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A python script to perform sha2 in terms of if-statements and for-loops.
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| """ | |
| Bit level SHA2. | |
| Script to perform sha2 in terms of if-statements and for-loops. This runs 1 batch iteration | |
| (i.e. about 50 bytes max input, but should be easy to extend to any size.) | |
| No warranty. | |
| Explanation video: | |
| https://youtu.be/UziK-Hqzwi4 | |
| 2019 | |
| Nikolaj Kuntner | |
| """ | |
| ################################################## online hashing tool | |
| ### https://passwordsgenerator.net/sha256-hash-generator | |
| HELLO_HASH = '2cf24dba5fb0a30e26e83b2ac5b9e29e1b161e5c1fa7425e73043362938b9824' ## hash of "hello" | |
| HELLP_HASH = 'fdd7585e08c4e2afd71dcabdb4636c89d557a3f42db9e2040c8bbd1708aa4ce7' ## hash of "hellp" | |
| ## ouptut is base 16=2**4 and has 64 chars or 64 * 4 = 256 bits | |
| def num2arr(n): | |
| bs = [] | |
| while n > 1: | |
| bs = [n % 2] + bs ## [remaider] + [accumulation] | |
| n = n // 2 ## integer division, i.e. quotient without remainder | |
| return [1] + bs if n else bs | |
| ################################################ bit functions | |
| F = 'some value' ## respresents False, 0, fNumber | |
| T = 'a different value' ## respresents True, 1, tNumber | |
| def TRUE(x): return x==T | |
| def IF(x, a, b): return a if TRUE(x) else b | |
| ## return a if x else b | |
| ## return x * a + (1-x) * b | |
| ## return 'some polynomials of x, a, b with coefficients being simple functions of nF and nT' | |
| def NOT(x): return IF(x, F, T) | |
| def AND(x, y): return IF(x, y, F) | |
| def XOR(x, y): return IF(x, NOT(y), y) | |
| def MAJ(x, y, z): return IF(x, IF(y, T, z), IF(y, z, F)) | |
| def XORXOR(x, y, z): return XOR(x, XOR(y, z)) | |
| #IF(x, IF(y, z, NOT(z)), IF(y, NOT(z), z)) | |
| ## return x+y+z mod 2 | |
| ## return XOR(x, XOR(y, z)) | |
| ################################################ bit array functions | |
| ####################### component-wise functions | |
| def if_(x, y, z): return [IF(xi, yi, zi) for xi, yi, zi in zip(x, y, z)] | |
