This document presents and discusses an extension to GNU Taler that provides anonymous age-restriction.
Merchants are legally obliged to perform age verification of customers when they buy certain goods and services. Current mechanisms for age verification are either ID-based or require the usage of credit/debit cards. In all cases sensitive private information is disclosed.
We want to offer a better mechanism for age-restriction with GNU Taler that
The mechanism is presented as an ‘extension’ to GNU Taler, that is, as an optional feature that can be switched on by the exchange operator.
We propose an extension to GNU Taler for age-restriction that can be enabled by an Exchange¹).
Once enabled, coins with age restrictions can be withdrawn by parents/warden who can choose to commit the coins to a certain maximum age out of a predefined list of age groups.
The minors/wards receive those coins and can now attest a required minimum age (provided that age is less or equal to the committed age of the coins) to merchants, who can verify the minimum age.
For the rest values (change) after an transaction, the minor/ward can derive new age-restricted coins. The exchange can compare the equality of the age-restriction of the old coin with the new coin (in a zero-knowledge 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. We have published a paper Zero Knowledge Age Restriction for GNU Taler 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.
The main ideas are as follows:
TODO: Summarize the design based on the five functions Commit()
,
Attest()
, Verify()
, Derive()
, Compare()
, once the paper from
Özgür and Christian is published.
The necessary changes in the exchange involve
Note
Registering an extension is defined in design document 006 ― Extensions.
The exchange indicates support for age-restriction in response to /keys
by
registering the extension age_restriction
with a value type
ExtensionAgeRestriction
:
interface ExtensionAgeRestriction {
// 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;
}
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 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
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
.
// 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;
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
apply for each denomination in the list:
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 (see above).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.
interface ExchangeKeysResponse {
//...
// List of denominations that support age-restriction with the age groups
// given in age_groups. This is only set **iff** the extension
// 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
// 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
//
// 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[];
//...
}
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:
-- 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.
The withdraw protocol is affected in the following situations:
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
The values ,
and
are known to the
Exchange and the Wallet. Then, Wallet and Exchange run the following protocol
for the withdrawal of one coin:
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
.
The actual implementation of the protocol above will have major optimizations to keep the bandwidth usage to a minimum and also ensure that a denomination in the commitment doesn’t expire before the reveal.
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
For the age commitment, calculate:
Then the vector is then the age commitment
associated to the coin’s private key
. For the non-disclosed coins,
the wallet can use the vector
of
private keys for the attestation.
Provided with the secret , the exchange can therefore calculate the
private key
, the blinding
, the nonce
(if
needed) and the age commitment
, along with the coin’s public
key
and use the value of
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:
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/$COIN_PUB/melt
POST request, the
MeltRequest
object is extended with an optional field
age_commitment_hash
:
interface MeltRequest {
...
// SHA256 hash of the age commitment of the coin, IFF the denomination
// has age restriction support. MUST be omitted otherwise.
age_commitment_hash?: AgeCommitmentHash;
...
}
type AgeCommitmentHash = SHA256HashCode;
The responses to the POST request remain the same.
For normal denominations without support for age restriction, the calculation for the signature check is as before (borrowing notation from Florian’s thesis):
Here, is the EdDSA public key of a coin,
is its
signature and
is the RSA public key of the
denomination.
For denominations with support for age restriction, the exchange takes the
hash value age_commitment_hash
(abbreviated as ) into account
when verifying the coin’s signature:
During the reveal phase – that is upon POST to /refreshes/$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
.
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 is extended to perform the following additional computation and checks:
Using the κ-1 transfer secrets 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
as the seed, and then calculates the corresponding κ-1 hash values
of those age commitments.
It then calculates the κ-1 blinded hashes
(using the notation from Florian’s
thesis) of the disclosed coins and together with the
of the
undisclosed coin, calculates the hash
which is then used in the
final verification step of the cut&choose protocol.
As always, the merchant has to provide the public key of a coin during a POST
to /coins/$COIN_PUB/deposit
. However, for coins with age restriction, the
signature check requires the hash of the age commitment. Therefore the request
object DepositRequest
is extended by an optional field
age_commitment_hash
which MUST be set (with the SHA256 hash of the age
commitment), iff the corresponding denomination had support for age restriction
enabled. The merchant has received this value prior from the customer during
purchase.
interface DepositRequest {
...
// Iff the corresponding denomination had support for age restriction
// enabled, this field MUST contain the SHA256 value of the age commitment that
// was provided during the purchase.
age_commitment_hash?: AgeCommitmentHash;
...
}
Again, the exchange can now check the validity of the coin with age restriction by evaluating
Also again, is the EdDSA public key of a coin,
is
its signature,
is the RSA public key of the
denomination and
is the value from
age_commitment_hash
.
If an order requires a minimum age, the merchant MUST express that required
minimum age in response to order claim by the wallet, that is, a POST to
[/instances/$INSTANCE]/orders/$ORDER_ID/claim
.
The object ContractTerms
is extended by an optional field
minimum_age
that can be any integer greater than 0. In reality
this value will not be smaller than, say, 8, and not larger than, say, 21.
interface ContractTerms {
...
// If the order requires a minimum age greater than 0, this field is set
// to the integer value of that age. In reality this value will not be
// smaller than, say, 8, and not larger than, say, 21.
minimum_age?: Integer;
...
}
By sending the contract term with the field minimum_age
set to an
non-zero integer value, the merchant implicetly signals that it understands the
extension age_restriction
for age restriction from the exchange.
If the ContractTerms
had a non-zero value in field
minimum_age
, the wallet has to provide evidence of that minimum
age by
The object CoinPaySig
used within a PayRequest
during a POST to
[/instances/$INSTANCE]/orders/$ORDER_ID/pay
is extended as follows:
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
Again, is the EdDSA public key of a coin,
is
its signature,
is the RSA public key of the
denomination and
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.
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.
Also discuss:
We had some very engaged discussions on the GNU Taler mailing list:
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.
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)
/* Carefully calculate the new value for a */
a1 := a / 8;
a2 := (h * a1) % L
a' := (a2 * 8) % L
/* Update b as well, binding it to h.
This is an additional step compared to GNS. */
b' := SHA256(b ∥ h)
return (a', b')
}
Edx25519_derive_public(P, seed) {
h := Edx25519_blinding_factor(P, seed)
return [h]*P
}
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
}