wip on primtive root with Hensel lifting

Cargo.lock

@@ -8,6 +8,50 @@ version = "1.4.0"
 source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "ace50bade8e6234aa140d9a2f552bbee1db4d353f69b8217bc503490fc1a9f26"
 
+[[package]]
+name = "byteorder"
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+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "1fd0f2584146f6f2ef48085050886acf353beff7305ebd1ae69500e27c67f64b"
+
+[[package]]
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+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "baf1de4339761588bc0619e3cbc0120ee582ebb74b53b4efbf79117bd2da40fd"
+
+[[package]]
+name = "either"
+version = "1.13.0"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "60b1af1c220855b6ceac025d3f6ecdd2b7c4894bfe9cd9bda4fbb4bc7c0d4cf0"
+
+[[package]]
+name = "getrandom"
+version = "0.2.15"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "c4567c8db10ae91089c99af84c68c38da3ec2f087c3f82960bcdbf3656b6f4d7"
+dependencies = [
+ "cfg-if",
+ "libc",
+ "wasi",
+]
+
+[[package]]
+name = "itertools"
+version = "0.10.5"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "b0fd2260e829bddf4cb6ea802289de2f86d6a7a690192fbe91b3f46e0f2c8473"
+dependencies = [
+ "either",
+]
+
+[[package]]
+name = "libc"
+version = "0.2.167"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "09d6582e104315a817dff97f75133544b2e094ee22447d2acf4a74e189ba06fc"
+
 [[package]]
 name = "math"
 version = "0.1.0"
@@ -15,6 +59,21 @@ dependencies = [
  "num-bigint",
  "num-traits",
  "primality-test",
+ "prime_factorization",
+]
+
+[[package]]
+name = "num"
+version = "0.4.3"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "35bd024e8b2ff75562e5f34e7f4905839deb4b22955ef5e73d2fea1b9813cb23"
+dependencies = [
+ "num-bigint",
+ "num-complex",
+ "num-integer",
+ "num-iter",
+ "num-rational",
+ "num-traits",
 ]
 
 [[package]]
@@ -27,6 +86,15 @@ dependencies = [
  "num-traits",
 ]
 
+[[package]]
+name = "num-complex"
+version = "0.4.6"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "73f88a1307638156682bada9d7604135552957b7818057dcef22705b4d509495"
+dependencies = [
+ "num-traits",
+]
+
 [[package]]
 name = "num-integer"
 version = "0.1.46"
@@ -36,6 +104,28 @@ dependencies = [
  "num-traits",
 ]
 
+[[package]]
+name = "num-iter"
+version = "0.1.45"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "1429034a0490724d0075ebb2bc9e875d6503c3cf69e235a8941aa757d83ef5bf"
+dependencies = [
+ "autocfg",
+ "num-integer",
+ "num-traits",
+]
+
+[[package]]
+name = "num-rational"
+version = "0.4.2"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "f83d14da390562dca69fc84082e73e548e1ad308d24accdedd2720017cb37824"
+dependencies = [
+ "num-bigint",
+ "num-integer",
+ "num-traits",
+]
+
 [[package]]
 name = "num-traits"
 version = "0.2.19"
@@ -45,8 +135,120 @@ dependencies = [
  "autocfg",
 ]
 
