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poseidonperm_x17.sage
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poseidonperm_x17.sage
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# Modified from Appendix B in the Poseidon paper, width 3 hash for BLS12-377
import time
# M is the targeted security level
M = 128
alpha = 17
t = 3
prime = 8444461749428370424248824938781546531375899335154063827935233455917409239041
F = GF(prime)
R_P = 31
R_F = 8
R_f = R_F / 2
R_T = R_F + R_P
# Omega is the linear algebra constant
# See Poseidon paper p. 24
# Varies between 2-3, here we assume $\omega=2$
omega = 2
# d in the paper is alpha for us
# D is the F_q vector space dimension
d = alpha
def resist_eigenpolynomial_computation(r_in, r_out):
D = d ** (2 * r_in * R_f + R_P)
# r_in is the input rate of poseidon
# kappa in the paper is the targeted security level, M here
print((log(min(r_in, r_out),2).n() + omega * log(D, 2)).n())
return (log(min(r_in, r_out),2).n() + omega * log(D, 2)).n() >= M
print("instances secure vs iacr/2024/310 generic eigenpolynomial computation?")
print(resist_eigenpolynomial_computation(2, 1))
print(resist_eigenpolynomial_computation(3, 1))
print(resist_eigenpolynomial_computation(4, 1))
print(resist_eigenpolynomial_computation(6, 1))
print(resist_eigenpolynomial_computation(7, 1))
print(resist_eigenpolynomial_computation(8, 1))
def resist_root_extraction(r_in):
D = d ** (2 * r_in * R_f + R_P)
q = log(prime, 2)
if D <= q:
return (D * log(D) * log(log(D)) * (log(D) + log(q))).n() >= M
else:
return (q * log(q) * log(log(q)) * (log(q) + log(D))).n() >= M
print("instances secure vs iacr/2024/310 generic root extraction?")
print(resist_root_extraction(2))
print(resist_root_extraction(3))
print(resist_root_extraction(4))
print(resist_root_extraction(5))
print(resist_root_extraction(6))
print(resist_root_extraction(7))
print(resist_root_extraction(8))
round_constants = [308026635595114235070436728341841505234226384644787941764356225291780075012,
686850750308311448868354907988153221833589417264043199872750834851275630399,
5458865526113744175375673481036999502881423789202235030915223710930508573500,
1216889461603982466063117074419064018993731784023337352219629352951004218382,
4580374146984258872617301222640071415348151863297599652351895199406510624060,
5287771711632967718595430906600106184880872479312192055075552617141548501299,
3037526442503690560777271665669625925917538366486234291090702161060916614832,
6275277408809697928512465960441767403986852341417079924634963619646806124417,
7335650489313165022076032570688161581492191665821494053773844209042883340886,
1627952039309156476645184308670263708019542166435650091304574646631569460339,
6094265973203525089006037274771888959193635664689776329087130682272196094008,
6490696528492405721785907440795129872072544933360586449368276289112880330670,
1838969713611020994526552299650788115168140980815959904769759411371437475085,
2150051935070463751493305482799641725706245753717668882294497822824388319578,
4575572148360756475907353900681447955312802247778987169199474643005130716935,
1851688896784243289932019446285888654652306219713142676419351172260600922714,
6973552312635424934570970915726931835821737587964001373829651198305564713244,
1813003948570365248649794664717915544584605337173583303735237517614852010262,
8263838364638315756819655988900910418618512340908078920307324632543945164500,
757943113036795101065823745544829115197604837832768830141778672857097207622,
659325027542376965992085727974783614933698097545036724992593606308630964139,
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4896435516099794294013100518299784209896728776935133585568100103105644366269,
2205611631605917342771043739003168054091728635889814050523595535007173267903,
4474292819278150418223394712870944390214136577384608881113789172943901756185,
5587482766701385940251260739243227887661785673403464848010833438080581211679,
2641477529317380932697589512697916502009860625009330516388196585651681493176,
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1978766321165168589630826892562241348143601476846182828696106373368314589991,
7868843219594886750750407514795570643227076640179151649282544892407534950592,
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6764013719997591825457793918699801796014086921189886289817845875572992948924,
