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add the PoL for the staking notes

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thomaslavaur 2025-03-31 08:47:32 +02:00
parent 0d98123326
commit 5fcffb74c2
2 changed files with 530 additions and 0 deletions
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199
circom_circuits/proof_of_leadership/PoL_staking.circom Normal file
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//test
pragma circom 2.1.9;
include "../hash_bn/poseidon2_hash.circom";
include "../ledger/notes.circom";
include "../misc/comparator.circom";
include "../circomlib/circuits/bitify.circom";
include "../misc/constants.circom";
template ticket_calculator(){
signal input epoch_nonce;
signal input slot;
signal input commitment;
signal input secret_key;
signal output out;
component hash = Poseidon2_hash(5);
component dst = LEAD();
hash.inp[0] <== dst.out;
hash.inp[1] <== epoch_nonce;
hash.inp[2] <== slot;
hash.inp[3] <== commitment;
hash.inp[4] <== secret_key;
out <== hash.out;
}
template derive_secret_key(){
signal input starting_slot;
signal input secrets_root;
signal output out;
component hash = Poseidon2_hash(3);
component dst = NOMOS_POL_SK();
hash.inp[0] <== dst.out;
hash.inp[1] <== starting_slot;
hash.inp[2] <== secrets_root;
out <== hash.out;
}
template derive_entropy(){
signal input slot;
signal input commitment;
signal input secret_key;
signal output out;
component hash = Poseidon2_hash(4);
component dst = NOMOS_NONCE_CONTRIB();
hash.inp[0] <== dst.out;
hash.inp[1] <== slot;
hash.inp[2] <== commitment;
hash.inp[3] <== secret_key;
out <== hash.out;
}
template staking_proof_of_leadership(){
signal input slot;
signal input epoch_nonce;
signal input t0;
signal input t1;
signal input slot_secret;
signal input slot_secret_path[25];
//Part of the commitment proof of membership to prove aged
signal input cm_aged_nodes[32];
signal input cm_aged_selectors[32]; // must be bits
signal input commitments_aged_root;
//Part of the commitment proof of membership to prove aged
signal input cm_unspent_nodes[32];
signal input cm_unspent_selectors[32]; // must be bits
signal input commitments_unspent_root;
//Part of the secret key
signal input starting_slot;
signal input secrets_root;
// The winning note. The unit is supposed to be NMO and the ZoneID is PAYMENT
signal input state;
signal input value;
signal input nonce;
signal input one_time_key;
//Avoid the circom optimisation that removes unused public input
signal dummy;
dummy <== one_time_key * one_time_key;
signal output entropy_contrib;
// Derive the secret key
component sk = derive_secret_key();
sk.starting_slot <== starting_slot;
sk.secrets_root <== secrets_root;
// Derive the public key from the secret key
component pk = derive_public_key();
pk.secret_key <== sk.out;
// Derive the commitment from the note and the public key
component cm = commitment();
cm.state <== state;
cm.value <== value;
component nmo = NMO();
cm.unit <== nmo.out;
cm.nonce <== nonce;
component payment = PAYMENT();
cm.zoneID <== payment.out;
cm.public_key <== pk.out;
// Check commitment membership (is aged enough)