+[[package]]
+name = "ppv-lite86"
+version = "0.2.20"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "77957b295656769bb8ad2b6a6b09d897d94f05c41b069aede1fcdaa675eaea04"
+dependencies = [
+ "zerocopy",
+]
+
 [[package]]
 name = "primality-test"
 version = "0.3.0"
 source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "98439e9658b9548a33abdab8c82532554dc08e49ddc5398a9262222fb360ae24"
+
+[[package]]
+name = "prime_factorization"
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+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "61b43cd4d5e49fa3c769f72033129f07eeaa102c3db2aa11be0c7f1a0cb50f0c"
+dependencies = [
+ "itertools",
+ "num",
+ "rand",
+]
+
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+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "37d3544b3f2748c54e147655edb5025752e2303145b5aefb3c3ea2c78b973bb0"
+dependencies = [
+ "unicode-ident",
+]
+
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+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "b5b9d34b8991d19d98081b46eacdd8eb58c6f2b201139f7c5f643cc155a633af"
+dependencies = [
+ "proc-macro2",
+]
+
+[[package]]
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+version = "0.8.5"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "34af8d1a0e25924bc5b7c43c079c942339d8f0a8b57c39049bef581b46327404"
+dependencies = [
+ "libc",
+ "rand_chacha",
+ "rand_core",
+]
+
+[[package]]
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+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "e6c10a63a0fa32252be49d21e7709d4d4baf8d231c2dbce1eaa8141b9b127d88"
+dependencies = [
+ "ppv-lite86",
+ "rand_core",
+]
+
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+name = "rand_core"
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+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "ec0be4795e2f6a28069bec0b5ff3e2ac9bafc99e6a9a7dc3547996c5c816922c"
+dependencies = [
+ "getrandom",
+]
+
+[[package]]
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+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "919d3b74a5dd0ccd15aeb8f93e7006bd9e14c295087c9896a110f490752bcf31"
+dependencies = [
+ "proc-macro2",
+ "quote",
+ "unicode-ident",
+]
+
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+source = "registry+https://github.com/rust-lang/crates.io-index"
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+
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+version = "0.11.0+wasi-snapshot-preview1"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "9c8d87e72b64a3b4db28d11ce29237c246188f4f51057d65a7eab63b7987e423"
+
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+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "1b9b4fd18abc82b8136838da5d50bae7bdea537c574d8dc1a34ed098d6c166f0"
+dependencies = [
+ "byteorder",
+ "zerocopy-derive",
+]
+
+[[package]]
+name = "zerocopy-derive"
+version = "0.7.35"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "fa4f8080344d4671fb4e831a13ad1e68092748387dfc4f55e356242fae12ce3e"
+dependencies = [
+ "proc-macro2",
+ "quote",
+ "syn",
+]

Cargo.toml

@@ -6,4 +6,5 @@ edition = "2021"
 [dependencies]
 primality-test = "0.3.0"
 num-bigint = "0.4.6"
-num-traits = "0.2.19"
+num-traits = "0.2.19"
+prime_factorization = "1.0.4"

src/dft.rs

@@ -0,0 +1 @@
+pub(crate) mod primitive_root;

src/modulus/prime.rs

@@ -1,12 +1,24 @@
 use primality_test::is_prime;
+use prime_factorization::Factorization;
 
-pub struct Prime {
+pub struct Prime<O> {
-	q: u64,
+	q: O, /// q_base^q_powers
+    q_base: O,
+    q_powers: O,
+    factors: Vec<O>, /// distinct factors of q-1
+    nth_root: O,
 }
 
-impl Prime {
+impl Prime<u64>{
-	pub fn new(q: u64) -> Self{
+    pub fn new(q_base: u64, q_power: u64) -> Self{
 		assert!(is_prime(q) && q > 2);
+        assert!()
+
+        q_exp
+        for i in 0..q_power{
+
+        }
+
         Self::new_unchecked(q)
 	}
 
@@ -16,4 +28,51 @@ impl Prime {
             q,
         }
     }
+
+    /// Returns returns Phi(BaseModulus^BaseModulusPower)
+    pub fn phi() -> u64 {
+
+    }
+
+    /// Returns the smallest primitive root. The unique factors
+    /// can be given as argument to avoid factorization of q-1.
+    pub fn primitive_root(&self) -> u64{
+        if self.factors.len() != 0{
+            self.check_factors();
+        }else{
+            let factors = Factorization::run(q).prime_factor_repr();
+            let mut distincts_factors: Vec<u64> = Vec::with_capacity(factors.len());
+            for factor in factors.iter(){
+                distincts_factors.push(factor.0)
+            }
+            self.factors = distincts_factors
+        }
+
+        let log_nth_root = 64 - self.q.leading_zeros() as usize;
+
+        0
+    }
+
+    pub fn check_factors(&self){
+
+        if self.factors.len() == 0{
+            panic!("invalid factor list: empty")
+        }
+
+        let mut q = self.q;
+
+        for &factor in &self.factors{
+            if !is_prime(factor){
+                panic!("invalid factor list: factor {} is not prime", factor)
+            }
+
+            while q%factor != 0{
+                q /= factor
+            }
+        }
+
+        if q != 1{
+            panic!("invalid factor list: does not fully divide q: q % (alll factors) = {}", q)
+        }
+    }
 }