zok eg and tests for hashing state

zok/Eg1/case_14.zok

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+
+import "hashes/poseidon/poseidon" as poseidon
+
+def main(field[14] arr) -> field:
+     field h3 = poseidon(arr[8..14])
+     field h2 = poseidon(arr[2..8])
+     field h1 = poseidon(arr[0..2])
+     field out = poseidon([h1,h2,h3])
+     return out

zok/Eg1/case_41.zok

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+
+import "hashes/poseidon/poseidon" as poseidon
+
+def main(field[41] arr) -> field:
+     field h7 = poseidon(arr[35..41])
+     field h6 = poseidon(arr[29..35])
+     field h5 = poseidon(arr[23..29])
+     field h4 = poseidon(arr[17..23])
+     field h3 = poseidon(arr[11..17])
+     field h2 = poseidon(arr[5..11])
+     field h1 = poseidon(arr[0..5])
+     field hh2 = poseidon([h2,h3,h4,h5,h6,h7])
+     field hh1 = poseidon([h1])
+     field out = poseidon([hh1,hh2])
+     return out

zok/Eg1/case_99.zok

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+
+import "hashes/poseidon/poseidon" as poseidon
+
+def main(field[99] arr) -> field:
+     field h17 = poseidon(arr[93..99])
+     field h16 = poseidon(arr[87..93])
+     field h15 = poseidon(arr[81..87])
+     field h14 = poseidon(arr[75..81])
+     field h13 = poseidon(arr[69..75])
+     field h12 = poseidon(arr[63..69])
+     field h11 = poseidon(arr[57..63])
+     field h10 = poseidon(arr[51..57])
+     field h9 = poseidon(arr[45..51])
+     field h8 = poseidon(arr[39..45])
+     field h7 = poseidon(arr[33..39])
+     field h6 = poseidon(arr[27..33])
+     field h5 = poseidon(arr[21..27])
+     field h4 = poseidon(arr[15..21])
+     field h3 = poseidon(arr[9..15])
+     field h2 = poseidon(arr[3..9])
+     field h1 = poseidon(arr[0..3])
+     field hh3 = poseidon([h12,h13,h14,h15,h16,h17])
+     field hh2 = poseidon([h6,h7,h8,h9,h10,h11])
+     field hh1 = poseidon([h1,h2,h3,h4,h5])
+     field out = poseidon([hh1,hh2,hh3])
+     return out

zok/Eg1/gen_pos_14.zok

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+
+import "hashes/poseidon/poseidon" as poseidon 
+import "utils/casts/u32_to_field" as u32_to_field
+import "utils/casts/field_to_u32" as field_to_u32
+
+
+const u32 N = 14 
+const u32 INTERNAL_NODES = 4
+const u32[INTERNAL_NODES] HashSeq = [6, 6, 2, 3]
+
+def main(field[N] OrigInp) -> field:
+    u32 HeapSz = INTERNAL_NODES+N
+    field[HeapSz] Heap = [0; HeapSz]
+    //Initialize to 0 field
+
+    u32 j = 0
+    for u32 i in 0..N do
+       j = (HeapSz-1)-i
+       Heap[j]=OrigInp[(N-1)-i]
+    endfor
+    //The last N nodes of the Heap field array are set to the input fields
+
+    u32 leftChildOffset = HeapSz
+    u32 parent = INTERNAL_NODES
+    for u32 i in 0..INTERNAL_NODES do
+       parent = parent-1
+       leftChildOffset = leftChildOffset-HashSeq[i]
+       Heap[parent] = poseidon(Heap[leftChildOffset..leftChildOffset+HashSeq[i]])
+    endfor
+    return Heap[0]
+

zok/Eg1/gen_pos_41.zok

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+
+import "hashes/poseidon/poseidon" as poseidon 
+import "utils/casts/u32_to_field" as u32_to_field
+import "utils/casts/field_to_u32" as field_to_u32
+
+
+const u32 N = 41 
+const u32 INTERNAL_NODES = 10
+const u32[INTERNAL_NODES] HashSeq = [6, 6, 6, 6, 6, 6, 5, 6, 1, 2]
+
+def main(field[N] OrigInp) -> field:
+    u32 HeapSz = INTERNAL_NODES+N
+    field[HeapSz] Heap = [0; HeapSz]
+    //Initialize to 0 field
+
+    u32 j = 0
+    for u32 i in 0..N do
+       j = (HeapSz-1)-i
+       Heap[j]=OrigInp[(N-1)-i]
+    endfor
+    //The last N nodes of the Heap field array are set to the input fields
+
+    u32 leftChildOffset = HeapSz
+    u32 parent = INTERNAL_NODES
+    for u32 i in 0..INTERNAL_NODES do
+       parent = parent-1
+       leftChildOffset = leftChildOffset-HashSeq[i]
+       Heap[parent] = poseidon(Heap[leftChildOffset..leftChildOffset+HashSeq[i]])
+    endfor
+    return Heap[0]
+