//First check selectors are indeed bits
for(var i = 0; i < 32; i++){
cm_aged_selectors[i] * (1 - cm_aged_selectors[i]) === 0;
}
//Then check the proof of membership
component cm_aged_membership = proof_of_membership(32);
for(var i = 0; i < 32; i++){
cm_aged_membership.nodes[i] <== cm_aged_nodes[i];
cm_aged_membership.selector[i] <== cm_aged_selectors[i];
}
cm_aged_membership.root <== commitments_aged_root;
cm_aged_membership.leaf <== cm.out;
// Compute the lottery ticket
component ticket = ticket_calculator();
ticket.epoch_nonce <== epoch_nonce;
ticket.slot <== slot;
ticket.commitment <== cm.out;
ticket.secret_key <== sk.out;
// Compute the lottery threshold
signal intermediate;
signal threshold;
intermediate <== t1 * value;
threshold <== value * (t0 + intermediate);
// Check that the ticket is winning
component winning = FullLessThan();
winning.a <== ticket.out;
winning.b <== threshold;
winning.out === 1;
// Check commitment membership (is unspent)
//First check selectors are indeed bits
for(var i = 0; i < 32; i++){
cm_unspent_selectors[i] * (1 - cm_unspent_selectors[i]) === 0;
}
//Then check the proof of membership
component cm_unspent_membership = proof_of_membership(32);
for(var i = 0; i < 32; i++){
cm_unspent_membership.nodes[i] <== cm_unspent_nodes[i];
cm_unspent_membership.selector[i] <== cm_unspent_selectors[i];
}
cm_unspent_membership.root <== commitments_unspent_root;
cm_unspent_membership.leaf <== cm.out;
// Check the knowledge of the secret at position slot - starting_slot
// Verify that the substraction wont underflow (starting_slot < slot)
component checker = SafeLessEqThan(252);
checker.in[0] <== starting_slot;
checker.in[1] <== slot;
checker.out === 1;
// Compute the positions related to slot - starting_slot
component bits = Num2Bits(25);
bits.in <== slot - starting_slot;
// Check the membership of the secret_slot against the secrets_root
component secret_membership = proof_of_membership(25);
for(var i =0; i<25; i++){
secret_membership.nodes[i] <== slot_secret_path[i];
secret_membership.selector[i] <== bits.out[24-i];
}
secret_membership.root <== secrets_root;
secret_membership.leaf <== slot_secret;
// Compute the entropy contribution
component entropy = derive_entropy();
entropy.slot <== slot;
entropy.commitment <== cm.out;
entropy.secret_key <== sk.out;
entropy_contrib <== entropy.out;
}
component main {public [slot,epoch_nonce,t0,t1,commitments_aged_root,commitments_unspent_root,one_time_key]}= staking_proof_of_leadership();

331
circom_circuits/proof_of_leadership/generate_inputs_for_staking.py Executable file
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#!/usr/bin/sage
# -*- mode: python ; -*-
from sage.all import *
p = 21888242871839275222246405745257275088548364400416034343698204186575808495617
F = FiniteField(p)
def poseidon2_hash(data):
return PoseidonSponge(data,2,1)[0]
def Poseidon2_sponge_hash_rate_1(data, n):
return PoseidonSponge(data,3,2,n,1)
def Poseidon2_sponge_hash_rate_2(data, n):
return PoseidonSponge(data,3,1,n,1)
def SBox(inp):
return inp**5
def InternalRound(inp, i):
