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working sqrt in field

This commit is contained in:
Christoph J. Scherr 2023-05-22 10:49:36 +02:00
parent 27530769de
commit b4d55517ff
Signed by: PlexSheep
GPG Key ID: 25B4ACF7D88186CC
3 changed files with 91 additions and 11 deletions
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4
src/cplex/printing.rs
View File

@ -122,10 +122,10 @@ pub fn proc_tup_num<T>(num: (T, T), args: Cli)
seperator(); seperator();
} }
if args.machine { if args.machine {
println!("({}{}) (({:#x}, {:#x})", num.0, num.1, num.0, num.1); println!("({}, {}) (({:#x}, {:#x})", num.0, num.1, num.0, num.1);
} }
else { else {
println!("result is ({}{}) (({:#x}, {:#x})", num.0, num.1, num.0, num.1); println!("result is ({}, {}) (({:#x}, {:#x})", num.0, num.1, num.0, num.1);
} }
} }

95
src/math/gallois.rs
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@ -176,6 +176,7 @@ impl GalloisFiled {
if self.reduce(b_pm1_2) == self.reduce_neg(-1) { if self.reduce(b_pm1_2) == self.reduce_neg(-1) {
b = Some(b_candidate); b = Some(b_candidate);
if self.verbose { if self.verbose {
println!("b^([p-1]/[2]) = {}^({pm1_2}) = -1 (mod {})", b.unwrap(), self.base);
println!("found a b that fits the criteria: {}", b.unwrap()); println!("found a b that fits the criteria: {}", b.unwrap());
seperator(); seperator();
} }
@ -193,25 +194,101 @@ impl GalloisFiled {
let mut n: Vec<u128> = vec![0]; let mut n: Vec<u128> = vec![0];
let mut c: Vec<u128> = vec![]; let mut c: Vec<u128> = vec![];
let mut tmp: u128; let mut tmp: u128;
if self.verbose {
println!("l = {l}\tt = {t}\tb = {b}");
println!("let n_0 = 0");
}
for index in 0..l { for index in 0..l {
if self.verbose {
println!("Calculating c_{index}");
}
// l-(i+1) // l-(i+1)
tmp = l - (index+1); tmp = l - (index+1);
if self.verbose {
println!("{index}.\tl-(i+1) = {l}-({index}+1) = {tmp}");
}
tmp = modexp::modular_exponentiation_wrapper(2, tmp, self.base, false); tmp = modexp::modular_exponentiation_wrapper(2, tmp, self.base, false);
c[index as usize] = a.pow(2u32.pow((self.reduce(l as u128 - (index as u128 + 1)) * t) as u32) as u32) * b.pow(n[index as usize] as u32); if self.verbose {
println!("{index}.\t2^[l-(i+1)] = 2^[{l}-({index}+1)] = {tmp}");
}
tmp *= t;
if self.verbose {
println!("{index}.\t2^[l-(i+1)]*t = 2^[{l}-({index}+1)]*t = {tmp}");
}
tmp = self.reduce(tmp);
if self.verbose {
println!("{index}.\t2^[l-(i+1)]*t = 2^[{l}-({index}+1)]*t = {tmp} (mod {})", self.base);
}
// multiplication with overflow vvvvvvvvvvvvvv
tmp = modexp::modular_exponentiation_wrapper(a, tmp, self.base, false);
if self.verbose {
println!("{index}.\ta^(2^[l-(i+1)]*t) = {a}^(2^[{l}-({index}+1)]*t) = {tmp}");
}
tmp *= modexp::modular_exponentiation_wrapper(b, n[index as usize], self.base, false);
tmp = self.reduce(tmp);
if self.verbose {
println!("{index}.\ta^(2^[l-(i+1)]*t) * b^(n_{index}) = {a}^(2^[{l}-({index}+1)]*{t}) * {b}^({}) = {tmp} (mod {})",
n[index as usize],
self.base
);
}
c.push(tmp);
if self.verbose { if self.verbose {
println!("{index}.\tc_{index} = {}", c[index as usize]); println!("{index}.\tc_{index} = {}", c[index as usize]);
println!("Calculating n_{}", index + 1);
}
if c[index as usize] == 1 {
if self.verbose {
println!("{index}.\tc_{index} = 1 => n_{} = [n_{index}]/[2]", index + 1);
}
n.push(n[index as usize].checked_div(2).expect("could not compute n[i+1]"));
