WIP: age-withdraw, continue verify_commitment_and_max_age, 7/n

- coin, blinding, nonce and age restriction now derived from
  TALER_PlanchetMasterSecretP
- use max_age instead than max_age_group as argument
- Also, docs updated in other repo.
This commit is contained in:
Özgür Kesim 2023-03-13 00:31:49 +01:00
parent 62da9cca27
commit 187ae6f8a2
Signed by: oec
GPG Key ID: 3D76A56D79EDD9D7
7 changed files with 210 additions and 59 deletions

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@ -321,8 +321,8 @@ TEH_handler_age_withdraw (struct TEH_RequestContext *rc,
TALER_JSON_spec_amount ("amount", TALER_JSON_spec_amount ("amount",
TEH_currency, TEH_currency,
&awc.commitment.amount_with_fee), &awc.commitment.amount_with_fee),
GNUNET_JSON_spec_uint32 ("max_age_group", GNUNET_JSON_spec_uint32 ("max_age",
&awc.commitment.max_age_group), &awc.commitment.max_age),
GNUNET_JSON_spec_end () GNUNET_JSON_spec_end ()
}; };
@ -353,7 +353,7 @@ TEH_handler_age_withdraw (struct TEH_RequestContext *rc,
if (GNUNET_OK != if (GNUNET_OK !=
TALER_wallet_age_withdraw_verify (&awc.commitment.h_commitment, TALER_wallet_age_withdraw_verify (&awc.commitment.h_commitment,
&awc.commitment.amount_with_fee, &awc.commitment.amount_with_fee,
awc.commitment.max_age_group, awc.commitment.max_age,
&awc.commitment.reserve_pub, &awc.commitment.reserve_pub,
&awc.commitment.reserve_sig)) &awc.commitment.reserve_sig))
{ {

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@ -79,9 +79,9 @@ struct AgeRevealContext
struct TALER_BlindedCoinHashP *coin_evs; struct TALER_BlindedCoinHashP *coin_evs;
/** /**
* #num_coins*(kappa - 1) disclosed coins. * secrets for #num_coins*(kappa - 1) disclosed coins.
*/ */
struct GNUNET_CRYPTO_EddsaPrivateKey *disclosed_coins; struct TALER_PlanchetMasterSecretP *disclosed_coin_secrets;
/** /**
* The data from the original age-withdraw. Will be retrieved from * The data from the original age-withdraw. Will be retrieved from
@ -99,7 +99,7 @@ age_reveal_context_free (struct AgeRevealContext *actx)
GNUNET_free (actx->denoms_h); GNUNET_free (actx->denoms_h);
GNUNET_free (actx->denom_keys); GNUNET_free (actx->denom_keys);
GNUNET_free (actx->coin_evs); GNUNET_free (actx->coin_evs);
GNUNET_free (actx->disclosed_coins); GNUNET_free (actx->disclosed_coin_secrets);
} }
@ -111,7 +111,7 @@ age_reveal_context_free (struct AgeRevealContext *actx)
* @param connection The MHD connection to handle * @param connection The MHD connection to handle
* @param j_denoms_h Array of hashes of the denominations for the withdrawal, in JSON format * @param j_denoms_h Array of hashes of the denominations for the withdrawal, in JSON format
* @param j_coin_evs The blinded envelopes in JSON format for the coins that are not revealed and will be signed on success * @param j_coin_evs The blinded envelopes in JSON format for the coins that are not revealed and will be signed on success
* @param j_disclosed_coins The n*(kappa-1) disclosed coins' private keys in JSON format, from which all other attributes (age restriction, blinding, nonce) will be derived from * @param j_disclosed_coin_secrets The n*(kappa-1) disclosed coins' private keys in JSON format, from which all other attributes (age restriction, blinding, nonce) will be derived from
* @param[out] actx The context of the operation, only partially built at call time * @param[out] actx The context of the operation, only partially built at call time
* @param[out] mhd_mret The result if a reply is queued for MHD * @param[out] mhd_mret The result if a reply is queued for MHD
* @return true on success, false on failure, with a reply already queued for MHD. * @return true on success, false on failure, with a reply already queued for MHD.
