feat(constraints): add rpo constraints

constraints/miden-vm/hash.air

@@ -1,12 +1,49 @@
 mod HashChipletAir
 
 ### Constants and periodic columns ################################################################
+const MDS = [
+    [7, 23, 8, 26, 13, 10, 9, 7, 6, 22, 21, 8],
+    [8, 7, 23, 8, 26, 13, 10, 9, 7, 6, 22, 21],
+    [21, 8, 7, 23, 8, 26, 13, 10, 9, 7, 6, 22],
+    [22, 21, 8, 7, 23, 8, 26, 13, 10, 9, 7, 6],
+    [6, 22, 21, 8, 7, 23, 8, 26, 13, 10, 9, 7],
+    [7, 6, 22, 21, 8, 7, 23, 8, 26, 13, 10, 9],
+    [9, 7, 6, 22, 21, 8, 7, 23, 8, 26, 13, 10],
+    [10, 9, 7, 6, 22, 21, 8, 7, 23, 8, 26, 13],
+    [13, 10, 9, 7, 6, 22, 21, 8, 7, 23, 8, 26],
+    [26, 13, 10, 9, 7, 6, 22, 21, 8, 7, 23, 8],
+    [8, 26, 13, 10, 9, 7, 6, 22, 21, 8, 7, 23],
+    [23, 8, 26, 13, 10, 9, 7, 6, 22, 21, 8, 7]
+]
 
 periodic_columns:
     cycle_row_0: [1, 0, 0, 0, 0, 0, 0, 0]
     cycle_row_6: [0, 0, 0, 0, 0, 0, 1, 0]
     cycle_row_7: [0, 0, 0, 0, 0, 0, 0, 1]
-
+    ark_0: [5789762306288267264, 12987190162843097088, 18072785500942327808, 5674685213610122240, 4887609836208846848, 16308865189192448000, 7123075680859040768, 0]
+    ark_1: [6522564764413702144, 653957632802705280, 6200974112677013504, 5759084860419474432, 3027115137917284352, 11977192855656443904, 1034205548717903104, 0]
+    ark_2: [17809893479458207744, 4441654670647621120, 17682092219085883392, 13943282657648898048, 9595098600469471232, 12532242556065779712, 7717824418247931904, 0]
+    ark_3: [107145243989736512, 4038207883745915904, 10599526828986757120, 1352748651966375424, 10528569829048483840, 14594890931430969344, 3019070937878604288, 0]
+    ark_4: [6388978042437517312, 5613464648874829824, 975003873302957312, 17110913224029904896, 7864689113198940160, 7291784239689209856, 11403792746066868224, 0]
+    ark_5: [15844067734406017024, 13222989726778339328, 8264241093196931072, 1003883795902368384, 17533723827845969920, 5514718540551361536, 10280580802233112576, 0]
+    ark_6: [9975000513555218432, 3037761201230264320, 10065763900435474432, 4141870621881018368, 5781638039037711360, 10025733853830934528, 337153209462421248, 0]
+    ark_7: [3344984123768313344, 16683759727265179648, 2181131744534710272, 8121410972417424384, 17024078752430718976, 7293794580341021696, 13333398568519923712, 0]
+    ark_8: [9959189626657347584, 8337364536491240448, 6317303992309419008, 14300518605864919040, 109659393484013504, 6728552937464861696, 3596153696935337472, 0]
+    ark_9: [12960773468763564032, 3227397518293416448, 1401440938888741632, 13712227150607669248, 7158933660534805504, 6332385040983343104, 8104208463525993472, 0]
+    ark_10: [9602914297752487936, 8110510111539675136, 8884468225181997056, 17021852944633065472, 2955076958026921984, 13277683694236792832, 14345062289456084992, 0]
+    ark_11: [16657542370200465408, 2872078294163232256, 13066900325715521536, 6252096473787587584, 7433723648458773504, 2600778905124452864, 17036731477169661952, 0]
+    ark_12: [6077062762357203968, 6202948458916100096, 8023374565629191168, 18389244934624493568, 6982293561042363392, 3736792340494631424, 17130398059294019584, 0]
+    ark_13: [15277620170502010880, 17690140365333231616, 15013690343205953536, 16731736864863924224, 14065426295947720704, 577852220195055360, 519782857322262016, 0]
+    ark_14: [5358738125714196480, 3595001575307484672, 4485500052507913216, 4440209734760478208, 16451845770444974080, 6689998335515780096, 9625384390925084672, 0]
+    ark_15: [14233283787297595392, 373995945117666496, 12489737547229155328, 17208448209698889728, 7139138592091307008, 13886063479078012928, 1664893052631119104, 0]
+    ark_16: [13792579614346651648, 1235734395091296000, 9500452585969031168, 8739495587021565952, 9012006439959783424, 14358505101923203072, 7629576092524553216, 0]
+    ark_17: [11614812331536766976, 14172757457833930752, 2054001340201038848, 17000774922218162176, 14619614108529063936, 7744142531772273664, 3485239601103661568, 0]
+    ark_18: [14871063686742261760, 707573103686350208, 12420704059284934656, 13533282547195531264, 1394813199588124416, 16135070735728404480, 9755891797164034048, 0]
+    ark_19: [10148237148793042944, 15453217512188186624, 355990932618543744, 525402848358706240, 4635111139507788800, 12290902521256030208, 15218148195153268736, 0]
+    ark_20: [4457428952329675776, 219777875004506016, 9071225051243524096, 16987541523062161408, 16217473952264204288, 12059913662657710080, 16460604813734957056, 0]
+    ark_21: [15590786458219171840, 17876696346199468032, 12766199826003447808, 5466806524462796800, 10782018226466330624, 16456018495793752064, 9643968136937730048, 0]
+    ark_22: [10063319113072093184, 17731621626449383424, 9045979173463557120, 14512769585918244864, 6844229992533661696, 4571485474751953408, 3611348709641382912, 0]
+    ark_23: [14200078843431360512, 2897136237748376064, 12934431667190679552, 10973956031244050432, 7446486531695178752, 17200392109565784064, 18256379591337758720, 0]    
 