| def and_(x, y): return [AND(xi, yi) for xi, yi in zip(x, y)] | |
| def xor(x, y): return [XOR(xi, yi) for xi, yi in zip(x, y)] | |
| def maj(x, y, z): return [MAJ(xi, yi, zi) for xi, yi, zi in zip(x, y, z)] | |
| def xorxor(x, y, z): return [XORXOR(xi, yi, zi) for xi, yi, zi in zip(x, y, z)] | |
| ####################### addition | |
| N = 32 | |
| def add(x, y): ## binary addition of N bit numbers (automatically mod 2**N) | |
| res = list(range(N)) | |
| ci = F ## carry bit | |
| for i in range(N-1, -1, -1): | |
| res[i] = XORXOR(x[i], y[i], ci) | |
| ci = MAJ(x[i], y[i], ci) | |
| return res | |
| ####################### utility functions | |
| def rotr(x, n): return x[-n:] + x[:-n] | |
| def cut(x, n): return n * [F] + x[:(len(x) - n)] | |
| ################################################## "random" numbers used in SHA256 | |
| K = [ ## 64 * 32 = 2048 bits (256 bytes) | |
| [F,T,F,F,F,F,T,F,T,F,F,F,T,F,T,F,F,F,T,F,T,T,T,T,T,F,F,T,T,F,F,F], ## 32 bits (4 bytes) | |
| [F,T,T,T,F,F,F,T,F,F,T,T,F,T,T,T,F,T,F,F,F,T,F,F,T,F,F,T,F,F,F,T], | |
| [T,F,T,T,F,T,F,T,T,T,F,F,F,F,F,F,T,T,T,T,T,F,T,T,T,T,F,F,T,T,T,T], | |
| [T,T,T,F,T,F,F,T,T,F,T,T,F,T,F,T,T,T,F,T,T,F,T,T,T,F,T,F,F,T,F,T], | |
| [F,F,T,T,T,F,F,T,F,T,F,T,F,T,T,F,T,T,F,F,F,F,T,F,F,T,F,T,T,F,T,T], | |
| [F,T,F,T,T,F,F,T,T,T,T,T,F,F,F,T,F,F,F,T,F,F,F,T,T,T,T,T,F,F,F,T], | |
| [T,F,F,T,F,F,T,F,F,F,T,T,T,T,T,T,T,F,F,F,F,F,T,F,T,F,T,F,F,T,F,F], | |
| [T,F,T,F,T,F,T,T,F,F,F,T,T,T,F,F,F,T,F,T,T,T,T,F,T,T,F,T,F,T,F,T], | |
| [T,T,F,T,T,F,F,F,F,F,F,F,F,T,T,T,T,F,T,F,T,F,T,F,T,F,F,T,T,F,F,F], | |
| [F,F,F,T,F,F,T,F,T,F,F,F,F,F,T,T,F,T,F,T,T,F,T,T,F,F,F,F,F,F,F,T], | |
| [F,F,T,F,F,T,F,F,F,F,T,T,F,F,F,T,T,F,F,F,F,T,F,T,T,F,T,T,T,T,T,F], | |
| [F,T,F,T,F,T,F,T,F,F,F,F,T,T,F,F,F,T,T,T,T,T,F,T,T,T,F,F,F,F,T,T], | |
| [F,T,T,T,F,F,T,F,T,F,T,T,T,T,T,F,F,T,F,T,T,T,F,T,F,T,T,T,F,T,F,F], | |
| [T,F,F,F,F,F,F,F,T,T,F,T,T,T,T,F,T,F,T,T,F,F,F,T,T,T,T,T,T,T,T,F], | |
| [T,F,F,T,T,F,T,T,T,T,F,T,T,T,F,F,F,F,F,F,F,T,T,F,T,F,T,F,F,T,T,T], | |
| [T,T,F,F,F,F,F,T,T,F,F,T,T,F,T,T,T,T,T,T,F,F,F,T,F,T,T,T,F,T,F,F], | |
