/rev/6693b04e60a4
changeset: 1241:6693b04e60a4
user: Janus Dam Nielsen <[email protected]>
date: Thu Oct 08 11:55:36 2009 +0200
summary: Documentation for the Orlandi runtime.
diffstat:
doc/implementation.txt | 2 +
doc/orlandi.txt | 15 +++++++
viff/orlandi.py | 76 +++++++++++++++++++++-----------------
3 files changed, 59 insertions(+), 34 deletions(-)
diffs (173 lines):
diff -r 986c5b82c655 -r 6693b04e60a4 doc/implementation.txt
--- a/doc/implementation.txt Thu Oct 08 11:53:47 2009 +0200
+++ b/doc/implementation.txt Thu Oct 08 11:55:36 2009 +0200
@@ -20,3 +20,5 @@
config
aes
constants
+ orlandi
+
diff -r 986c5b82c655 -r 6693b04e60a4 doc/orlandi.txt
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/doc/orlandi.txt Thu Oct 08 11:55:36 2009 +0200
@@ -0,0 +1,15 @@
+
+An Actively Secure Protocol with Self Trust
+===========================================
+
+.. automodule:: viff.orlandi
+
+ .. autoclass:: OrlandiException
+ :members:
+
+ .. autoclass:: OrlandiShare
+ :members:
+
+ .. autoclass:: OrlandiRuntime
+ :members:
+
diff -r 986c5b82c655 -r 6693b04e60a4 viff/orlandi.py
--- a/viff/orlandi.py Thu Oct 08 11:53:47 2009 +0200
+++ b/viff/orlandi.py Thu Oct 08 11:55:36 2009 +0200
@@ -345,9 +345,10 @@
Communication cost: none.
- Each party ``P_i`` computes:
- ``[z]_i = [x]_i + [y]_i
- = (x_i + y_i mod p, rho_xi + rho_yi mod p, C_x * C_y)``.
+ Each party ``P_i`` computes::
+
+ [z]_i = [x]_i + [y]_i
+ = (x_i + y_i mod p, rho_xi + rho_yi mod p, C_x * C_y)
"""
def is_share(s, field):
@@ -378,9 +379,10 @@
Communication cost: none.
- Each party ``P_i`` computes:
- ``[z]_i = [x]_i - [y]_i
- = (x_i - y_i mod p, rho_x,i - rho_y,i mod p, C_x * C_y)``.
+ Each party ``P_i`` computes::
+
+ [z]_i = [x]_i - [y]_i
+ = (x_i - y_i mod p, rho_x,i - rho_y,i mod p, C_x * C_y)
"""
def is_share(s, field):
@@ -424,11 +426,11 @@
Assume the parties are given a random share ``[r]`` by a trusted
dealer.
Then we denote the following protocol but ``[x] = Shift(P_i, x, [r])``.
- 1) ``r = OpenTo(P_i, [r]``
+ 1. ``r = OpenTo(P_i, [r]``
- 2) ``P_i broadcasts Delta = r - x``
+ 2. ``P_i broadcasts Delta = r - x``
- 3) ``[x] = [r] - Delta``
+ 3. ``[x] = [r] - Delta``
"""
# TODO: Communitcation costs?
@@ -440,7 +442,7 @@
def hack(_, peer_id):
# Assume the parties are given a random share [r] by a trusted
dealer.
share_r = self.random_share(field)
- # 1) r = OpenTo(P_i, [r])
+ # 1. r = OpenTo(P_i, [r])
open_r = self.open(share_r, [peer_id])
def subtract_delta(delta, share_r):
delta = field(long(delta))
@@ -676,20 +678,21 @@
Assuming a set of multiplicative triples:
``M = ([a_i], [b_i], [c_i]) for 1 <= i <= 2d + 1``.