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173252929061996890901264974543899995780593767283643983973014427458683001541,
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6095291956682197100095438891582653659020834282561205807326323590973913331048,
1222469665268606145803729120426500156401953546226735560453940247824615064170,
3553916981699410215413275982884160504425690320454695706786765040400435191673,
4597893035276850283590548632351419824369725156115729763845407308233992233881,
4098945751589637585349322721645137714901277398725764380413825257514636605490,
896241425392348667316141178956455644228372721471824108535546494759067376393,
3992502368943038378368897680594056578803163431114935312687627167974272071263,
2916896099606045408059702536614926909593404178656347225235372099792450298246,
120269880148157352408037220674298509372962320809264336091966259007633284713,
7722392890376228197239026921734213343834699657441777356614625170525296088221,
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983738301417603757808483219105286248075595155162538643758190406964355750696,
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6325608705322012724565293795590543306557376953836287094512934948871034460300]
MDS_matrix = [[5629641166285580282832549959187697687583932890102709218623488970611606159361, 6333346312071277818186618704086159898531924501365547870951425091938056929281, 6755569399542696339399059951025237225100719468123251062348186764733927391233],
[6333346312071277818186618704086159898531924501365547870951425091938056929281, 6755569399542696339399059951025237225100719468123251062348186764733927391233, 7037051457856975353540687448984622109479916112628386523279361213264507699201],
[6755569399542696339399059951025237225100719468123251062348186764733927391233, 7037051457856975353540687448984622109479916112628386523279361213264507699201, 7238110070938603220784707090384182741179342287274911852515914390786350776321]]
MDS_matrix_field = matrix(F, t, t)
for i in range(0, t):
for j in range(0, t):
MDS_matrix_field[i, j] = F(MDS_matrix[i][j])
round_constants_field = []
for i in range(0, (R_F + R_P) * t):
round_constants_field.append(F(round_constants[i]))
def calc_equivalent_constants(constants):
constants_temp = [constants[index:index+t] for index in range(0, len(constants), t)]
MDS_matrix_field_transpose = MDS_matrix_field.transpose()
# Start moving round constants up
# Calculate c_i' = M^(-1) * c_(i+1)
# Split c_i': Add c_i'[0] AFTER the S-box, add the rest to c_i
# I.e.: Store c_i'[0] for each of the partial rounds, and make c_i = c_i + c_i' (where now c_i'[0] = 0)
for i in range(R_T - 2 - R_f, R_f - 1, -1):
inv_cip1 = list(vector(constants_temp[i+1]) * MDS_matrix_field_transpose.inverse())
constants_temp[i] = list(vector(constants_temp[i]) + vector([0] + inv_cip1[1:]))
constants_temp[i+1] = [inv_cip1[0]] + [0] * (t-1)
return constants_temp
def calc_equivalent_matrices():
# Following idea: Split M into M' * M'', where M'' is "cheap" and M' can move before the partial nonlinear layer
# The "previous" matrix layer is then M * M'. Due to the construction of M', the M[0,0] and v values will be the same for the new M' (and I also, obviously)
# Thus: Compute the matrices, store the w_hat and v_hat values
MDS_matrix_field_transpose = MDS_matrix_field.transpose()
w_hat_collection = []
v_collection = []
v = MDS_matrix_field_transpose[[0], list(range(1,t))]
M_mul = MDS_matrix_field_transpose
M_i = matrix(F, t, t)
for i in range(R_P - 1, -1, -1):
M_hat = M_mul[list(range(1,t)), list(range(1,t))]
w = M_mul[list(range(1,t)), [0]]
v = M_mul[[0], list(range(1,t))]
v_collection.append(v.list())
w_hat = M_hat.inverse() * w
w_hat_collection.append(w_hat.list())
# Generate new M_i, and multiplication M * M_i for "previous" round
M_i = matrix.identity(t)
M_i[list(range(1,t)), list(range(1,t))] = M_hat
M_mul = MDS_matrix_field_transpose * M_i
return [M_i, v_collection, w_hat_collection]
def cheap_matrix_mul(state_words, v, w_hat, M_0_0):
state_words_new = [0] * t
column_1 = [M_0_0] + w_hat
state_words_new[0] = sum([column_1[i] * state_words[i] for i in range(0, t)])
mul_row = [(state_words[0] * v[i]) for i in range(0, t-1)]
add_row = [(mul_row[i] + state_words[i+1]) for i in range(0, t-1)]
state_words_new = [state_words_new[0]] + add_row
return state_words_new
def perm(input_words):
round_constants_field_new = calc_equivalent_constants(round_constants_field)