| [T,T,T,F,F,T,F,F,T,F,F,T,T,F,T,T,F,T,T,F,T,F,F,T,T,T,F,F,F,F,F,T], | |
| [T,T,T,F,T,T,T,T,T,F,T,T,T,T,T,F,F,T,F,F,F,T,T,T,T,F,F,F,F,T,T,F], | |
| [F,F,F,F,T,T,T,T,T,T,F,F,F,F,F,T,T,F,F,T,T,T,F,T,T,T,F,F,F,T,T,F], | |
| [F,F,T,F,F,T,F,F,F,F,F,F,T,T,F,F,T,F,T,F,F,F,F,T,T,T,F,F,T,T,F,F], | |
| [F,F,T,F,T,T,F,T,T,T,T,F,T,F,F,T,F,F,T,F,T,T,F,F,F,T,T,F,T,T,T,T], | |
| [F,T,F,F,T,F,T,F,F,T,T,T,F,T,F,F,T,F,F,F,F,T,F,F,T,F,T,F,T,F,T,F], | |
| [F,T,F,T,T,T,F,F,T,F,T,T,F,F,F,F,T,F,T,F,T,F,F,T,T,T,F,T,T,T,F,F], | |
| [F,T,T,T,F,T,T,F,T,T,T,T,T,F,F,T,T,F,F,F,T,F,F,F,T,T,F,T,T,F,T,F], | |
| [T,F,F,T,T,F,F,F,F,F,T,T,T,T,T,F,F,T,F,T,F,F,F,T,F,T,F,T,F,F,T,F], | |
| [T,F,T,F,T,F,F,F,F,F,T,T,F,F,F,T,T,T,F,F,F,T,T,F,F,T,T,F,T,T,F,T], | |
| [T,F,T,T,F,F,F,F,F,F,F,F,F,F,T,T,F,F,T,F,F,T,T,T,T,T,F,F,T,F,F,F], | |
| [T,F,T,T,T,T,T,T,F,T,F,T,T,F,F,T,F,T,T,T,T,T,T,T,T,T,F,F,F,T,T,T], | |
| [T,T,F,F,F,T,T,F,T,T,T,F,F,F,F,F,F,F,F,F,T,F,T,T,T,T,T,T,F,F,T,T], | |
| [T,T,F,T,F,T,F,T,T,F,T,F,F,T,T,T,T,F,F,T,F,F,F,T,F,T,F,F,F,T,T,T], | |
| [F,F,F,F,F,T,T,F,T,T,F,F,T,F,T,F,F,T,T,F,F,F,T,T,F,T,F,T,F,F,F,T], | |
| [F,F,F,T,F,T,F,F,F,F,T,F,T,F,F,T,F,F,T,F,T,F,F,T,F,T,T,F,F,T,T,T], | |
| [F,F,T,F,F,T,T,T,T,F,T,T,F,T,T,T,F,F,F,F,T,F,T,F,T,F,F,F,F,T,F,T], | |
| [F,F,T,F,T,T,T,F,F,F,F,T,T,F,T,T,F,F,T,F,F,F,F,T,F,F,T,T,T,F,F,F], | |
| [F,T,F,F,T,T,F,T,F,F,T,F,T,T,F,F,F,T,T,F,T,T,F,T,T,T,T,T,T,T,F,F], | |
| [F,T,F,T,F,F,T,T,F,F,T,T,T,F,F,F,F,F,F,F,T,T,F,T,F,F,F,T,F,F,T,T], | |
| [F,T,T,F,F,T,F,T,F,F,F,F,T,F,T,F,F,T,T,T,F,F,T,T,F,T,F,T,F,T,F,F], | |
| [F,T,T,T,F,T,T,F,F,T,T,F,T,F,T,F,F,F,F,F,T,F,T,F,T,F,T,T,T,F,T,T], | |
| [T,F,F,F,F,F,F,T,T,T,F,F,F,F,T,F,T,T,F,F,T,F,F,T,F,F,T,F,T,T,T,F], | |
| [T,F,F,T,F,F,T,F,F,T,T,T,F,F,T,F,F,F,T,F,T,T,F,F,T,F,F,F,F,T,F,T], | |
| [T,F,T,F,F,F,T,F,T,F,T,T,T,T,T,T,T,T,T,F,T,F,F,F,T,F,T,F,F,F,F,T], | |
| [T,F,T,F,T,F,F,F,F,F,F,T,T,F,T,F,F,T,T,F,F,T,T,F,F,T,F,F,T,F,T,T], | |
| [T,T,F,F,F,F,T,F,F,T,F,F,T,F,T,T,T,F,F,F,T,F,T,T,F,T,T,T,F,F,F,F], | |
| [T,T,F,F,F,T,T,T,F,T,T,F,T,T,F,F,F,T,F,T,F,F,F,T,T,F,T,F,F,F,T,T], | |
| [T,T,F,T,F,F,F,T,T,F,F,T,F,F,T,F,T,T,T,F,T,F,F,F,F,F,F,T,T,F,F,T], | |
