Add 'spake2/' from commit 'f6e9d07dffa9a9b39f203c23043f93337ebe1ab6'

git-subtree-dir: spake2
git-subtree-mainline: 1afa40d15b0c2cecc989bdfc67a5251aa5cd5954
git-subtree-split: f6e9d07dffa9a9b39f203c23043f93337ebe1ab6

This moves https://github.com/warner/spake2.rs into the "spake2/"
subdirectory of https://github.com/RustCrypto/PAKEs .

I'll move the release tags over next, then update the travis config and
READMEs.

8 files changed, 1044 insertions, 0 deletions

diff --git a/spake2/.gitignore b/spake2/.gitignore
new file mode 100644
index 0000000..8006158
--- /dev/null
+++ b/spake2/.gitignore
@@ -0,0 +1,11 @@
+# Generated by Cargo
+# will have compiled files and executables
+/target/
+
+# Remove Cargo.lock from gitignore if creating an executable, leave it for libraries
+# More information here http://doc.crates.io/guide.html#cargotoml-vs-cargolock
+Cargo.lock
+
+# These are backup files generated by rustfmt
+**/*.rs.bk
+/cobertura.xml
diff --git a/spake2/.travis.yml b/spake2/.travis.yml
new file mode 100644
index 0000000..3998753
--- /dev/null
+++ b/spake2/.travis.yml
@@ -0,0 +1,40 @@
+language: rust
+
+rust:
+  - stable
+  - beta
+  - nightly
+
+os:
+  - linux
+  - osx
+
+branches:
+  except:
+    - /^WIP-.*$/
+
+matrix:
+  include:
+    - rust: 1.26.0 # lock down for consistent rustfmt behavior
+      env: RUSTFMT
+      install:
+        - rustup component add rustfmt-preview
+      script:
+        - cargo fmt -- --write-mode=diff
+  allow_failures:
+    - rust: nightly
+
+script:
+  - cargo clean
+  - cargo build --verbose --all
+#  - cargo run --verbose --example XYZ
+#  - cargo test --verbose --features "test" --all
+  - cargo test --verbose --all
+
+after_success: |
+  if [[ "$TRAVIS_RUST_VERSION" == stable ]]; then
+    bash <(curl https://raw.githubusercontent.com/xd009642/tarpaulin/master/travis-install.sh)
+    # Uncomment the following two lines create and upload a report for codecov.io
+    cargo tarpaulin --out Xml
+    bash <(curl -s https://codecov.io/bash)
+  fi
diff --git a/spake2/Cargo.toml b/spake2/Cargo.toml
new file mode 100644
index 0000000..8736f35
--- /dev/null
+++ b/spake2/Cargo.toml
@@ -0,0 +1,33 @@
+[package]
+name = "spake2"
+version = "0.1.1-alpha.0"
+authors = ["Brian Warner <warner@lothar.com>"]
+description = "The SPAKE2 password-authenticated key-exchange algorithm, in Rust."
+documentation = "https://docs.rs/spake2"
+homepage = "https://github.com/warner/spake2.rs"
+repository = "https://github.com/warner/spake2.rs"
+license = "MIT"
+categories = ["cryptography"]
+exclude = [
+    ".gitignore"
+]
+
+[badges]
+travis-ci = { repository = "warner/spake2.rs" }
+is-it-maintained-issue-resolution = { repository = "warner/spake2.rs" }
+is-it-maintained-open-issues = { repository = "warner/spake2.rs" }
+
+[dependencies]
+curve25519-dalek = "0.19"
+rand = "0.5"
+sha2 = "0.7"
+hkdf = "0.6"
+num-bigint = "0.2"
+hex = "0.3"
+
+[dev-dependencies]
+bencher = "0.1"
+
+[[bench]]
+name = "spake2"
+harness = false
diff --git a/spake2/LICENSE b/spake2/LICENSE
new file mode 100644
index 0000000..5953125
--- /dev/null
+++ b/spake2/LICENSE
@@ -0,0 +1,21 @@
+MIT License
+
+Copyright (c) 2017 Brian Warner
+
+Permission is hereby granted, free of charge, to any person obtaining a copy
+of this software and associated documentation files (the "Software"), to deal
+in the Software without restriction, including without limitation the rights
+to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+copies of the Software, and to permit persons to whom the Software is
+furnished to do so, subject to the following conditions:
+
+The above copyright notice and this permission notice shall be included in all
+copies or substantial portions of the Software.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+SOFTWARE.