@ -121,7 +121,7 @@ parse_age_withdraw_reveal_json (
struct MHD_Connection *connection, struct MHD_Connection *connection,
const json_t *j_denoms_h, const json_t *j_denoms_h,
const json_t *j_coin_evs, const json_t *j_coin_evs,
const json_t *j_disclosed_coins, const json_t *j_disclosed_coin_secrets,
struct AgeRevealContext *actx, struct AgeRevealContext *actx,
MHD_RESULT *mhd_ret) MHD_RESULT *mhd_ret)
{ {
@ -137,8 +137,8 @@ parse_age_withdraw_reveal_json (
error = "denoms_h must be an array"; error = "denoms_h must be an array";
else if (! json_is_array (j_coin_evs)) else if (! json_is_array (j_coin_evs))
error = "coin_evs must be an array"; error = "coin_evs must be an array";
else if (! json_is_array (j_disclosed_coins)) else if (! json_is_array (j_disclosed_coin_secrets))
error = "disclosed_coins must be an array"; error = "disclosed_coin_secrets must be an array";
else if (actx->num_coins == 0) else if (actx->num_coins == 0)
error = "denoms_h must not be empty"; error = "denoms_h must not be empty";
else if (actx->num_coins != json_array_size (j_coin_evs)) else if (actx->num_coins != json_array_size (j_coin_evs))
@ -151,8 +151,8 @@ parse_age_withdraw_reveal_json (
**/ **/
error = "maximum number of coins that can be withdrawn has been exceeded"; error = "maximum number of coins that can be withdrawn has been exceeded";
else if (actx->num_coins * (TALER_CNC_KAPPA - 1) else if (actx->num_coins * (TALER_CNC_KAPPA - 1)
!= json_array_size (j_disclosed_coins)) != json_array_size (j_disclosed_coin_secrets))
error = "the size of array disclosed_coins must be " error = "the size of array disclosed_coin_secrets must be "
TALER_CNC_KAPPA_MINUS_ONE_STR " times the size of denoms_h"; TALER_CNC_KAPPA_MINUS_ONE_STR " times the size of denoms_h";
if (NULL != error) if (NULL != error)
@ -223,13 +223,13 @@ parse_age_withdraw_reveal_json (
}; };
/* Parse diclosed keys */ /* Parse diclosed keys */
actx->disclosed_coins = GNUNET_new_array ( actx->disclosed_coin_secrets = GNUNET_new_array (
actx->num_coins * (TALER_CNC_KAPPA - 1), actx->num_coins * (TALER_CNC_KAPPA - 1),
struct GNUNET_CRYPTO_EddsaPrivateKey); struct TALER_PlanchetMasterSecretP);
json_array_foreach (j_disclosed_coins, idx, value) { json_array_foreach (j_disclosed_coin_secrets, idx, value) {
struct GNUNET_JSON_Specification spec[] = { struct GNUNET_JSON_Specification spec[] = {
GNUNET_JSON_spec_fixed_auto (NULL, &actx->disclosed_coins[idx]), GNUNET_JSON_spec_fixed_auto (NULL, &actx->disclosed_coin_secrets[idx]),
GNUNET_JSON_spec_end () GNUNET_JSON_spec_end ()
}; };
@ -239,7 +239,7 @@ parse_age_withdraw_reveal_json (
char msg[256] = {0}; char msg[256] = {0};
GNUNET_snprintf (msg, GNUNET_snprintf (msg,
sizeof(msg), sizeof(msg),
"couldn't parse entry no. %d in array disclosed_coins", "couldn't parse entry no. %d in array disclosed_coin_secrets",
idx + 1); idx + 1);
*mhd_ret = TALER_MHD_reply_with_error (connection, *mhd_ret = TALER_MHD_reply_with_error (connection,
MHD_HTTP_BAD_REQUEST, MHD_HTTP_BAD_REQUEST,
@ -306,7 +306,7 @@ find_original_commitment (
break; break;
case GNUNET_DB_STATUS_SOFT_ERROR: case GNUNET_DB_STATUS_SOFT_ERROR:
/* FIXME: Do we queue a result in this case or retry? */ /* FIXME:oec: Do we queue a result in this case or retry? */
default: default:
GNUNET_break (0); /* should be impossible */ GNUNET_break (0); /* should be impossible */
*result = TALER_MHD_reply_with_error (connection, *result = TALER_MHD_reply_with_error (connection,
@ -525,8 +525,8 @@ are_denominations_valid (
* - blinded hashes * - blinded hashes
* - Computes h_commitment with those calculated and the undisclosed hashes * - Computes h_commitment with those calculated and the undisclosed hashes
* - Compares h_commitment with the value from the original commitment * - Compares h_commitment with the value from the original commitment
* - Verifies that all public keys in indices larger than max_age_group are * - Verifies that all public keys in indices larger than the age group
* derived from the constant public key. * corresponding to max_age are derived from the constant public key.