[M_i, v_collection, w_hat_collection] = calc_equivalent_matrices()
M_0_0 = MDS_matrix_field[0, 0]
#[M_i, test_mat] = calc_equivalent_matrices()
global timer_start, timer_end
timer_start = time.time()
R_f = int(R_F / 2)
round_constants_round_counter = 0
state_words = list(input_words)
# First full rounds
for r in range(0, R_f):
# Round constants, nonlinear layer, matrix multiplication
for i in range(0, t):
state_words[i] = state_words[i] + round_constants_field_new[round_constants_round_counter][i]
for i in range(0, t):
state_words[i] = (state_words[i])^alpha
state_words = list(MDS_matrix_field * vector(state_words))
round_constants_round_counter += 1
# Middle partial rounds
# Initial constants addition
for i in range(0, t):
state_words[i] = state_words[i] + round_constants_field_new[round_constants_round_counter][i]
# First full matrix multiplication
state_words = list(vector(state_words) * M_i)
for r in range(0, R_P):
# Round constants, nonlinear layer, matrix multiplication
state_words[0] = (state_words[0])^alpha
# Moved constants addition
if r < (R_P - 1):
round_constants_round_counter += 1
state_words[0] = state_words[0] + round_constants_field_new[round_constants_round_counter][0]
# Optimized multiplication with cheap matrices
state_words = cheap_matrix_mul(state_words, v_collection[R_P - r - 1], w_hat_collection[R_P - r - 1], M_0_0)
round_constants_round_counter += 1
# Last full rounds
for r in range(0, R_f):
# Round constants, nonlinear layer, matrix multiplication
for i in range(0, t):
state_words[i] = state_words[i] + round_constants_field_new[round_constants_round_counter][i]
for i in range(0, t):
state_words[i] = (state_words[i])^alpha
state_words = list(MDS_matrix_field * vector(state_words))
round_constants_round_counter += 1
timer_end = time.time()
return state_words
def perm_original(input_words):
round_constants_field_new = [round_constants_field[index:index+t] for index in range(0, len(round_constants_field), t)]
global timer_start, timer_end
timer_start = time.time()
R_f = int(R_F / 2)
round_constants_round_counter = 0
state_words = list(input_words)
# First full rounds
for r in range(0, R_f):
# Round constants, nonlinear layer, matrix multiplication
for i in range(0, t):
state_words[i] = state_words[i] + round_constants_field_new[round_constants_round_counter][i]
for i in range(0, t):
state_words[i] = (state_words[i])^alpha
state_words = list(MDS_matrix_field * vector(state_words))
round_constants_round_counter += 1
# Middle partial rounds
for r in range(0, R_P):
# Round constants, nonlinear layer, matrix multiplication
for i in range(0, t):
state_words[i] = state_words[i] + round_constants_field_new[round_constants_round_counter][i]
state_words[0] = (state_words[0])^alpha
state_words = list(MDS_matrix_field * vector(state_words))
round_constants_round_counter += 1
# Last full rounds
for r in range(0, R_f):
# Round constants, nonlinear layer, matrix multiplication
for i in range(0, t):
state_words[i] = state_words[i] + round_constants_field_new[round_constants_round_counter][i]
for i in range(0, t):
state_words[i] = (state_words[i])^alpha
state_words = list(MDS_matrix_field * vector(state_words))
round_constants_round_counter += 1
timer_end = time.time()
return state_words
# For checking optimized parameter code
M_i, v_collection, w_hat_collection = calc_equivalent_matrices()
#print('M_i', M_i)
#print('v_col', v_collection)
#print('w_hat_collection', w_hat_collection)
new_constants = calc_equivalent_constants(round_constants)
#[print(new_constants[index:index+t]) for index in range(0, len(new_constants), t)]
input_words = []
for i in range(0, t):
input_words.append(F(i))
output_words = None
num_iterations = 1
total_time_passed = 0
for i in range(0, num_iterations):
output_words = perm_original(input_words)
print(output_words)
time_passed = timer_end - timer_start
total_time_passed += time_passed
average_time = total_time_passed / float(num_iterations)
print("Average time for unoptimized:", average_time)
total_time_passed = 0
for i in range(0, num_iterations):
opt_output_words = perm(input_words)
print(opt_output_words)
time_passed = timer_end - timer_start
total_time_passed += time_passed
average_time = total_time_passed / float(num_iterations)
print("Average time for optimized:", average_time)
# Check optimized is equal to the unoptimized
assert opt_output_words == output_words