diff --git a/Cargo.lock b/Cargo.lock
index 835918c..65d3027 100644
--- a/Cargo.lock
+++ b/Cargo.lock
@@ -3,24 +3,10 @@
 version = 4
 
 [[package]]
-name = "anyhow"
-version = "1.0.102"
+name = "allocator-api2"
+version = "0.2.21"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "7f202df86484c868dbad7eaa557ef785d5c66295e41b460ef922eca0723b842c"
-
-[[package]]
-name = "auto-impl-ops"
-version = "0.2.1"
-source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "d207fb0594e71ec5aade80886716c6f1adc6c9b570a7feef6e173f35f4f4d4cc"
-dependencies = [
- "derive-syn-parse",
- "proc-macro2",
- "quote",
- "strum",
- "syn 1.0.109",
- "take_mut",
-]
+checksum = "683d7910e743518b0e34f1186f92494becacb047c7b6bf616c96772180fef923"
 
 [[package]]
 name = "autocfg"
@@ -29,10 +15,16 @@ source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "c08606f8c3cbf4ce6ec8e28fb0014a2c086708fe954eaa885384a6165172e7e8"
 
 [[package]]
-name = "bitflags"
-version = "2.11.1"
+name = "bitvec"
+version = "1.0.1"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "c4512299f36f043ab09a583e57bceb5a5aab7a73db1805848e8fef3c9e8c78b3"
+checksum = "1bc2832c24239b0141d5674bb9174f9d68a8b5b3f2753311927c172ca46f7e9c"
+dependencies = [
+ "funty",
+ "radium",
+ "tap",
+ "wyz",
+]
 
 [[package]]
 name = "cfg-if"
@@ -40,47 +32,23 @@ version = "1.0.4"
 source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "9330f8b2ff13f34540b44e946ef35111825727b38d33286ef986142615121801"
 
-[[package]]
-name = "chacha20"
-version = "0.10.0"
-source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "6f8d983286843e49675a4b7a2d174efe136dc93a18d69130dd18198a6c167601"
-dependencies = [
- "cfg-if",
- "cpufeatures",
- "rand_core",
-]
-
-[[package]]
-name = "cpufeatures"
-version = "0.3.0"
-source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "8b2a41393f66f16b0823bb79094d54ac5fbd34ab292ddafb9a0456ac9f87d201"
-dependencies = [
- "libc",
-]
-
-[[package]]
-name = "derive-syn-parse"
-version = "0.1.5"
-source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "e79116f119dd1dba1abf1f3405f03b9b0e79a27a3883864bfebded8a3dc768cd"
-dependencies = [
- "proc-macro2",
- "quote",
- "syn 1.0.109",
-]
-
 [[package]]
 name = "diffie-hellman"
 version = "0.1.0"
 dependencies = [
- "ntt",
- "primes",
+ "num-bigint",
+ "num-prime",
+ "num-traits",
  "rand",
  "rpassword",
 ]
 
+[[package]]
+name = "either"
+version = "1.15.0"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "48c757948c5ede0e46177b7add2e67155f70e33c07fea8284df6576da70b3719"
+
 [[package]]
 name = "equivalent"
 version = "1.0.2"
@@ -89,81 +57,38 @@ checksum = "877a4ace8713b0bcf2a4e7eec82529c029f1d0619886d18145fea96c3ffe5c0f"
 
 [[package]]
 name = "foldhash"
-version = "0.1.5"
+version = "0.2.0"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "d9c4f5dac5e15c24eb999c26181a6ca40b39fe946cbe4c263c7209467bc83af2"
+checksum = "77ce24cb58228fbb8aa041425bb1050850ac19177686ea6e0f41a70416f56fdb"
+
+[[package]]
+name = "funty"
+version = "2.0.0"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "e6d5a32815ae3f33302d95fdcb2ce17862f8c65363dcfd29360480ba1001fc9c"
 
 [[package]]
 name = "getrandom"
-version = "0.4.2"
+version = "0.2.17"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "0de51e6874e94e7bf76d726fc5d13ba782deca734ff60d5bb2fb2607c7406555"
+checksum = "ff2abc00be7fca6ebc474524697ae276ad847ad0a6b3faa4bcb027e9a4614ad0"
 dependencies = [
  "cfg-if",
  "libc",
- "r-efi",
- "rand_core",
- "wasip2",
- "wasip3",
+ "wasi",
 ]
 