zok/Eg1/gen_pos_99.zok

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+
+import "hashes/poseidon/poseidon" as poseidon 
+import "utils/casts/u32_to_field" as u32_to_field
+import "utils/casts/field_to_u32" as field_to_u32
+
+
+const u32 N = 99 
+const u32 INTERNAL_NODES = 21
+const u32[INTERNAL_NODES] HashSeq = [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 3, 6, 6, 5, 3]
+
+def main(field[N] OrigInp) -> field:
+    u32 HeapSz = INTERNAL_NODES+N
+    field[HeapSz] Heap = [0; HeapSz]
+    //Initialize to 0 field
+
+    u32 j = 0
+    for u32 i in 0..N do
+       j = (HeapSz-1)-i
+       Heap[j]=OrigInp[(N-1)-i]
+    endfor
+    //The last N nodes of the Heap field array are set to the input fields
+
+    u32 leftChildOffset = HeapSz
+    u32 parent = INTERNAL_NODES
+    for u32 i in 0..INTERNAL_NODES do
+       parent = parent-1
+       leftChildOffset = leftChildOffset-HashSeq[i]
+       Heap[parent] = poseidon(Heap[leftChildOffset..leftChildOffset+HashSeq[i]])
+    endfor
+    return Heap[0]
+

zok/Eg1/generate_hash_zok.py

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+#!/usr/bin/env python
+
+import sys
+max_poseidon_arity = 6
+
+#Zok program that given an N-field input OrigInp will generate 
+#a tree in which the N OrigInp fileds form the leaf-layer
+#and each parent is a poseidon hash. The arity of each poseidon 
+#hash is governed by the HashSeq array, which is computed 
+#quite simply in the prepare_zok_args function
+
+hashgen_zok = """
+import "hashes/poseidon/poseidon" as poseidon 
+import "utils/casts/u32_to_field" as u32_to_field
+import "utils/casts/field_to_u32" as field_to_u32
+
+
+const u32 N = %s 
+const u32 INTERNAL_NODES = %s
+const u32[INTERNAL_NODES] HashSeq = %s
+
+def main(field[N] OrigInp) -> field:
+    u32 HeapSz = INTERNAL_NODES+N
+    field[HeapSz] Heap = [0; HeapSz]
+    //Initialize to 0 field
+
+    u32 j = 0
+    for u32 i in 0..N do
+       j = (HeapSz-1)-i
+       Heap[j]=OrigInp[(N-1)-i]
+    endfor
+    //The last N nodes of the Heap field array are set to the input fields
+
+    u32 leftChildOffset = HeapSz
+    u32 parent = INTERNAL_NODES
+    for u32 i in 0..INTERNAL_NODES do
+       parent = parent-1
+       leftChildOffset = leftChildOffset-HashSeq[i]
+       Heap[parent] = poseidon(Heap[leftChildOffset..leftChildOffset+HashSeq[i]])
+    endfor
+    return Heap[0]
+"""
+
+#function that takes the number of fields in the transaction that
+#needs to be hashed and generates an appropriate Zok program from 
+#hashgen_zok. 
+def print_zok_program(NumInputs) :
+    levelSz=NumInputs
+    if levelSz <= max_poseidon_arity:
+        hash_seq = [levelSz]
+    else: 
+        hash_seq = []
+        while levelSz > 1:
+            if levelSz%max_poseidon_arity==0:
+                nextLevelSz = levelSz//max_poseidon_arity
+                hash_seq += [max_poseidon_arity]*nextLevelSz
+            else:
+                nextLevelSz = levelSz//max_poseidon_arity+1
+                hash_seq += [max_poseidon_arity]*(levelSz//max_poseidon_arity)+[levelSz%max_poseidon_arity]
+            levelSz = nextLevelSz
+    #print(levelSz)
+    #print(hash_seq)
+    print(hashgen_zok%(str(NumInputs),str(len(hash_seq)),str(hash_seq)))
+
+
+
+if __name__ == '__main__':
+  print_zok_program(int(sys.argv[1])) 
+
+
+
+