Function bitcoin_signingprovider::poly_mod

pub fn poly_mod(c: u64, val: i32) -> u64

| Interprets c as 8 groups of 5 bits which | are the coefficients of a degree 8 polynomial | over | | GF(32), multiplies that polynomial | by x, computes its remainder modulo | a generator, and adds the constant term | val. | | This generator is G(x) = x^8 + {30}x^7 | + {23}x^6 + {15}x^5 + {14}x^4 + {10}x^3 | + {6}x^2 + {12}x + {9}. | | It is chosen to define an cyclic error | detecting code which is selected by: | | - Starting from all BCH codes over GF(32) | of degree 8 and below, which by construction | guarantee detecting 3 errors in windows | up to 19000 symbols. | | - Taking all those generators, and for | degree 7 ones, extend them to degree | 8 by adding all degree-1 factors. | | - Selecting just the set of generators | that guarantee detecting 4 errors in | a window of length 512. | | - Selecting one of those with best worst-case | behavior for 5 errors in windows of length | up to 512. | | The generator and the constants to implement | it can be verified using this Sage code: | | ———– | @code | | B = GF(2) # Binary field | BP. = B[] # Polynomials over the binary field | F_mod = b5 + b3 + 1 | F. = GF(32, modulus=F_mod, repr=‘int’) # GF(32) definition | FP. = F[] # Polynomials over GF(32) | E_mod = x3 + x + F.fetch_int(8) | E. = F.extension(E_mod) # Extension field definition | alpha = e2743 # Choice of an element in extension field | for p in divisors(E.order() - 1): # Verify alpha has order 32767. | assert((alphap == 1) == (p % 32767 == 0)) | G = lcm([(alphai).minpoly() for i in [1056,1057,1058]] + [x + 1]) | print(G) # Print out the generator | for i in [1,2,4,8,16]: # Print out {1,2,4,8,16}(G mod x^8), packed in hex integers. | v = 0 | for coef in reversed((F.fetch_int(i)(G % x**8)).coefficients(sparse=True)): | v = v*32 + coef.integer_representation() | print(“0x%x” % v) |