round_consts = [ 0x15ce7e5ae220e8623a40b3a3b22d441eff0c9be1ae1d32f1b777af84eea7e38c
, 0x1bf60ac8bfff0f631983c93e218ca0d4a4059c254b4299b1d9984a07edccfaf0
, 0x0fab0c9387cb2bec9dc11b2951088b9e1e1d2978542fc131f74a8f8fdac95b40
, 0x07d085a48750738019784663bccd460656dc62c1b18964a0d27a5bd0c27ee453
, 0x10d57b1fad99da9d3fe16cf7f5dae05be844f67b2e7db3472a2e96e167578bc4
, 0x0c36c40f7bd1934b7d5525031467aa39aeaea461996a70eda5a2a704e1733bb0
, 0x0e4b65a0f3e1f9d3166a2145063c999bd08a4679676d765f4d11f97ed5c080ae
, 0x1ce5561061120d5c7ea09da2528c4c041b9ad0f05d655f38b10d79878b69f29d
, 0x2d323f651c3da8f0e0754391a10fa111b25dfa00471edf5493c44dfc3f28add6
, 0x05a0741ee5bdc3e099fd6bdad9a0865bc9ceecd13ea4e702e536dd370b8f1953
, 0x176a2ec4746fc0e0eca9e5e11d6facaee05524a92e5785c8b8161780a4435136
, 0x0691faf0f42a9ed97629b1ae0dc7f1b019c06dd852cb6efe57f7eeb1aa865aef
, 0x0e46cf138dad09d61b9a7cab95a23b5c8cb276874f3715598bacb55d5ad271de
, 0x0f18c3d95bac1ac424160d240cdffc2c44f7b6315ba65ed3ff2eff5b3e48b4f2
, 0x2eea6af14b592ec45a4119ac1e6e6f0312ecd090a096e340d472283e543ddff7
, 0x06b0d7a8f4ce97d049ae994139f5f71dca4899d4f1cd3dd83a32a89a58c0a8e6
, 0x019df0b9828eed5892dd55c1ad6408196f6293d600ef4491703a1b37e119ba8e
, 0x08ca5e3c93817cdb1c2b2a12d02c779d74c1bb12b6668f3ab3ddd7837f3a4a00
, 0x28382d747e3fd6cb2e0d8e8edd79c5313eed307a3517c11046245b1476e4f701
, 0x0ca89aecd5675b77c8271765da98cfcb6875b3053d4742c9ff502861bd16ad28
, 0x19046bc0b03ca90802ec83f212001e7ffd7f9224cfffae523451deb52eab3787
, 0x036fd7dfa1c05110b3428e6abcc43e1de9abba915320c4a600f843bfb676ca51
, 0x08f0a7abcb1a2f6595a9b7380c5028e3999db4fe5cb21892e5bb5cb11a7757ba
, 0x0b614acc1ce3fbe9048f8385e4ee24c3843deea186bacea3c904c9f6340ad8cb
, 0x00b2d98c5d988f9b41f2c98e017fc954a6ae423b2261575941f8eac8835d985c
, 0x1457f18555b7973ba5b311d57ec5d77e936980b97f5973875f1f7cc765a4fc95
, 0x002b453debc1bee525cb751bc10641a6b86f847d696418cf1144950982591bfa
, 0x0c2af1abcc6ece77218315d2af445ccbfc6647b7af2510682882cc792c6bb8cf
, 0x0e2825d9eb84b59902a1adb49ac0c2c291dee7c45d2e8c30369a4d595039e8ad
, 0x297e2e86a8c672d39f3343b8dfce7a6f20f3571bfd5c8a28e3905aa2dcfeca44
, 0x00d397281d902e49ec6504ba9186e806db9ad4fc8f86e7277aa7f1467eb6f9de
, 0x2fb7c89c372d7e2050e7377ed471000c73544a2b9fd66557f3577c09cac98b4b
, 0x16125247be4387a8c3e62490167f0cffdba02eda4f018d0b40639a13bb0cfef9
, 0x2291fd9d442f2d9b97ab22f7d4d52c2a82e41f852cf620b144612650a39e26e8
, 0x1eec61f16a275ae238540feaeeadfec56d32171b1cc393729d06f37f476fde71
, 0x259ce871ba5dacbb48d8aed3d8513eef51558dc0b360f28c1a15dbfc5e7f6ca2
, 0x2d3376a14ddbf95587e2f7567ff04fe13a3c7cb17363c8b9c5dd1d9262a210cb
, 0x13b843d9f65f4cddd7ce10d9cad9b8b99ac5e9a8c4269288173a91c0f3c3b084
, 0x0b52e9b2f1aa9fd204e4a42c481cc76c704783e34114b8e93e026a50fa9764e8
, 0x1fd083229276c7f27d3ad941476b394ff37bd44d3a1e9caca1400d9077a2056c
, 0x22743c328a6283f3ba7379af22c684c498568fd7ad9fad5151368c913197cbd9
, 0x043007aefd9741070d95caaaba0c1b070e4eec8eef8c1e512c8e579c6ed64f76
, 0x17ab175144f64bc843074f6b3a0c57c5dd2c954af8723c029ee642539496a7b3
, 0x2befcad3d53fba5eeef8cae9668fed5c1e9e596a46e8458e218f7a665fddf4eb
, 0x15151c4116d97de74bfa6ca3178f73c8fe8fe612c70c6f85a7a1551942cb71cc