diff --git a/spake2/README.md b/spake2/README.md
new file mode 100644
index 0000000..0d32749
--- /dev/null
+++ b/spake2/README.md
@@ -0,0 +1,29 @@
+# spake2.rs
+The SPAKE2 password-authenticated key-exchange algorithm, in Rust.
+
+[![Build Status][build-status-image]][build-status-url]
+[![Codecov][codecov-image]][codecov-url]
+[![Is-It-Maintained-Resolution-Time][iim-resolution-image]][iim-resolution-url]
+[![Is-It-Maintained-Open-Issues][iim-open-image]][iim-open-url]
+[![Crates.io][crates-io-image]][crates-io-url]
+[![Docs.rs][docs-image]][docs-url]
+[![License][license-image]][license-url]
+
+This is still pretty early, but seems to do the job. It needs a proper security review before you should consider using it for anything serious.
+
+Note that the API has changed since 0.0.8 . I released 0.0.9 by mistake.
+
+[build-status-image]: https://travis-ci.org/warner/spake2.rs.svg?branch=master
+[build-status-url]: https://travis-ci.org/warner/spake2.rs
+[codecov-image]: https://codecov.io/gh/warner/spake2.rs/branch/master/graph/badge.svg
+[codecov-url]: https://codecov.io/gh/warner/spake2.rs
+[crates-io-image]: https://img.shields.io/crates/v/spake2.svg
+[crates-io-url]: https://crates.io/crates/spake2
+[docs-image]: https://docs.rs/spake2/badge.svg
+[docs-url]: https://docs.rs/spake2
+[license-image]: https://img.shields.io/badge/License-MIT-blue.svg
+[license-url]: LICENSE
+[iim-resolution-image]: http://isitmaintained.com/badge/resolution/warner/spake2.rs.svg
+[iim-resolution-url]: http://isitmaintained.com/project/warner/spake2.rs
+[iim-open-image]: http://isitmaintained.com/badge/open/warner/spake2.rs.svg
+[iim-open-url]: http://isitmaintained.com/project/warner/spake2.rs
diff --git a/spake2/benches/spake2.rs b/spake2/benches/spake2.rs
new file mode 100644
index 0000000..8323342
--- /dev/null
+++ b/spake2/benches/spake2.rs
@@ -0,0 +1,60 @@
+#[macro_use]
+extern crate bencher;
+
+extern crate spake2;
+
+use bencher::Bencher;
+use spake2::{Ed25519Group, Identity, Password, SPAKE2};
+
+fn spake2_start(bench: &mut Bencher) {
+    bench.iter(|| {
+        let (_, _) = SPAKE2::<Ed25519Group>::start_a(
+            &Password::new(b"password"),
+            &Identity::new(b"idA"),
+            &Identity::new(b"idB"),
+        );
+    })
+}
+
+/*
+fn spake2_finish(bench: &mut Bencher) {
+    // this doesn't work, because s1 is consumed by doing finish()
+    let (s1, msg1) = SPAKE2::<Ed25519Group>::start_a(
+        &Password::new(b"password"),
+        &Identity::new(b"idA"),
+        &Identity::new(b"idB"),
+    );
+    let (s2, msg2) = SPAKE2::<Ed25519Group>::start_b(
+        &Password::new(b"password"),
+        &Identity::new(b"idA"),
+        &Identity::new(b"idB"),
+    );
+    let msg2_slice = msg2.as_slice();
+    bench.iter(|| s1.finish(msg2_slice))
+}
+*/
+
+fn spake2_start_and_finish(bench: &mut Bencher) {
+    let (_, msg2) = SPAKE2::<Ed25519Group>::start_b(
+        &Password::new(b"password"),
+        &Identity::new(b"idA"),
+        &Identity::new(b"idB"),
+    );
+    let msg2_slice = msg2.as_slice();
+    bench.iter(|| {