- 1) ``for i = 1, ..., d do [f_i] = rand(), [g_i] = rand()``
+ 1. ``for i = 1, ..., d do [f_i] = rand(), [g_i] = rand()``
- 2) ``for j = 1, ..., 2d+1 do
+ 2. Compute::
+
+ for j = 1, ..., 2d+1 do
[F_j] = [x] + SUM_i=1^d [f_i]*j^i
and
- [G_j] = [y] + SUM_i=1^d [g_i]*j^i``
+ [G_j] = [y] + SUM_i=1^d [g_i]*j^i
- 3) for j = 1, ..., 2d+1 do [H_j] = Mul([F_j], [G_j], [a_j], [b_j],
[c_j])
+ 3. ``for j = 1, ..., 2d+1 do [H_j] = Mul([F_j], [G_j], [a_j], [b_j],
[c_j])``
- 4) compute [H_0] = SUM_j=1^2d+1 delta_j[H_j]
+ 4. compute ``[H_0] = SUM_j=1^2d+1 delta_j[H_j]`` where
+ ``delta_j = PRODUCT_k=1, k!=j^2d+1 k/(k-j)``
- 5) output [z] = [H_0]
-
- delta_j = PRODUCT_k=1, k!=j^2d+1 k/(k-j).
+ 5. output ``[z] = [H_0]``
"""
assert isinstance(share_x, Share) or isinstance(share_y, Share), \
"At least one of share_x and share_y must be a Share."
@@ -703,7 +706,7 @@
if cmul_result is not None:
return cmul_result
- # 1) for i = 1, ..., d do [f_i] = rand(), [g_i] = rand()
+ # 1. for i = 1, ..., d do [f_i] = rand(), [g_i] = rand()
d = (len(M) - 1) // 2
deltas = self.compute_delta(d)
f = []
@@ -787,30 +790,35 @@
def triple_gen(self, field):
"""Generate a triple ``a, b, c`` s.t. ``c = a * b``.
- 1) Every party ``P_i`` chooses random values ``a_i, r_i in Z_p X
(Z_p)^2``,
- compute ``alpha_i = Enc_eki(a_i)`` and ``Ai = Com_ck(a_i, r_i)``, and
- broadcast them.
+ 1. Every party ``P_i`` chooses random values ``a_i, r_i in Z_p X
(Z_p)^2``,
+ compute ``alpha_i = Enc_eki(a_i)`` and ``Ai = Com_ck(a_i, r_i)``,
and
+ broadcast them.
- 2) Every party ``P_j`` does:
- (a) choose random ``b_j, s_j in Z_p X (Z_p)^2``.
+ 2. Every party ``P_j`` does:
- (b) compute ``B_j = ``Com_ck(b_j, s_j)`` and broadcast it.
+ a. choose random ``b_j, s_j in Z_p X (Z_p)^2``.
- (c) ``P_j`` do towards every other party:
+ b. compute ``B_j = ``Com_ck(b_j, s_j)`` and broadcast it.
+
+ c. ``P_j`` do towards every other party:
+
i. choose random ``d_ij in Z_p^3``
- ii. compute and send
- ``gamma_ij = alpha_i^b_j Enc_ek_i(1;1)^d_ij`` to ``P_i``.
- 3) Every party ``P_i`` does:
- (a) compute ``c_i = SUM_j Dec_sk_i(gamma_ij) - SUM_j d_ij mod p``
+ ii. compute and send
+ ``gamma_ij = alpha_i^b_j Enc_ek_i(1;1)^d_ij`` to ``P_i``.
- (b) pick random ``t_i in (Z_p)^2``, compute and
- broadcast ``C_i = Com_ck(c_i, t_i)``
- 4) Everyone computes:
+ 3. Every party ``P_i`` does:
+
+ a. compute ``c_i = SUM_j Dec_sk_i(gamma_ij) - SUM_j d_ij mod p``
+
+ b. pick random ``t_i in (Z_p)^2``, compute and
+ broadcast ``C_i = Com_ck(c_i, t_i)``
+
+ 4. Everyone computes:
``(A, B, C) = (PRODUCT_i A_i, PRODUCT_i B_i, PRODUCT_i C_i)``
- 5) Every party ``P_i`` outputs shares ``[a_i] = (a_i, r_i, A)``,
+ 5. Every party ``P_i`` outputs shares ``[a_i] = (a_i, r_i, A)``,
``[b_i] = (b_i, s_i, B)``, and ``[c_i] = (c_i, t_i, C)``.
"""
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