, 0x2ac40bf6c3176300a6835d5fc7cc4fd5e5d299fb1baa86487268ec1b9eedfa97
, 0x0f151de1f01b4e24ffe04279318f0a68efabb485188f191e37e6915ff6059f6e
, 0x2e43dffc34537535182aebac1ad7bf0a5533b88f65f9652f0ad584e2ffc4dd1f
, 0x2ebabc2c37ef53d8b13b24a2a2b729d536735f58956125a3876da0664c2442d7
, 0x0dc3beceb34e49f5ad7226dd202c5cf879dffcc9a6dd32a300e8f2a4b59edf03
, 0x2f1ddeccce83adf68779c53b639871a8f81d4d00aefe1e812efce8ec999d457d
, 0x1f63e41280ff5c021715d52b19780298ed8bd3d5eb506316b527e24149d4d4f1
, 0x1b8c1252a5888f8cb2672effb5df49c633d3fd7183271488a1c40d0f88e7636e
, 0x0f45697130f5498e2940568ef0d5e9e16b1095a6cdbb6411df20a973c605e70b
, 0x0780ccc403cdd68983acbd34cda41cacfb2cf911a93076bc25587b4b0aed4929
, 0x238d26ca97c691591e929f32199a643550f325f23a85d420080b289d7cecc9d4
]
sb = SBox(inp[0] + round_consts[i])
out = [F(0) for i in range(3)]
out[0] = 2*sb + inp[1] + inp[2];
out[1] = sb + 2*inp[1] + inp[2];
out[2] = sb + inp[1] + 3*inp[2];
return out
def ExternalRound(inp, i):
out = [F(0) for j in range(3)]
round_consts = [ [ F(0x2c4c51fd1bb9567c27e99f5712b49e0574178b41b6f0a476cddc41d242cf2b43)
, F(0x1c5f8d18acb9c61ec6fcbfcda5356f1b3fdee7dc22c99a5b73a2750e5b054104)
, F(0x2d3c1988b4541e4c045595b8d574e98a7c2820314a82e67a4e380f1c4541ba90 )
]
, [ F(0x052547dc9e6d936cab6680372f1734c39f490d0cb970e2077c82f7e4172943d3)
, F(0x29d967f4002adcbb5a6037d644d36db91f591b088f69d9b4257694f5f9456bc2)
, F(0x0350084b8305b91c426c25aeeecafc83fc5feec44b9636cb3b17d2121ec5b88a)
]
, [ F(0x1815d1e52a8196127530cc1e79f07a0ccd815fb5d94d070631f89f6c724d4cbe)
, F(0x17b5ba882530af5d70466e2b434b0ccb15b7a8c0138d64455281e7724a066272)
, F(0x1c859b60226b443767b73cd1b08823620de310bc49ea48662626014cea449aee)
]
, [ F(0x1b26e7f0ac7dd8b64c2f7a1904c958bb48d2635478a90d926f5ff2364effab37)
, F(0x2da7f36850e6c377bdcdd380efd9e7c419555d3062b0997952dfbe5c54b1a22e)
, F(0x17803c56450e74bc6c7ff97275390c017f682db11f3f4ca6e1f714efdfb9bd66)
]
, [ F(0x25672a14b5d085e31a30a7e1d5675ebfab034fb04dc2ec5e544887523f98dede)
, F(0x0cf702434b891e1b2f1d71883506d68cdb1be36fa125674a3019647b3a98accd)
, F(0x1837e75235ff5d112a5eddf7a4939448748339e7b5f2de683cf0c0ae98bdfbb3)
]
, [ F(0x1cd8a14cff3a61f04197a083c6485581a7d836941f6832704837a24b2d15613a)
, F(0x266f6d85be0cef2ece525ba6a54b647ff789785069882772e6cac8131eecc1e4)
, F(0x0538fde2183c3f5833ecd9e07edf30fe977d28dd6f246d7960889d9928b506b3)
]
, [ F(0x07a0693ff41476abb4664f3442596aa8399fdccf245d65882fce9a37c268aa04)
, F(0x11eb49b07d33de2bd60ea68e7f652beda15644ed7855ee5a45763b576d216e8e)
, F(0x08f8887da6ce51a8c06041f64e22697895f34bacb8c0a39ec12bf597f7c67cfc)
]
, [ F(0x2a912ec610191eb7662f86a52cc64c0122bd5ba762e1db8da79b5949fdd38092)
, F(0x2031d7fd91b80857aa1fef64e23cfad9a9ba8fe8c8d09de92b1edb592a44c290)
, F(0x0f81ebce43c47711751fa64d6c007221016d485641c28c507d04fd3dc7fba1d2)
]
]
sb = [F(0) for j in range(3)]
for j in range(3):
sb[j] = SBox(F(inp[j] + round_consts[i][j]))
out = [F(0) for j in range(3)]
out[0] = 2*sb[0] + sb[1] + sb[2]
out[1] = sb[0] + 2*sb[1] + sb[2]
out[2] = sb[0]+ sb[1] + 2*sb[2]
return out
def LinearLayer(inp):
out = [F(0) for i in range(3)]
out[0] = 2*inp[0] + inp[1] + inp[2]