+        let (s1, _) = SPAKE2::<Ed25519Group>::start_a(
+            &Password::new(b"password"),
+            &Identity::new(b"idA"),
+            &Identity::new(b"idB"),
+        );
+        s1.finish(msg2_slice)
+    })
+}
+
+benchmark_group!(
+    benches,
+    spake2_start,
+    //spake2_finish,
+    spake2_start_and_finish
+);
+benchmark_main!(benches);
diff --git a/spake2/src/lib.rs b/spake2/src/lib.rs
new file mode 100644
index 0000000..c2858ba
--- /dev/null
+++ b/spake2/src/lib.rs
@@ -0,0 +1,109 @@
+#![forbid(unsafe_code)]
+#![cfg_attr(test, deny(warnings))]
+
+extern crate curve25519_dalek;
+extern crate hex;
+extern crate hkdf;
+extern crate num_bigint;
+extern crate rand;
+extern crate sha2;
+
+mod spake2;
+pub use spake2::*;
+
+#[cfg(test)]
+mod tests {
+    use spake2::{Ed25519Group, ErrorType, Identity, Password, SPAKE2, SPAKEErr};
+
+    #[test]
+    fn test_basic() {
+        let (s1, msg1) = SPAKE2::<Ed25519Group>::start_a(
+            &Password::new(b"password"),
+            &Identity::new(b"idA"),
+            &Identity::new(b"idB"),
+        );
+        let (s2, msg2) = SPAKE2::<Ed25519Group>::start_b(
+            &Password::new(b"password"),
+            &Identity::new(b"idA"),
+            &Identity::new(b"idB"),
+        );
+        let key1 = s1.finish(msg2.as_slice()).unwrap();
+        let key2 = s2.finish(msg1.as_slice()).unwrap();
+        assert_eq!(key1, key2);
+    }
+
+    #[test]
+    fn test_mismatch() {
+        let (s1, msg1) = SPAKE2::<Ed25519Group>::start_a(
+            &Password::new(b"password"),
+            &Identity::new(b"idA"),
+            &Identity::new(b"idB"),
+        );
+        let (s2, msg2) = SPAKE2::<Ed25519Group>::start_b(
+            &Password::new(b"password2"),
+            &Identity::new(b"idA"),
+            &Identity::new(b"idB"),
+        );
+        let key1 = s1.finish(msg2.as_slice()).unwrap();
+        let key2 = s2.finish(msg1.as_slice()).unwrap();
+        assert_ne!(key1, key2);
+    }
+
+    #[test]
+    fn test_reflected_message() {
+        let (s1, msg1) = SPAKE2::<Ed25519Group>::start_a(
+            &Password::new(b"password"),
+            &Identity::new(b"idA"),
+            &Identity::new(b"idB"),
+        );
+        let r = s1.finish(msg1.as_slice());
+        assert_eq!(
+            r.unwrap_err(),
+            SPAKEErr {
+                kind: ErrorType::BadSide,
+            }
+        );
+    }
+
+    #[test]
+    fn test_bad_length() {
+        let (s1, msg1) = SPAKE2::<Ed25519Group>::start_a(
+            &Password::new(b"password"),
+            &Identity::new(b"idA"),
+            &Identity::new(b"idB"),
+        );
+        let mut msg2 = Vec::<u8>::with_capacity(msg1.len() + 1);
+        msg2.resize(msg1.len() + 1, 0u8);
+        let r = s1.finish(&msg2);
+        assert_eq!(
+            r.unwrap_err(),
+            SPAKEErr {
+                kind: ErrorType::WrongLength,
+            }
+        );
+    }
+
+    #[test]
+    fn test_basic_symmetric() {
+        let (s1, msg1) = SPAKE2::<Ed25519Group>::start_symmetric(
+            &Password::new(b"password"),