* *
* The derivation of the blindings, (potential) nonces and age-commitment from * The derivation of the blindings, (potential) nonces and age-commitment from
* a coin's private keys is defined in * a coin's private keys is defined in
@ -534,12 +534,12 @@ are_denominations_valid (
* *
* @param connection HTTP-connection to the client * @param connection HTTP-connection to the client
* @param h_commitment_orig Original commitment * @param h_commitment_orig Original commitment
* @param max_age_group Maximum age group allowed for the age restriction * @param max_age Maximum age allowed for the age restriction
* @param noreveal_idx Index that was given to the client in response to the age-withdraw request * @param noreveal_idx Index that was given to the client in response to the age-withdraw request
* @param num_coins Number of coins * @param num_coins Number of coins
* @param coin_evs The Hashes of the undisclosed, blinded coins * @param coin_evs The Hashes of the undisclosed, blinded coins, @a num_coins many
* @param discloded_coins The private keys of the disclosed coins * @param denom_keys The array of denomination keys, @a num_coins. Needed to detect Clause-Schnorr-based denominations
* @param denom_keys The array of denomination keys. Needed to detect Clause-Schnorr-based denominations * @param discloded_coin_secrets The secrets of the disclosed coins, (TALER_CNC_KAPPA - 1)*num_coins many
* @param[out] result On error, a HTTP-response will be queued and result set accordingly * @param[out] result On error, a HTTP-response will be queued and result set accordingly
* @return GNUNET_OK on success, GNUNET_SYSERR otherwise * @return GNUNET_OK on success, GNUNET_SYSERR otherwise
*/ */
@ -547,29 +547,180 @@ static enum GNUNET_GenericReturnValue
verify_commitment_and_max_age ( verify_commitment_and_max_age (
struct MHD_Connection *connection, struct MHD_Connection *connection,
const struct TALER_AgeWithdrawCommitmentHashP *h_commitment_orig, const struct TALER_AgeWithdrawCommitmentHashP *h_commitment_orig,
uint32_t max_age_group, const uint32_t max_age,
uint32_t noreveal_idx, const uint32_t noreveal_idx,
uint32_t num_coins, const uint32_t num_coins,
const struct TALER_BlindedCoinHashP *coin_evs, const struct TALER_BlindedCoinHashP *coin_evs,
const struct GNUNET_CRYPTO_EddsaPrivateKey *disclosed_coins,
const struct TEH_DenominationKey *denom_keys, const struct TEH_DenominationKey *denom_keys,
const struct TALER_PlanchetMasterSecretP *disclosed_coin_secrets,
MHD_RESULT *result) MHD_RESULT *result)
{ {
struct TALER_BlindedCoinHashP *disclosed_evs; /* Will contain all calculated hashes */ enum GNUNET_GenericReturnValue ret = GNUNET_SYSERR;
struct GNUNET_HashContext *hash_context;
disclosed_evs = GNUNET_new_array ( hash_context = GNUNET_CRYPTO_hash_context_start ();
num_coins * (TALER_CNC_KAPPA - 1),
struct TALER_BlindedCoinHashP);
for (uint32_t i = 0; i < num_coins; i++) for (size_t c = 0; c < num_coins; c++)
{ {
/* FIXME:oec: Calculate new coins and blinded hashes */ size_t k = 0; /* either 0 or 1, to index into coin_evs */
/*TALER_age_restriction_commit_from_base(); */
for (size_t idx = 0; idx<3; idx++)
{
if (idx == (size_t) noreveal_idx)
{
GNUNET_CRYPTO_hash_context_read (hash_context,
&coin_evs[c],
sizeof(coin_evs[c]));
}
else
{
/* FIXME:oec: Refactor this block out into its own function */
size_t j = 2 * c + k; /* Index into disclosed_coin_secrets[] */
const struct TALER_PlanchetMasterSecretP *secret;
struct TALER_AgeCommitmentHash ach;
GNUNET_assert (k<2);
GNUNET_assert (num_coins * (TALER_CNC_KAPPA - 1) > j);
secret = &disclosed_coin_secrets[j];