if self.verbose {
println!("{index}.\tn_{} = [n_{index} / 2] = [{}]/[2] = {}",
index + 1,
n[index as usize],
n[index as usize]
);
} }
if self.reduce(c[index as usize]) == 1 {
n[(index + 1) as usize] = n[index as usize].checked_div(2).expect("could not compute n[i+1]");
} }
else { else {
n[(index + 1) as usize] = n[index as usize].checked_div(2).expect("could not compute n[i+1]") if self.verbose {
+ pm1.checked_div(4).expect("could not compute n[i+1]"); println!("{index}.\tc_{index} != 1 => n_{} = [n_{index}]/[2] + [p-1]/[4]", index + 1);
}
let mut tmp: u128 = n[index as usize].checked_div(2).expect("could not compute n[i+1]");
tmp += pm1.checked_div(4).expect("could not compute n[i+1]");
n.push(tmp);
assert_eq!(n.last().unwrap(), &tmp);
if self.verbose {
println!("{index}.\tn_{} = [n_{index} / 2] + [p-1]/[4] = [{}]/[2] + [{pm1}]/[4] = {}",
index + 1,
n[index as usize],
n.last().unwrap()
);
} }
} }
let w1 = a.pow((t + 1).checked_div(2).expect("could not compute w") as u32) * b.pow(n[l as usize] as u32); }
let w1 = self.reduce(w1); let exp = (t+1).checked_div(2).expect("cant divide to int");
let mut w1: u128 = modexp::modular_exponentiation_wrapper(a, exp, self.base, false);
if self.verbose {
seperator();
println!("a^([t+1]/[2]) = {w1}");
}
w1 *= modexp::modular_exponentiation_wrapper(b, n[l as usize], self.base, false);
if self.verbose {
println!("w_1 = [a^(t+1)]/[2] * b^(n_l) = [{a}^([{t}+1])]/[2] * {b}^{} = {}", n[l as usize], w1);
}
w1 = self.reduce(w1);
if self.verbose {
println!("w_1 = [a^(t+1)]/[2] * b^(n_l) = [{a}^([{t}+1])]/[2] * {b}^{} = {} (mod {})",
n[l as usize],
w1,
self.base
);
}
let w2 = self.a_inverse(w1); let w2 = self.a_inverse(w1);
if self.verbose {
println!("w_2 = -w_1 = -{w1} = {w2} (mod {})", self.base);
}
if self.verbose { if self.verbose {
println!("found sqrt of {a} as ({w1}, {w2})"); println!("found sqrt of {a} as ({w1}, {w2})");
} }
@ -223,8 +300,8 @@ impl GalloisFiled {
/////////////////////////////////////////////////////////////////////////////////////////////////// ///////////////////////////////////////////////////////////////////////////////////////////////////
#[test] #[test]
fn test_gallois_sqrt() { fn test_gallois_sqrt() {
let field = GalloisFiled::new(977, false); let field = GalloisFiled::new(977, true);
assert_eq!(field.sqrt(269).expect("function says there is no root but there is"), (313, 474)); assert_eq!(field.sqrt(269).expect("function says there is no root but there is"), (313, 664));
assert_eq!(field.sqrt(524).expect("function says there is no root but there is"), (115, 862)); assert_eq!(field.sqrt(524).expect("function says there is no root but there is"), (115, 862));
assert_eq!(field.sqrt(275).expect("function says there is no root but there is"), (585, 392)); assert_eq!(field.sqrt(275).expect("function says there is no root but there is"), (585, 392));
} }

3
src/math/modexp.rs
View File

@ -32,6 +32,9 @@ pub fn modular_exponentiation(
if verbose { if verbose {
println!("args:\nbase {base}\nexp {exp}\nfield {field}\nverbose {verbose}"); println!("args:\nbase {base}\nexp {exp}\nfield {field}\nverbose {verbose}");
} }
if exp == BigInt::from(0) {
return BigInt::from(1);
}
let mut instructions: Vec<bool> = bigint_to_bools(exp.clone()); let mut instructions: Vec<bool> = bigint_to_bools(exp.clone());
// remove the signing bit // remove the signing bit