 ### Helper functions ##############################################################################
 
@@ -83,6 +120,13 @@ fn get_f_out(s: vector[3]) -> scalar:
 fn get_f_out_next(s: vector[3]) -> scalar:
     return cycle_row_6 & binary_not(s[0]') & binary_not(s[1]')
 
+fn apply_mds(state: vector[12]) -> vector[12]:
+    let result = [sum([state[i] * mds_row[i] for i in 0..12]) for mds_row in MDS]
+    return result
+
+fn apply_sbox(state: vector[12]) -> vector[12]:
+    let result = [s^7 for s in state]
+    return result
 
 ### Helper evaluators #############################################################################
 
@@ -181,6 +225,33 @@ ev hasher_state(main: [s[3], h[12], i]):
         is_unchanged(h[j + 4]) for j in 0..4 when !b & f_absorb_node
         h[j + 8]' = h[j + 4] for j in 0..4 when b & f_absorb_node
 
+ev enforce_rpo_round(main: [h[12]]):
+    let ark = [ark_0, ark_1, ark_2, ark_3, ark_4, ark_5, ark_6, ark_7, ark_8, ark_9, ark_10,
+        ark_11, ark_12, ark_13, ark_14, ark_15, ark_16, ark_17, ark_18, ark_19, ark_20, ark_21,
+        ark_22, ark_23]
+
+    # compute the state that should result from applying the first 5 operations of the RPO round to
+    # the current hash state.
+    let step1_initial = apply_mds(h)
+
+    # add constants
+    let step1_with_constants = [step1_initial[i] + ark[i] for i in 0..12]
+
+    # apply sbox
+    let step1_with_sbox = apply_sbox(step1_with_constants)
+
+    # apply mds
+    let step1_with_mds = apply_mds(step1_with_sbox)
+
+    # add constants
+    let step1 = [step1_with_mds[i] + ark[i + 12] for i in 0..12]
+
+    # compute the state that should result from applying the inverse of the last operation of the
+    # RPO round to the next step of the computation.
+    let step2 = apply_sbox(h)
+
+    # make sure that the results are equal.
+    enf step1[i] = step2[i] for i in 0..12 when !k0
 
 ### Hash Chiplet Air Constraints ##################################################################
 
@@ -198,7 +269,8 @@ ev hash_chiplet(main: [s[3], r, h[12], i]):
     enf node_index([s, i])
 
     ## Hasher state constraints ##
-    # TODO: apply RPO constraints to the hasher state
+    enf enforce_rpo_round([h])
+
     enf hasher_state([s, h, i])
 
     # Multiset check constraints