+            &Identity::new(b"idS"),
+        );
+        let (s2, msg2) = SPAKE2::<Ed25519Group>::start_symmetric(
+            &Password::new(b"password"),
+            &Identity::new(b"idS"),
+        );
+        let key1 = s1.finish(msg2.as_slice()).unwrap();
+        let key2 = s2.finish(msg1.as_slice()).unwrap();
+        assert_eq!(key1, key2);
+    }
+
+    #[test]
+    fn it_works() {}
+
+    #[test]
+    #[should_panic(expected = "nope")]
+    fn it_panics() {
+        assert!(false, "nope");
+    }
+}
diff --git a/spake2/src/spake2.rs b/spake2/src/spake2.rs
new file mode 100644
index 0000000..a258c4c
--- /dev/null
+++ b/spake2/src/spake2.rs
@@ -0,0 +1,741 @@
+#![allow(dead_code)]
+
+use curve25519_dalek::constants::ED25519_BASEPOINT_POINT;
+use curve25519_dalek::edwards::CompressedEdwardsY;
+use curve25519_dalek::edwards::EdwardsPoint as c2_Element;
+use curve25519_dalek::scalar::Scalar as c2_Scalar;
+use hex;
+use hkdf::Hkdf;
+use num_bigint::BigUint;
+use rand::{CryptoRng, OsRng, Rng};
+use sha2::{Digest, Sha256};
+use std::fmt;
+use std::ops::Deref;
+
+//use hex::ToHex;
+
+/* "newtype pattern": it's a Vec<u8>, but only used for a specific argument
+ * type, to distinguish between ones that are meant as passwords, and ones
+ * that are meant as identity strings */
+
+#[derive(PartialEq, Eq, Clone)]
+pub struct Password(Vec<u8>);
+impl Password {
+    pub fn new(p: &[u8]) -> Password {
+        Password(p.to_vec())
+    }
+}
+impl Deref for Password {
+    type Target = Vec<u8>;
+    fn deref(&self) -> &Vec<u8> {
+        &self.0
+    }
+}
+
+#[derive(PartialEq, Eq, Clone)]
+pub struct Identity(Vec<u8>);
+impl Deref for Identity {
+    type Target = Vec<u8>;
+    fn deref(&self) -> &Vec<u8> {
+        &self.0
+    }
+}
+impl Identity {
+    pub fn new(p: &[u8]) -> Identity {
+        Identity(p.to_vec())
+    }
+}
+
+#[derive(Debug, PartialEq, Eq)]
+pub enum ErrorType {
+    BadSide,
+    WrongLength,
+    CorruptMessage,
+}
+
+#[derive(Debug, PartialEq, Eq)]
+pub struct SPAKEErr {
+    pub kind: ErrorType,
+}
+
+pub trait Group {
+    type Scalar;
+    type Element;
+    //type Element: Add<Output=Self::Element>
+    //    + Mul<Self::Scalar, Output=Self::Element>;
+    // const element_length: usize; // in unstable, or u8
+    //type ElementBytes : Index<usize, Output=u8>+IndexMut<usize>; // later
+    type TranscriptHash;
+    fn const_m() -> Self::Element;
+    fn const_n() -> Self::Element;
+    fn const_s() -> Self::Element;
+    fn hash_to_scalar(s: &[u8]) -> Self::Scalar;
+    fn random_scalar<T>(cspring: &mut T) -> Self::Scalar
+    where
+        T: Rng + CryptoRng;
+    fn scalar_neg(s: &Self::Scalar) -> Self::Scalar;
+    fn element_to_bytes(e: &Self::Element) -> Vec<u8>;
+    fn bytes_to_element(b: &[u8]) -> Option<Self::Element>;
+    fn element_length() -> usize;
+    fn basepoint_mult(s: &Self::Scalar) -> Self::Element;
+    fn scalarmult(e: &Self::Element, s: &Self::Scalar) -> Self::Element;
+    fn add(a: &Self::Element, b: &Self::Element) -> Self::Element;
+}
+
+#[derive(Debug, PartialEq, Eq)]
+pub struct Ed25519Group;