k++;
/* First: calculate age commitment hash */
{
struct TALER_AgeCommitmentProof acp;
ret = TALER_age_restriction_from_secret (
secret,
&denom_keys[c].denom_pub.age_mask,
max_age,
&acp);
if (GNUNET_OK != ret)
{
GNUNET_break (0);
*result = TALER_MHD_reply_json_pack (connection,
MHD_HTTP_INTERNAL_SERVER_ERROR,
"{sssi}",
"failed to derive age restriction from base key",
"index",
j);
return ret;
} }
TALER_age_commitment_hash (&acp.commitment, &ach);
}
/* Next: calculate planchet */
{
struct TALER_CoinPubHashP c_hash;
struct TALER_PlanchetDetail detail;
struct TALER_BlindedCoinHashP bch;
struct TALER_CoinSpendPrivateKeyP coin_priv;
union TALER_DenominationBlindingKeyP bks;
struct TALER_ExchangeWithdrawValues alg_values = {
.cipher = denom_keys[c].denom_pub.cipher,
};
if (TALER_DENOMINATION_CS == alg_values.cipher)
{
struct TALER_CsNonce nonce;
TALER_cs_withdraw_nonce_derive (
secret,
&nonce);
{
enum TALER_ErrorCode ec;
struct TEH_CsDeriveData cdd = {
.h_denom_pub = &denom_keys[c].h_denom_pub,
.nonce = &nonce,
};
ec = TEH_keys_denomination_cs_r_pub (&cdd,
false,
&alg_values.details.
cs_values);
#pragma message ("FIXME:oec: return value of needs handling!")
/* FIXME:oec: Handle error */
GNUNET_assert (TALER_EC_NONE == ec);
}
}
TALER_planchet_blinding_secret_create (secret,
&alg_values,
&bks);
TALER_planchet_setup_coin_priv (secret,
&alg_values,
&coin_priv);
ret = TALER_planchet_prepare (&denom_keys[c].denom_pub,
&alg_values,
&bks,
&coin_priv,
&ach,
&c_hash,
&detail);
if (GNUNET_OK != ret)
{
GNUNET_break (0);
*result = TALER_MHD_reply_json_pack (connection,
MHD_HTTP_INTERNAL_SERVER_ERROR,
"{sssi}",
"details",
"failed to prepare planchet from base key",
"index",
j);
return ret;
}
ret = TALER_coin_ev_hash (&detail.blinded_planchet,
&denom_keys[c].h_denom_pub,
&bch);
if (GNUNET_OK != ret)
{
GNUNET_break (0);
*result = TALER_MHD_reply_json_pack (connection,
MHD_HTTP_INTERNAL_SERVER_ERROR,
"{sssi}",
"details",
"failed to hash planchet from base key",
"index",
j);
return ret;
}
GNUNET_CRYPTO_hash_context_read (hash_context,
&detail.blinded_planchet,
sizeof(detail.blinded_planchet));
}
}
}
}
/* Finally, compare the calculated hash with the original commitment */
{
struct GNUNET_HashCode calc_hash;
GNUNET_CRYPTO_hash_context_finish (hash_context,
&calc_hash);
if (0 != GNUNET_CRYPTO_hash_cmp (&h_commitment_orig->hash,
&calc_hash))
{
GNUNET_break_op (0);
*result = TALER_MHD_reply_with_ec (connection,
TALER_EC_EXCHANGE_AGE_WITHDRAW_REVEAL_INVALID_HASH,
NULL);
return GNUNET_SYSERR; return GNUNET_SYSERR;
} }
}
return ret;
}
MHD_RESULT MHD_RESULT
TEH_handler_age_withdraw_reveal ( TEH_handler_age_withdraw_reveal (
@ -582,12 +733,12 @@ TEH_handler_age_withdraw_reveal (
struct AgeRevealContext actx = {0}; struct AgeRevealContext actx = {0};
json_t *j_denoms_h; json_t *j_denoms_h;
json_t *j_coin_evs; json_t *j_coin_evs;
json_t *j_disclosed_coins; json_t *j_disclosed_coin_secrets;
struct GNUNET_JSON_Specification spec[] = { struct GNUNET_JSON_Specification spec[] = {
GNUNET_JSON_spec_fixed_auto ("reserve_pub", &actx.reserve_pub), GNUNET_JSON_spec_fixed_auto ("reserve_pub", &actx.reserve_pub),
GNUNET_JSON_spec_json ("denoms_h", &j_denoms_h), GNUNET_JSON_spec_json ("denoms_h", &j_denoms_h),
GNUNET_JSON_spec_json ("coin_evs", &j_coin_evs), GNUNET_JSON_spec_json ("coin_evs", &j_coin_evs),
GNUNET_JSON_spec_json ("disclosed_coins", &j_disclosed_coins), GNUNET_JSON_spec_json ("disclosed_coin_secrets", &j_disclosed_coin_secrets),
GNUNET_JSON_spec_end () GNUNET_JSON_spec_end ()
}; };
@ -612,7 +763,7 @@ TEH_handler_age_withdraw_reveal (