out[1] = inp[0] + 2*inp[1] + inp[2]
out[2] = inp[0] + inp[1] + 2*inp[2]
return out
def Permutation(inp):
out = [F(0) for i in range(3)]
state = LinearLayer(inp)
for k in range(4):
state = ExternalRound(state, k)
for k in range(56):
state = InternalRound(state, k)
for k in range(4):
state = ExternalRound(state, k+4)
return state
def Compression(inp):
return Permutation([inp[0],inp[1],F(0)])
def PoseidonSponge(data, capacity, output_len):
rate = 3 - capacity;
output = [F(0) for i in range(output_len)]
assert( capacity > 0 )
assert( rate > 0 )
assert( capacity < 3 )
assert( rate < 3 )
# round up to rate the input + 1 field element ("10*" padding)
nblocks = ((len(data) + 1) + (rate-1)) // rate;
nout = (output_len + (rate-1)) // rate;
padded_len = nblocks * rate;
padded = []
for i in range(len(data)):
padded.append(F(data[i]))
padded.append(F(1))
for i in range(len(data)+1,padded_len):
padded.append(F(0))
civ = F(2**64 + 256*3 + rate)
state = [F(0),F(0),F(civ)]
sorbed = [F(0) for j in range(rate)]
for m in range(nblocks):
for i in range(rate):
a = state[i]
b = padded[m*rate+i]
sorbed[i] = a + b
state = Permutation(sorbed[0:rate] + state[rate:3])
q = min(rate, output_len)
for i in range(q):
output[i] = state[i]
out_ptr = rate
for n in range(1,nout):
state[nblocks+n] = Permutation(state[nblocks+n-1])
q = min(rate, output_len-out_ptr)
for i in range(q):
output[out_ptr+i] = state[nblocks+n][i]
out_ptr += rate
return output
R = RealField(500) #Real numbers with precision 500 bits
if len(sys.argv) != Integer(4):
print("Usage: <script> <epoch_nonce> <slot_number> <total_stake>")
exit()
epoch_nonce = int(sys.argv[Integer(1)])
slot_number = int(sys.argv[Integer(2)])
total_stake = int(sys.argv[Integer(3)])
if epoch_nonce >= p:
print("epoch nonce must be less than p")
exit()
if total_stake >= p:
print("total stake must be less than p")
exit()
t0 = F(int(-((R(p) * ln(R(1) - 0.05))) / R(total_stake)))
t1 = F(int(-((R(p) * ln(R(1) - 0.05))**2) / R(total_stake)**2))
value = F(50)
unit = F(161796427070100155131822184769584603407573991022311108406630770340454367555)
state = F(randrange(0,p,1))
note_nonce = F(0)
threshold = (t0 + t1 * value) * value
starting_slot = randrange(max(0,slot_number-2**25+1),slot_number,1)
slot_secret = F(randrange(0,p,1))
slot_secret_indexes = format(slot_number - starting_slot,'025b')
slot_secret_path = [F(randrange(0,p,1)) for i in range(25)]
secret_root = slot_secret
for i in range(25):
if int(slot_secret_indexes[24-i]) == 0:
secret_root = poseidon2_hash([secret_root,slot_secret_path[i]])
else:
secret_root = poseidon2_hash([slot_secret_path[i],secret_root])
sk = poseidon2_hash([F(313763129738690320248895675268201668175331181115752393250540330459318963992),starting_slot,secret_root])
pk = poseidon2_hash([F(355994159511987982411097843485998670968942801951585260613801918349630142543),sk])
note_cm = poseidon2_hash([F(181645510297841241569044198526601622686169271532834574969543446901055041748),state,value,unit,note_nonce,pk,F(281646683567839822174419720505039861445414630574005374635737888376398200354)])