+
+impl Group for Ed25519Group {
+    type Scalar = c2_Scalar;
+    type Element = c2_Element;
+    //type ElementBytes = Vec<u8>;
+    //type ElementBytes = [u8; 32];
+    //type ScalarBytes
+    type TranscriptHash = Sha256;
+
+    fn const_m() -> c2_Element {
+        // python -c "import binascii, spake2; b=binascii.hexlify(spake2.ParamsEd25519.M.to_bytes()); print(', '.join(['0x'+b[i:i+2] for i in range(0,len(b),2)]))"
+        // 15cfd18e385952982b6a8f8c7854963b58e34388c8e6dae891db756481a02312
+        CompressedEdwardsY([
+            0x15, 0xcf, 0xd1, 0x8e, 0x38, 0x59, 0x52, 0x98, 0x2b, 0x6a, 0x8f, 0x8c, 0x78, 0x54,
+            0x96, 0x3b, 0x58, 0xe3, 0x43, 0x88, 0xc8, 0xe6, 0xda, 0xe8, 0x91, 0xdb, 0x75, 0x64,
+            0x81, 0xa0, 0x23, 0x12,
+        ]).decompress()
+            .unwrap()
+    }
+
+    fn const_n() -> c2_Element {
+        // python -c "import binascii, spake2; b=binascii.hexlify(spake2.ParamsEd25519.N.to_bytes()); print(', '.join(['0x'+b[i:i+2] for i in range(0,len(b),2)]))"
+        // f04f2e7eb734b2a8f8b472eaf9c3c632576ac64aea650b496a8a20ff00e583c3
+        CompressedEdwardsY([
+            0xf0, 0x4f, 0x2e, 0x7e, 0xb7, 0x34, 0xb2, 0xa8, 0xf8, 0xb4, 0x72, 0xea, 0xf9, 0xc3,
+            0xc6, 0x32, 0x57, 0x6a, 0xc6, 0x4a, 0xea, 0x65, 0x0b, 0x49, 0x6a, 0x8a, 0x20, 0xff,
+            0x00, 0xe5, 0x83, 0xc3,
+        ]).decompress()
+            .unwrap()
+    }
+
+    fn const_s() -> c2_Element {
+        // python -c "import binascii, spake2; b=binascii.hexlify(spake2.ParamsEd25519.S.to_bytes()); print(', '.join(['0x'+b[i:i+2] for i in range(0,len(b),2)]))"
+        // 6f00dae87c1be1a73b5922ef431cd8f57879569c222d22b1cd71e8546ab8e6f1
+        CompressedEdwardsY([
+            0x6f, 0x00, 0xda, 0xe8, 0x7c, 0x1b, 0xe1, 0xa7, 0x3b, 0x59, 0x22, 0xef, 0x43, 0x1c,
+            0xd8, 0xf5, 0x78, 0x79, 0x56, 0x9c, 0x22, 0x2d, 0x22, 0xb1, 0xcd, 0x71, 0xe8, 0x54,
+            0x6a, 0xb8, 0xe6, 0xf1,
+        ]).decompress()
+            .unwrap()
+    }
+
+    fn hash_to_scalar(s: &[u8]) -> c2_Scalar {
+        ed25519_hash_to_scalar(s)
+    }
+    fn random_scalar<T>(cspring: &mut T) -> c2_Scalar
+    where
+        T: Rng + CryptoRng,
+    {
+        c2_Scalar::random(cspring)
+    }
+    fn scalar_neg(s: &c2_Scalar) -> c2_Scalar {
+        -s
+    }
+    fn element_to_bytes(s: &c2_Element) -> Vec<u8> {
+        s.compress().as_bytes().to_vec()
+    }
+    fn element_length() -> usize {
+        32
+    }
+    fn bytes_to_element(b: &[u8]) -> Option<c2_Element> {
+        if b.len() != 32 {
+            return None;
+        }
+        //let mut bytes: [u8; 32] =
+        let mut bytes = [0u8; 32];
+        bytes.copy_from_slice(b);
+        let cey = CompressedEdwardsY(bytes);
+        // CompressedEdwardsY::new(b)
+        cey.decompress()
+    }
+
+    fn basepoint_mult(s: &c2_Scalar) -> c2_Element {
+        //c2_Element::basepoint_mult(s)
+        ED25519_BASEPOINT_POINT * s
+    }
+    fn scalarmult(e: &c2_Element, s: &c2_Scalar) -> c2_Element {
+        e * s
+        //e.scalar_mult(s)
+    }
