak keys. */ + P' := [h] * P + if !( (h!=1) && (h!=0) && (P'!=E) ) { + return Edx25519_blinding_factor(P, seed+1) + } + + return h + } + + Edx25519_derive_private(private, seed) { + /* This is based on the definition in + * GNUNET_CRYPTO_eddsa_private_key_derive. But it accepts + * and returns a private pair (a, b) and allows for iteration. + */ + (a, b) := private + P := Edx25519_public_key_from_private(private) + h := Edx25519_blinding_factor(P, seed) -* Money with capabilities - `<https://lists.gnu.org/archive/html/taler/2021-08/msg00005.html>`_ - + /* Carefully calculate the new value for a */ + a1 := a / 8; + a2 := (h * a1) % L + a' := (a2 * 8) % L -* On age-restriction (was: online games in China) - `<https://lists.gnu.org/archive/html/taler/2021-09/msg00006.html>`_ + /* Update b as well, binding it to h. + This is an additional step compared to GNS. */ + b' := SHA256(b ∥ h) -* Age-restriction is about coins, not currencies - `<https://lists.gnu.org/archive/html/taler/2021-09/msg00021.html>`_ + return (a', b') + } + Edx25519_derive_public(P, seed) { + h := Edx25519_blinding_factor(P, seed) + return [h]*P + } -The upcoming paper on anonymous age-restriction for GNU Taler from Özgür Kesim -and Christian Grothoff will be cited here, once it is published. + Edx25519_sign(private, message) { + /* As in Ed25519, except for the origin of b */ + (d, b) := private + P := Edx25519_public_from_private(private) + r := SHA-512(b ∥ message) + R := [r] * G + s := r + SHA-512(R ∥ P ∥ message) * d % L + + return (R,s) + } + + Edx25519_verify(P, message, signature) { + /* Identical to Ed25519 */ + (R, s) := signature + return [s] * G == R + [SHA-512(R ∥ P ∥ message)] * P + } |