 [[package]]
 name = "hashbrown"
-version = "0.15.5"
+version = "0.16.1"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "9229cfe53dfd69f0609a49f65461bd93001ea1ef889cd5529dd176593f5338a1"
+checksum = "841d1cc9bed7f9236f321df977030373f4a4163ae1a7dbfe1a51a2c1a51d9100"
 dependencies = [
+ "allocator-api2",
+ "equivalent",
  "foldhash",
 ]
 
-[[package]]
-name = "hashbrown"
-version = "0.17.0"
-source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "4f467dd6dccf739c208452f8014c75c18bb8301b050ad1cfb27153803edb0f51"
-
-[[package]]
-name = "heck"
-version = "0.4.1"
-source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "95505c38b4572b2d910cecb0281560f54b440a19336cbbcb27bf6ce6adc6f5a8"
-
-[[package]]
-name = "heck"
-version = "0.5.0"
-source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "2304e00983f87ffb38b55b444b5e3b60a884b5d30c0fca7d82fe33449bbe55ea"
-
-[[package]]
-name = "id-arena"
-version = "2.3.0"
-source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "3d3067d79b975e8844ca9eb072e16b31c3c1c36928edf9c6789548c524d0d954"
-
-[[package]]
-name = "indexmap"
-version = "2.14.0"
-source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "d466e9454f08e4a911e14806c24e16fba1b4c121d1ea474396f396069cf949d9"
-dependencies = [
- "equivalent",
- "hashbrown 0.17.0",
- "serde",
- "serde_core",
-]
-
-[[package]]
-name = "itoa"
-version = "1.0.18"
-source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "8f42a60cbdf9a97f5d2305f08a87dc4e09308d1276d28c869c684d7777685682"
-
-[[package]]
-name = "leb128fmt"
-version = "0.1.0"
-source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "09edd9e8b54e49e587e4f6295a7d29c3ea94d469cb40ab8ca70b288248a81db2"
-
 [[package]]
 name = "libc"
 version = "0.2.185"
@@ -171,25 +96,59 @@ source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "52ff2c0fe9bc6cb6b14a0592c2ff4fa9ceb83eea9db979b0487cd054946a2b8f"
 
 [[package]]
-name = "log"
-version = "0.4.29"
+name = "lru"
+version = "0.16.4"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "5e5032e24019045c762d3c0f28f5b6b8bbf38563a65908389bf7978758920897"
-
-[[package]]
-name = "memchr"
-version = "2.8.0"
-source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "f8ca58f447f06ed17d5fc4043ce1b10dd205e060fb3ce5b979b8ed8e59ff3f79"
-
-[[package]]
-name = "ntt"
-version = "0.1.9"
-source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "dbc39fc0bc1ecd3086423a4b50b5b3cb1c13a2ef01d2c1437754f90e6f354850"
+checksum = "7f66e8d5d03f609abc3a39e6f08e4164ebf1447a732906d39eb9b99b7919ef39"
 dependencies = [
- "polynomial-ring",
- "reikna",
+ "hashbrown",
+]
+
+[[package]]
+name = "num-bigint"
+version = "0.4.6"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "a5e44f723f1133c9deac646763579fdb3ac745e418f2a7af9cd0c431da1f20b9"
+dependencies = [
+ "num-integer",
+ "num-traits",
+ "rand",
+]
+
+[[package]]
+name = "num-integer"
+version = "0.1.46"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "7969661fd2958a5cb096e56c8e1ad0444ac2bbcd0061bd28660485a44879858f"
+dependencies = [
+ "num-traits",
+]
+
+[[package]]
+name = "num-modular"
+version = "0.6.1"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "17bb261bf36fa7d83f4c294f834e91256769097b3cb505d44831e0a179ac647f"
+dependencies = [
+ "num-bigint",
+ "num-integer",
+ "num-traits",
+]
+
+[[package]]
+name = "num-prime"
+version = "0.5.0"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "b285c575532a33ef6fdd3a57640d0b1c70e6ca48644d6df7bbd4b7a0cfbbb12d"
+dependencies = [
+ "bitvec",
+ "either",
+ "lru",
+ "num-bigint",
+ "num-integer",
+ "num-modular",
+ "num-traits",
+ "rand",
 ]
 