rc->connection, rc->connection,
j_denoms_h, j_denoms_h,
j_coin_evs, j_coin_evs,
j_disclosed_coins, j_disclosed_coin_secrets,
&actx, &actx,
&result)) &result))
break; break;
@ -639,16 +790,16 @@ TEH_handler_age_withdraw_reveal (
break; break;
/* Verify the computed h_commitment equals the committed one and that /* Verify the computed h_commitment equals the committed one and that
* coins have a maximum age group of max_age_group */ * coins have a maximum age group corresponding max_age (age-mask dependend) */
if (GNUNET_OK != verify_commitment_and_max_age ( if (GNUNET_OK != verify_commitment_and_max_age (
rc->connection, rc->connection,
&actx.commitment.h_commitment, &actx.commitment.h_commitment,
actx.commitment.max_age_group, actx.commitment.max_age,
actx.commitment.noreveal_index, actx.commitment.noreveal_index,
actx.num_coins, actx.num_coins,
actx.coin_evs, actx.coin_evs,
actx.disclosed_coins,
actx.denom_keys, actx.denom_keys,
actx.disclosed_coin_secrets,
&result)) &result))
break; break;

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@ -29,7 +29,7 @@ BEGIN
',h_commitment BYTEA PRIMARY KEY CHECK (LENGTH(h_commitment)=64)' ',h_commitment BYTEA PRIMARY KEY CHECK (LENGTH(h_commitment)=64)'
',amount_with_fee_val INT8 NOT NULL' ',amount_with_fee_val INT8 NOT NULL'
',amount_with_fee_frac INT4 NOT NULL' ',amount_with_fee_frac INT4 NOT NULL'
',max_age_group INT2 NOT NULL' ',max_age INT2 NOT NULL'
',reserve_pub BYTEA NOT NULL CHECK (LENGTH(reserve_pub)=32)' ',reserve_pub BYTEA NOT NULL CHECK (LENGTH(reserve_pub)=32)'
',reserve_sig BYTEA CHECK (LENGTH(reserve_sig)=64)' ',reserve_sig BYTEA CHECK (LENGTH(reserve_sig)=64)'
',noreveal_index INT4 NOT NULL' ',noreveal_index INT4 NOT NULL'
@ -51,8 +51,8 @@ BEGIN
,partition_suffix ,partition_suffix
); );
PERFORM comment_partitioned_column( PERFORM comment_partitioned_column(
'The maximum age group that the client commits to with this request' 'The maximum age that the client commits to with this request'
,'max_age_group' ,'max_age'
,table_name ,table_name
,partition_suffix ,partition_suffix
); );

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@ -45,8 +45,8 @@ TEH_PG_get_age_withdraw_info (
&awc->reserve_sig), &awc->reserve_sig),
GNUNET_PQ_result_spec_auto_from_type ("reserve_pub", GNUNET_PQ_result_spec_auto_from_type ("reserve_pub",
&awc->reserve_pub), &awc->reserve_pub),
GNUNET_PQ_result_spec_uint32 ("max_age_group", GNUNET_PQ_result_spec_uint32 ("max_age",
&awc->max_age_group), &awc->max_age),
TALER_PQ_RESULT_SPEC_AMOUNT ("amount_with_fee", TALER_PQ_RESULT_SPEC_AMOUNT ("amount_with_fee",
&awc->amount_with_fee), &awc->amount_with_fee),
GNUNET_PQ_result_spec_uint32 ("noreveal_index", GNUNET_PQ_result_spec_uint32 ("noreveal_index",
@ -66,7 +66,7 @@ TEH_PG_get_age_withdraw_info (
" h_commitment" " h_commitment"
",reserve_sig" ",reserve_sig"
",reserve_pub" ",reserve_pub"
",max_age_group" ",max_age"
",amount_with_fee_val" ",amount_with_fee_val"
",amount_with_fee_frac" ",amount_with_fee_frac"
",noreveal_index" ",noreveal_index"

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@ -5952,16 +5952,16 @@ TALER_age_commitment_base_public_key;
* *
* See https://docs.taler.net/core/api-exchange.html#withdraw-with-age-restriction * See https://docs.taler.net/core/api-exchange.html#withdraw-with-age-restriction
* *
* @param secret The master secret of the coin from which we derive the age restriction
* @param mask The age mask, defining the age groups * @param mask The age mask, defining the age groups
* @param max_age The maximum age for this coin. * @param max_age The maximum age for this coin.
