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fix preparation for M+1st price auctions

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This commit is contained in:
Markus Teich 2016-10-14 23:40:38 +02:00
parent fc9fdd313b
commit da43b9311a
3 changed files with 18 additions and 9 deletions
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3
brandt.c
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@ -73,7 +73,10 @@ BRANDT_bidder_start (struct BRANDT_Auction *auction,
* encrypt_bid round to show that the bidder has chosen a valid bid and the
* outcome callback will remap the result to the original k price values. */
if (auction_mPlusFirstPrice == atype)
{
auction->k *= n;
auction->b = auction->b * n + n - i - 1;
}
if (handler_prep[atype][outcome][msg_init])
handler_prep[atype][outcome][msg_init] (auction);

4
crypto.c
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@ -741,7 +741,7 @@ smc_encrypt_bid (struct BRANDT_Auction *ad, size_t *buflen)
gcry_mpi_addm (r_sum, r_sum, r_part, ec_n);
/* prepare sum for additional M+1st price auction proof (see below) */
if (0 < ad->m && j >= ad->i && 0 == (j - ad->i) % ad->n)
if (0 < ad->m && 1 == (ad->k - j - ad->i) % ad->n)
gcry_mpi_addm (r_sum2, r_sum2, r_part, ec_n);
cur += 2 * sizeof (struct ec_mpi) + sizeof (struct proof_0og);
@ -809,7 +809,7 @@ smc_recv_encrypted_bid (struct BRANDT_Auction *ad,
/* precalculate ciphertext sums for second 2dle proof needed in M+1st
* price auctions */
if (0 < ad->m && j >= ad->i && 0 == (j - ad->i) % ad->n)
if (0 < ad->m && 1 == (ad->k - j - sender) % ad->n)
{
gcry_mpi_ec_add (alpha_sum2, alpha_sum2, ct[0][j], ec_ctx);
gcry_mpi_ec_add (beta_sum2, beta_sum2, ct[1][j], ec_ctx);

20
tex-stuff/math.tex
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@ -192,13 +192,19 @@ M+1st Price Auction schemes. We took the simplest one, interlacing the bids, so
that no two bidders are allowed to bid the same price. On the application level
we will still handle $k_{\text{app}}$ different prices, but within libbrandt we
will multiply that by a factor of $n$ to get $k_{\text{lib}}=nk_{\text{app}}$.
Then each bidder $i$ is only allowed to place his bid $b$ on prices $p$ with
$\exists a\in{[1,k_{\text{app}}]}:b=an-i+1$. This condition will be checked by
an additional proof in the first round of the protocol and ensures that the
bidders with a lower index win in case of ties. This expansion will be done
right at the beginning of an auction by libbrandt. In the remaining part about
the M+1st Price Auction Protocols we will use $k$ instead of $k_{\text{lib}}$,
so $k$ will be divisible by $n$ without remainder.
The bids are scaled up as well by the mapping $\forall
i\in{[1,n]}:b_{i,\text{lib}}=b_{i,\text{app}}n-i+1$. Therefore the set of
allowed bids for bidder $i$ is defined as $\{j|k_{\text{lib}}-j+1\equiv
i\pmod{n}\}$.
This restriction will be checked by an additional proof in the first round of
the protocol and ensures that the bidders with a lower index win in case of
ties. The expansion will be done right at the beginning of an auction by
libbrandt and the reverse mapping is applied before reporting the auction
outcome to the application, so this expansion is transparent to the application.
In the remaining part about the M+1st Price Auction Protocols we will use $k$
instead of $k_{\text{lib}}$, so $k$ will be divisible by $n$ without remainder.
Unfortunately this tie breaking simplification has the downside of revealing the
identity and bid of the bidder who had the highest bid amongst the losing