 [[package]]
@@ -202,32 +161,14 @@ dependencies = [
 ]
 
 [[package]]
-name = "polynomial-ring"
-version = "0.5.1"
+name = "ppv-lite86"
+version = "0.2.21"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "eff6265f2682d57d24b9a114996358dcc228d54239b64c7df0a0e2174f71d84c"
+checksum = "85eae3c4ed2f50dcfe72643da4befc30deadb458a9b590d720cde2f2b1e97da9"
 dependencies = [
- "auto-impl-ops",
- "num-traits",
- "ring-algorithm",
+ "zerocopy",
 ]
 
-[[package]]
-name = "prettyplease"
-version = "0.2.37"
-source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "479ca8adacdd7ce8f1fb39ce9ecccbfe93a3f1344b3d0d97f20bc0196208f62b"
-dependencies = [
- "proc-macro2",
- "syn 2.0.117",
-]
-
-[[package]]
-name = "primes"
-version = "0.4.0"
-source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "0466ef49edd4a5a4bc9d62804a34e89366810bd8bfc3ed537101e3d099f245c5"
-
 [[package]]
 name = "proc-macro2"
 version = "1.0.106"
@@ -247,41 +188,39 @@ dependencies = [
 ]
 
 [[package]]
-name = "r-efi"
-version = "6.0.0"
+name = "radium"
+version = "0.7.0"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "f8dcc9c7d52a811697d2151c701e0d08956f92b0e24136cf4cf27b57a6a0d9bf"
+checksum = "dc33ff2d4973d518d823d61aa239014831e521c75da58e3df4840d3f47749d09"
 
 [[package]]
 name = "rand"
-version = "0.10.1"
+version = "0.8.6"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "d2e8e8bcc7961af1fdac401278c6a831614941f6164ee3bf4ce61b7edb162207"
+checksum = "5ca0ecfa931c29007047d1bc58e623ab12e5590e8c7cc53200d5202b69266d8a"
 dependencies = [
- "chacha20",
- "getrandom",
+ "libc",
+ "rand_chacha",
+ "rand_core",
+]
+
+[[package]]
+name = "rand_chacha"
+version = "0.3.1"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "e6c10a63a0fa32252be49d21e7709d4d4baf8d231c2dbce1eaa8141b9b127d88"
+dependencies = [
+ "ppv-lite86",
  "rand_core",
 ]
 
 [[package]]
 name = "rand_core"
-version = "0.10.1"
+version = "0.6.4"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "63b8176103e19a2643978565ca18b50549f6101881c443590420e4dc998a3c69"
-
-[[package]]
-name = "reikna"
-version = "0.12.3"
-source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "587f2b12c725829d56d8192817535cbfe3c4b5daf294622765cec5969d980eca"
-
-[[package]]
-name = "ring-algorithm"
-version = "0.8.0"
-source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "1e7a0ad57623ce306fe34b975618445cbcf998e60ab576cc11497f51a6c97f97"
+checksum = "ec0be4795e2f6a28069bec0b5ff3e2ac9bafc99e6a9a7dc3547996c5c816922c"
 dependencies = [
- "num-traits",
+ "getrandom",
 ]
 
 [[package]]
@@ -305,93 +244,6 @@ dependencies = [
  "windows-sys",
 ]
 