* @param coin_priv The private key of the coin from which we derive the age restriction
* @param[out] comm_proof The commitment and proof for age restriction for age @a max_age * @param[out] comm_proof The commitment and proof for age restriction for age @a max_age
*/ */
enum GNUNET_GenericReturnValue enum GNUNET_GenericReturnValue
TALER_age_restriction_commit_from_base ( TALER_age_restriction_from_secret (
const struct TALER_CoinSpendPrivateKeyP *coin_priv, const struct TALER_PlanchetMasterSecretP *secret,
const struct TALER_AgeMask *mask, const struct TALER_AgeMask *mask,
uint8_t max_age, const uint8_t max_age,
struct TALER_AgeCommitmentProof *comm_proof); struct TALER_AgeCommitmentProof *comm_proof);

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@ -1064,9 +1064,9 @@ struct TALER_EXCHANGEDB_AgeWithdrawCommitment
struct TALER_Amount amount_with_fee; struct TALER_Amount amount_with_fee;
/** /**
* Maximum age group that the coins are restricted to. * Maximum age that the coins are restricted to.
*/ */
uint32_t max_age_group; uint32_t max_age;
/** /**
* The hash of the commitment of all n*kappa coins * The hash of the commitment of all n*kappa coins

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@ -585,10 +585,10 @@ TALER_age_mask_to_string (
enum GNUNET_GenericReturnValue enum GNUNET_GenericReturnValue
TALER_age_restriction_commit_from_base ( TALER_age_restriction_from_secret (
const struct TALER_CoinSpendPrivateKeyP *coin_priv, const struct TALER_PlanchetMasterSecretP *secret,
const struct TALER_AgeMask *mask, const struct TALER_AgeMask *mask,
uint8_t max_age, const uint8_t max_age,
struct TALER_AgeCommitmentProof *ncp) struct TALER_AgeCommitmentProof *ncp)
{ {
struct GNUNET_HashCode seed_i = {0}; struct GNUNET_HashCode seed_i = {0};
@ -596,7 +596,7 @@ TALER_age_restriction_commit_from_base (
uint8_t num_priv; uint8_t num_priv;
GNUNET_assert (NULL != mask); GNUNET_assert (NULL != mask);
GNUNET_assert (NULL != coin_priv); GNUNET_assert (NULL != secret);
GNUNET_assert (NULL != ncp); GNUNET_assert (NULL != ncp);
GNUNET_assert (mask->bits & 1); /* fist bit must have been set */ GNUNET_assert (mask->bits & 1); /* fist bit must have been set */
@ -629,7 +629,7 @@ TALER_age_restriction_commit_from_base (
const char *label = i < num_priv ? "age-commitment" : "age-factor"; const char *label = i < num_priv ? "age-commitment" : "age-factor";
ret = GNUNET_CRYPTO_kdf (&seed_i, sizeof(seed_i), ret = GNUNET_CRYPTO_kdf (&seed_i, sizeof(seed_i),
coin_priv, sizeof(*coin_priv), secret, sizeof(*secret),
label, strlen (label), label, strlen (label),
&i, sizeof(i), &i, sizeof(i),
NULL, 0); NULL, 0);