ticket = poseidon2_hash([F(137836078329650723736739065075984465408055658421620421917147974048265460598),F(epoch_nonce),F(slot_number),note_cm,sk])
while(ticket > threshold):
note_nonce += 1
note_cm = poseidon2_hash([F(181645510297841241569044198526601622686169271532834574969543446901055041748),state,value,unit,note_nonce,pk,F(281646683567839822174419720505039861445414630574005374635737888376398200354)])
ticket = poseidon2_hash([F(137836078329650723736739065075984465408055658421620421917147974048265460598),F(epoch_nonce),F(slot_number),note_cm,sk])
cm_aged_nodes = [F(randrange(0,p,1)) for i in range(32)]
cm_aged_selectors = randrange(0,2**32,1)
cm_aged_selectors = format(cm_aged_selectors,'032b')
cm_aged_root = note_cm
for i in range(32):
if int(cm_aged_selectors[31-i]) == 0:
cm_aged_root = poseidon2_hash([cm_aged_root,cm_aged_nodes[i]])
else:
cm_aged_root = poseidon2_hash([cm_aged_nodes[i],cm_aged_root])
cm_unspent_nodes = [F(randrange(0,p,1)) for i in range(32)]
cm_unspent_selectors = randrange(0,2**32,1)
cm_unspent_selectors = format(cm_unspent_selectors,'032b')
cm_unspent_root = note_cm
for i in range(32):
if int(cm_unspent_selectors[31-i]) == 0:
cm_unspent_root = poseidon2_hash([cm_unspent_root,cm_unspent_nodes[i]])
else:
cm_unspent_root = poseidon2_hash([cm_unspent_nodes[i],cm_unspent_root])
with open("input.json", "w") as file:
file.write('{\n\t"slot":\t\t\t\t\t\t"'+str(slot_number)+'",')
file.write('\n\t"epoch_nonce":\t\t\t\t\t\t"'+str(epoch_nonce)+'",')
file.write('\n\t"t0" :\t\t\t\t\t\t"'+str(t0)+'",')
file.write('\n\t"t1" :\t\t\t\t\t\t"'+str(t1)+'",')
file.write('\n\t"slot_secret" :\t\t\t\t\t\t"'+str(slot_secret)+'",')
file.write('\n\t"one_time_key" :\t\t\t\t\t\t"'+str(F(516548))+'",')
file.write('\n\t"slot_secret_path" :\t\t\t\t\t[')
for i in range(25):
file.write('"')
file.write(str(slot_secret_path[i]))
file.write('"')
if i == 24:
file.write('],')
else:
file.write(',')
file.write('\n\t"cm_aged_nodes" :\t\t\t\t\t[')
for i in range(32):
file.write('"')
file.write(str(cm_aged_nodes[i]))
file.write('"')
if i == 31:
file.write('],')
else:
file.write(',')
file.write('\n\t"cm_aged_selectors" :\t\t\t\t\t[')
for i in range(32):
file.write('"')
file.write(str(cm_aged_selectors[i]))
file.write('"')
if i == 31:
file.write('],')
else:
file.write(',')
file.write('\n\t"commitments_aged_root" :\t\t\t\t"'+str(cm_aged_root)+'",')
file.write('\n\t"cm_unspent_nodes" :\t\t\t\t\t[')
for i in range(32):
file.write('"')
file.write(str(cm_unspent_nodes[i]))
file.write('"')
if i == 31:
file.write('],')
else:
file.write(',')
file.write('\n\t"cm_unspent_selectors" :\t\t\t\t\t[')
for i in range(32):
file.write('"')
file.write(str(cm_unspent_selectors[i]))
file.write('"')
if i == 31:
file.write('],')
else:
file.write(',')
file.write('\n\t"commitments_unspent_root" :\t\t\t\t"'+str(cm_unspent_root)+'",')
file.write('\n\t"starting_slot" :\t\t\t\t"'+str(starting_slot)+'",')
file.write('\n\t"secrets_root" :\t\t\t\t"'+str(secret_root)+'",')
file.write('\n\t"state" :\t\t\t\t"'+str(state)+'",')
file.write('\n\t"value" :\t\t\t\t"'+str(value)+'",')
file.write('\n\t"nonce" :\t\t\t\t"'+str(note_nonce)+'"}')