-[[package]]
-name = "rustversion"
-version = "1.0.22"
-source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "b39cdef0fa800fc44525c84ccb54a029961a8215f9619753635a9c0d2538d46d"
-
-[[package]]
-name = "semver"
-version = "1.0.28"
-source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "8a7852d02fc848982e0c167ef163aaff9cd91dc640ba85e263cb1ce46fae51cd"
-
-[[package]]
-name = "serde"
-version = "1.0.228"
-source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "9a8e94ea7f378bd32cbbd37198a4a91436180c5bb472411e48b5ec2e2124ae9e"
-dependencies = [
- "serde_core",
-]
-
-[[package]]
-name = "serde_core"
-version = "1.0.228"
-source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "41d385c7d4ca58e59fc732af25c3983b67ac852c1a25000afe1175de458b67ad"
-dependencies = [
- "serde_derive",
-]
-
-[[package]]
-name = "serde_derive"
-version = "1.0.228"
-source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "d540f220d3187173da220f885ab66608367b6574e925011a9353e4badda91d79"
-dependencies = [
- "proc-macro2",
- "quote",
- "syn 2.0.117",
-]
-
-[[package]]
-name = "serde_json"
-version = "1.0.149"
-source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "83fc039473c5595ace860d8c4fafa220ff474b3fc6bfdb4293327f1a37e94d86"
-dependencies = [
- "itoa",
- "memchr",
- "serde",
- "serde_core",
- "zmij",
-]
-
-[[package]]
-name = "strum"
-version = "0.24.1"
-source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "063e6045c0e62079840579a7e47a355ae92f60eb74daaf156fb1e84ba164e63f"
-dependencies = [
- "strum_macros",
-]
-
-[[package]]
-name = "strum_macros"
-version = "0.24.3"
-source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "1e385be0d24f186b4ce2f9982191e7101bb737312ad61c1f2f984f34bcf85d59"
-dependencies = [
- "heck 0.4.1",
- "proc-macro2",
- "quote",
- "rustversion",
- "syn 1.0.109",
-]
-
-[[package]]
-name = "syn"
-version = "1.0.109"
-source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "72b64191b275b66ffe2469e8af2c1cfe3bafa67b529ead792a6d0160888b4237"
-dependencies = [
- "proc-macro2",
- "quote",
- "unicode-ident",
-]
-
 [[package]]
 name = "syn"
 version = "2.0.117"
@@ -404,10 +256,10 @@ dependencies = [
 ]
 
 [[package]]
-name = "take_mut"
-version = "0.2.2"
+name = "tap"
+version = "1.0.1"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "f764005d11ee5f36500a149ace24e00e3da98b0158b3e2d53a7495660d3f4d60"
+checksum = "55937e1799185b12863d447f42597ed69d9928686b8d88a1df17376a097d8369"
 
 [[package]]
 name = "unicode-ident"
@@ -416,62 +268,10 @@ source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "e6e4313cd5fcd3dad5cafa179702e2b244f760991f45397d14d4ebf38247da75"
 
 [[package]]
-name = "unicode-xid"
-version = "0.2.6"
+name = "wasi"
+version = "0.11.1+wasi-snapshot-preview1"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "ebc1c04c71510c7f702b52b7c350734c9ff1295c464a03335b00bb84fc54f853"
-
-[[package]]
-name = "wasip2"
-version = "1.0.3+wasi-0.2.9"
-source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "20064672db26d7cdc89c7798c48a0fdfac8213434a1186e5ef29fd560ae223d6"
-dependencies = [
- "wit-bindgen 0.57.1",
-]
-
-[[package]]
-name = "wasip3"
-version = "0.4.0+wasi-0.3.0-rc-2026-01-06"
-source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "5428f8bf88ea5ddc08faddef2ac4a67e390b88186c703ce6dbd955e1c145aca5"
-dependencies = [
- "wit-bindgen 0.51.0",
-]
-
-[[package]]
-name = "wasm-encoder"
-version = "0.244.0"
-source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "990065f2fe63003fe337b932cfb5e3b80e0b4d0f5ff650e6985b1048f62c8319"
-dependencies = [
- "leb128fmt",
- "wasmparser",
-]
-
-[[package]]
-name = "wasm-metadata"
-version = "0.244.0"
-source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "bb0e353e6a2fbdc176932bbaab493762eb1255a7900fe0fea1a2f96c296cc909"
-dependencies = [
- "anyhow",
- "indexmap",
- "wasm-encoder",
- "wasmparser",
-]
-
-[[package]]
-name = "wasmparser"
-version = "0.244.0"
-source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "47b807c72e1bac69382b3a6fb3dbe8ea4c0ed87ff5629b8685ae6b9a611028fe"
-dependencies = [
- "bitflags",
- "hashbrown 0.15.5",
- "indexmap",
- "semver",
-]
+checksum = "ccf3ec651a847eb01de73ccad15eb7d99f80485de043efb2f370cd654f4ea44b"
 
 [[package]]
 name = "windows-sys"
@@ -547,101 +347,30 @@ source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "589f6da84c646204747d1270a2a5661ea66ed1cced2631d546fdfb155959f9ec"
 