| [T,T,F,T,F,T,T,F,T,F,F,T,T,F,F,T,F,F,F,F,F,T,T,F,F,F,T,F,F,T,F,F], | |
| [T,T,T,T,F,T,F,F,F,F,F,F,T,T,T,F,F,F,T,T,F,T,F,T,T,F,F,F,F,T,F,T], | |
| [F,F,F,T,F,F,F,F,F,T,T,F,T,F,T,F,T,F,T,F,F,F,F,F,F,T,T,T,F,F,F,F], | |
| [F,F,F,T,T,F,F,T,T,F,T,F,F,T,F,F,T,T,F,F,F,F,F,T,F,F,F,T,F,T,T,F], | |
| [F,F,F,T,T,T,T,F,F,F,T,T,F,T,T,T,F,T,T,F,T,T,F,F,F,F,F,F,T,F,F,F], | |
| [F,F,T,F,F,T,T,T,F,T,F,F,T,F,F,F,F,T,T,T,F,T,T,T,F,T,F,F,T,T,F,F], | |
| [F,F,T,T,F,T,F,F,T,F,T,T,F,F,F,F,T,F,T,T,T,T,F,F,T,F,T,T,F,T,F,T], | |
| [F,F,T,T,T,F,F,T,F,F,F,T,T,T,F,F,F,F,F,F,T,T,F,F,T,F,T,T,F,F,T,T], | |
| [F,T,F,F,T,T,T,F,T,T,F,T,T,F,F,F,T,F,T,F,T,F,T,F,F,T,F,F,T,F,T,F], | |
| [F,T,F,T,T,F,T,T,T,F,F,T,T,T,F,F,T,T,F,F,T,F,T,F,F,T,F,F,T,T,T,T], | |
| [F,T,T,F,T,F,F,F,F,F,T,F,T,T,T,F,F,T,T,F,T,T,T,T,T,T,T,T,F,F,T,T], | |
| [F,T,T,T,F,T,F,F,T,F,F,F,T,T,T,T,T,F,F,F,F,F,T,F,T,T,T,F,T,T,T,F], | |
| [F,T,T,T,T,F,F,F,T,F,T,F,F,T,F,T,F,T,T,F,F,F,T,T,F,T,T,F,T,T,T,T], | |
| [T,F,F,F,F,T,F,F,T,T,F,F,T,F,F,F,F,T,T,T,T,F,F,F,F,F,F,T,F,T,F,F], | |
| [T,F,F,F,T,T,F,F,T,T,F,F,F,T,T,T,F,F,F,F,F,F,T,F,F,F,F,F,T,F,F,F], | |
| [T,F,F,T,F,F,F,F,T,F,T,T,T,T,T,F,T,T,T,T,T,T,T,T,T,T,T,T,T,F,T,F], | |
| [T,F,T,F,F,T,F,F,F,T,F,T,F,F,F,F,F,T,T,F,T,T,F,F,T,T,T,F,T,F,T,T], | |
| [T,F,T,T,T,T,T,F,T,T,T,T,T,F,F,T,T,F,T,F,F,F,T,T,T,T,T,T,F,T,T,T], | |
| [T,T,F,F,F,T,T,F,F,T,T,T,F,F,F,T,F,T,T,T,T,F,F,F,T,T,T,T,F,F,T,F] | |
| ] | |
| H = [ ## 64 * 32 = 256 bits (32 bytes), like the hash output (e.g. HELLO_HASH) | |
| [F,T,T,F,T,F,T,F,F,F,F,F,T,F,F,T,T,T,T,F,F,T,T,F,F,T,T,F,F,T,T,T], | |
| [T,F,T,T,T,F,T,T,F,T,T,F,F,T,T,T,T,F,T,F,T,T,T,F,T,F,F,F,F,T,F,T], | |
| [F,F,T,T,T,T,F,F,F,T,T,F,T,T,T,F,T,T,T,T,F,F,T,T,F,T,T,T,F,F,T,F], | |
| [T,F,T,F,F,T,F,T,F,T,F,F,T,T,T,T,T,T,T,T,F,T,F,T,F,F,T,T,T,F,T,F], | |
| [F,T,F,T,F,F,F,T,F,F,F,F,T,T,T,F,F,T,F,T,F,F,T,F,F,T,T,T,T,T,T,T], | |
| [T,F,F,T,T,F,T,T,F,F,F,F,F,T,F,T,F,T,T,F,T,F,F,F,T,F,F,F,T,T,F,F], | |
| [F,F,F,T,T,T,T,T,T,F,F,F,F,F,T,T,T,T,F,T,T,F,F,T,T,F,T,F,T,F,T,T], | |
| [F,T,F,T,T,F,T,T,T,T,T,F,F,F,F,F,T,T,F,F,T,T,F,T,F,F,F,T,T,F,F,T] | |
| ] | |
| ################################################## start SHA-256 | |