 [[package]]
-name = "wit-bindgen"
-version = "0.51.0"
+name = "wyz"
+version = "0.5.1"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "d7249219f66ced02969388cf2bb044a09756a083d0fab1e566056b04d9fbcaa5"
+checksum = "05f360fc0b24296329c78fda852a1e9ae82de9cf7b27dae4b7f62f118f77b9ed"
 dependencies = [
- "wit-bindgen-rust-macro",
+ "tap",
 ]
 
 [[package]]
-name = "wit-bindgen"
-version = "0.57.1"
+name = "zerocopy"
+version = "0.8.48"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "1ebf944e87a7c253233ad6766e082e3cd714b5d03812acc24c318f549614536e"
-
-[[package]]
-name = "wit-bindgen-core"
-version = "0.51.0"
-source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "ea61de684c3ea68cb082b7a88508a8b27fcc8b797d738bfc99a82facf1d752dc"
+checksum = "eed437bf9d6692032087e337407a86f04cd8d6a16a37199ed57949d415bd68e9"
 dependencies = [
- "anyhow",
- "heck 0.5.0",
- "wit-parser",
+ "zerocopy-derive",
 ]
 
 [[package]]
-name = "wit-bindgen-rust"
-version = "0.51.0"
+name = "zerocopy-derive"
+version = "0.8.48"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "b7c566e0f4b284dd6561c786d9cb0142da491f46a9fbed79ea69cdad5db17f21"
+checksum = "70e3cd084b1788766f53af483dd21f93881ff30d7320490ec3ef7526d203bad4"
 dependencies = [
- "anyhow",
- "heck 0.5.0",
- "indexmap",
- "prettyplease",
- "syn 2.0.117",
- "wasm-metadata",
- "wit-bindgen-core",
- "wit-component",
-]
-
-[[package]]
-name = "wit-bindgen-rust-macro"
-version = "0.51.0"
-source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "0c0f9bfd77e6a48eccf51359e3ae77140a7f50b1e2ebfe62422d8afdaffab17a"
-dependencies = [
- "anyhow",
- "prettyplease",
  "proc-macro2",
  "quote",
- "syn 2.0.117",
- "wit-bindgen-core",
- "wit-bindgen-rust",
+ "syn",
 ]
-
-[[package]]
-name = "wit-component"
-version = "0.244.0"
-source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "9d66ea20e9553b30172b5e831994e35fbde2d165325bec84fc43dbf6f4eb9cb2"
-dependencies = [
- "anyhow",
- "bitflags",
- "indexmap",
- "log",
- "serde",
- "serde_derive",
- "serde_json",
- "wasm-encoder",
- "wasm-metadata",
- "wasmparser",
- "wit-parser",
-]
-
-[[package]]
-name = "wit-parser"
-version = "0.244.0"
-source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "ecc8ac4bc1dc3381b7f59c34f00b67e18f910c2c0f50015669dde7def656a736"
-dependencies = [
- "anyhow",
- "id-arena",
- "indexmap",
- "log",
- "semver",
- "serde",
- "serde_derive",
- "serde_json",
- "unicode-xid",
- "wasmparser",
-]
-
-[[package]]
-name = "zmij"
-version = "1.0.21"
-source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "b8848ee67ecc8aedbaf3e4122217aff892639231befc6a1b58d29fff4c2cabaa"
diff --git a/Cargo.toml b/Cargo.toml
index 3951efc..a08062e 100644
--- a/Cargo.toml
+++ b/Cargo.toml
@@ -6,7 +6,8 @@ description = "toy implementation of diffie-hellman key exchange"
 homepage = "https://g.pyrope.net/diffie-hellman"
 
 [dependencies]
-ntt = "0.1.9"
-primes = "0.4.0"
-rand = "0.10.1"
+num-bigint = { version = "0.4.6", features = ["rand"] }
+num-prime = "0.5.0"
+num-traits = "0.2.19"
+rand = "0.8"
 rpassword = "7.4.0"
diff --git a/README.md b/README.md
index b7c7939..5759d12 100644
--- a/README.md
+++ b/README.md
@@ -1,5 +1,5 @@
 # toy Diffie-Hellman key exchange
-Only works for ~most 32 bit unsigned-integers.
+Uses 256-bit Sophie-Germain primes for stuff
 
 ```
 nix run git+https://git.pyrope.net/mbk/diffie-hellman
@@ -7,9 +7,5 @@ nix run git+https://git.pyrope.net/mbk/diffie-hellman
 
 Run with
 - 0 arguments to generate a public `p` and `g`
-- 2 arguments (`p` and `g`) to generate the public `g^a mod p`
-- 3 arguments (`p`, `g`, and `g^b mod p`) to generate the final shared secret
-
-`a` is provided with a passwordlike input.
-You have to make your own `a`, sorry
+- 2 arguments (`p` and `g`) to start with a given `p` and `g`
 
diff --git a/src/main.rs b/src/main.rs
index 8632989..b2b80b2 100644
--- a/src/main.rs
+++ b/src/main.rs
@@ -1,46 +1,71 @@
-use std::{env, thread, time::Duration};
+use std::env;
 
-use ntt::{mod_exp, primitive_root};
-use primes::is_prime;
-use rand::{CryptoRng, RngExt};
+use num_bigint::BigUint;
+use num_prime::{
+    RandPrime,
+    nt_funcs::{factors, is_prime},
+};
+use num_traits::One;
 
 fn main() {
-    if let Some(Ok(p)) = env::args().nth(1).map(|s| s.parse::<u32>())
-        && let Some(Ok(g)) = env::args().nth(2).map(|s| s.parse::<u32>())
+    let mut rng = rand::thread_rng();
+
+    let (p, g) = if let Some(Ok(p)) = env::args().nth(1).map(|s| s.parse::<BigUint>())
+        && let Some(Ok(g)) = env::args().nth(2).map(|s| s.parse::<BigUint>())
     {
-        let a = rpassword::prompt_password("a = ").unwrap();
-        let a = a.parse::<u32>().unwrap();
-
-        if let Some(Ok(gb)) = env::args().nth(3).map(|s| s.parse::<u32>()) {
-            let s = mod_exp(i64::from(gb), i64::from(a), i64::from(p));
-
-            println!("SECRET IN FIVE SECONDS");
-            thread::sleep(Duration::from_secs(5));
-            println!("s = {s}");
-        } else {
-            println!(
-                "gª mod p = {}",
-                mod_exp(i64::from(g), i64::from(a), i64::from(p))
-            );
-        }
+        (p, g)
     } else {
-        let rng = rand::rng();
+        gen_pub(&mut rng)
+    };
 
-        let (p, g) = gen_pub(rng);
+    println!("p = {p}, g = {g}");
 
-        println!("p = {p}, g = {g}");
-    }
+    let a: BigUint = rng.gen_safe_prime(256);
+    println!("a = {a}");
+
+    let ga = g.modpow(&a, &p);
+    println!("g^a mod p = {ga}");
+
+    let gb: BigUint = rpassword::prompt_password("g^b mod p = ")
+        .unwrap()
+        .parse()
+        .unwrap();
+
+    let s = gb.modpow(&a, &p);
+    println!("s = {s}");
 }
 
-fn gen_pub(mut rng: impl CryptoRng + RngExt) -> (u32, u32) {
+fn gen_pub(mut rng: impl RandPrime<BigUint>) -> (BigUint, BigUint) {
     loop {
-        let p: u32 = rng.random();
-        if !is_prime(u64::from(p)) {
+        let p = rng.gen_safe_prime(256);
+
+        if !is_prime(&p, None).probably() {
             continue;
         }
 
-        if let Ok(g) = primitive_root(i64::from(p), 1).try_into() {
+        if let Some(g) = primitive_root(&p) {
             return (p, g);
         }
     }
 }
+
+fn primitive_root(p: &BigUint) -> Option<BigUint> {
+    let one = BigUint::one();
+    let phi = p - &one;
+    let (factors, None) = factors(phi.clone(), None) else {
+        return None;
+    };
+
+    let mut g = BigUint::from(2u8);
+    while &g < p {
+        let is_primitive = factors.keys().all(|q| {
+            let exp = &phi / q;
+            g.modpow(&exp, p) != one
+        });
+        if is_primitive {
+            return Some(g);
+        }
+        g += &one;
+    }
+    None
+}