| def sha(w): | |
| for i in range(16, 64): ## fill rest of w | |
| w[i] = add(add(add( | |
| w[i-16], | |
| w[i- 7]), | |
| xorxor(rotr(w[i-15], 7), rotr(w[i-15], 18), cut(w[i-15], 3))), | |
| xorxor(rotr(w[i-2] , 17), rotr(w[i-2] , 19), cut(w[i-2] , 10))) | |
| a, b, c, d, e, f, g, h = H | |
| for j in range(64): ## digest | |
| temp1 = add(add(add(add( | |
| w[j], | |
| h), | |
| if_(e, f, g)), | |
| xorxor(rotr(e, 6), rotr(e, 11), rotr(e, 25))), | |
| K[j]) | |
| tempd = add( | |
| maj(a, b, c), | |
| xorxor(rotr(a, 2), rotr(a, 13), rotr(a, 22))) | |
| h = g | |
| g = f | |
| f = e | |
| e = add( | |
| temp1, | |
| d) | |
| d = c | |
| c = b | |
| b = a | |
| a = add( | |
| temp1, | |
| tempd) | |
| return [add(x, y) for x, y in zip([a, b, c, d, e, f, g, h], H)] | |
| ################################################## utility funcitons for base conversion | |
| def arrsToHex(arrs): | |
| def arr2dec(arr): | |
| return sum([b * 2**k for k, b in enumerate(arr[::-1])]) | |
| def arr2hex(arr): | |
| return '{:x}'.format(arr2dec(arr)) | |
| return (arr2hex(arr) for arr in arrs) | |
| def translateArrBits(arr, source, target): | |
| for i, row in enumerate(arr): | |
| for j, elem in enumerate(row): | |
| if arr[i][j]==source: | |
| arr[i][j] = target | |
| ################################################## initialize a message on w, run and print! | |
| w = [32*[F] for _ in range(64)] | |
| w[15] = [F,F,F,F,F,F,F,F, F,F,F,F,F,F,F,F, F,F,F,F,F,F,F,F, F,F,T,F,T,F,F,F] ## message length | |
| w[0] = [F,T,T,F,T,F,F,F, F,T,T,F,F,T,F,T, F,T,T,F,T,T,F,F, F,T,T,F,T,T,F,F] ## "hell" | |
| w[1] = [F,T,T,F,T,T,T,T, T,F,F,F,F,F,F,F, F,F,F,F,F,F,F,F, F,F,F,F,F,F,F,F] ## "o" and message end | |
| #w[1] = [F,T,T,T,F,F,F,F, T,F,F,F,F,F,F,F, F,F,F,F,F,F,F,F, F,F,F,F,F,F,F,F] ## "p" and message end | |
| digestBool = sha(w) # run! | |
| translateArrBits(digestBool, F, 0) | |
| translateArrBits(digestBool, T, 1) | |
| for row in digestBool: | |
| print("".join(map(str, row))) | |
| for row in arrsToHex(digestBool): | |
| print(row) |
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