+    fn add(a: &c2_Element, b: &c2_Element) -> c2_Element {
+        a + b
+        //a.add(b)
+    }
+}
+
+fn decimal_to_scalar(d: &[u8]) -> c2_Scalar {
+    let bytes = BigUint::parse_bytes(d, 10).unwrap().to_bytes_le();
+    assert_eq!(bytes.len(), 32);
+    let mut b2 = [0u8; 32];
+    b2.copy_from_slice(&bytes);
+    c2_Scalar::from_bytes_mod_order(b2)
+}
+
+fn ed25519_hash_to_scalar(s: &[u8]) -> c2_Scalar {
+    //c2_Scalar::hash_from_bytes::<Sha512>(&s)
+    // spake2.py does:
+    //  h = HKDF(salt=b"", ikm=s, hash=SHA256, info=b"SPAKE2 pw", len=32+16)
+    //  i = int(h, 16)
+    //  i % q
+
+    let mut okm = [0u8; 32 + 16];
+    Hkdf::<Sha256>::extract(Some(b""), s)
+        .expand(b"SPAKE2 pw", &mut okm)
+        .unwrap();
+    //println!("expanded:   {}{}", "................................", okm.iter().to_hex()); // ok
+
+    let mut reducible = [0u8; 64]; // little-endian
+    for (i, x) in okm.iter().enumerate().take(32 + 16) {
+        reducible[32 + 16 - 1 - i] = *x;
+    }
+    //println!("reducible:  {}", reducible.iter().to_hex());
+    c2_Scalar::from_bytes_mod_order_wide(&reducible)
+    //let reduced = c2_Scalar::reduce(&reducible);
+    //println!("reduced:    {}", reduced.as_bytes().to_hex());
+    //println!("done");
+    //reduced
+}
+
+fn ed25519_hash_ab(
+    password_vec: &[u8],
+    id_a: &[u8],
+    id_b: &[u8],
+    first_msg: &[u8],
+    second_msg: &[u8],
+    key_bytes: &[u8],
+) -> Vec<u8> {
+    assert_eq!(first_msg.len(), 32);
+    assert_eq!(second_msg.len(), 32);
+    // the transcript is fixed-length, made up of 6 32-byte values:
+    // byte 0-31   : sha256(pw)
+    // byte 32-63  : sha256(idA)
+    // byte 64-95  : sha256(idB)
+    // byte 96-127 : X_msg
+    // byte 128-159: Y_msg
+    // byte 160-191: K_bytes
+    let mut transcript = [0u8; 6 * 32];
+
+    let mut pw_hash = Sha256::new();
+    pw_hash.input(password_vec);
+    transcript[0..32].copy_from_slice(&pw_hash.result());
+
+    let mut ida_hash = Sha256::new();
+    ida_hash.input(id_a);
+    transcript[32..64].copy_from_slice(&ida_hash.result());
+
+    let mut idb_hash = Sha256::new();
+    idb_hash.input(id_b);
+    transcript[64..96].copy_from_slice(&idb_hash.result());
+
+    transcript[96..128].copy_from_slice(first_msg);
+    transcript[128..160].copy_from_slice(second_msg);
+    transcript[160..192].copy_from_slice(key_bytes);
+
+    //println!("transcript: {:?}", transcript.iter().to_hex());
+
+    //let mut hash = G::TranscriptHash::default();
+    let mut hash = Sha256::new();
+    hash.input(&transcript);
+    hash.result().to_vec()
+}
+
+fn ed25519_hash_symmetric(
+    password_vec: &[u8],
+    id_s: &[u8],
+    msg_u: &[u8],
+    msg_v: &[u8],
+    key_bytes: &[u8],
+) -> Vec<u8> {
+    assert_eq!(msg_u.len(), 32);
+    assert_eq!(msg_v.len(), 32);
+    // # since we don't know which side is which, we must sort the messages
+    // first_msg, second_msg = sorted([msg1, msg2])
+    // transcript = b"".join([sha256(pw).digest(),
+    //                        sha256(idSymmetric).digest(),
+    //                        first_msg, second_msg, K_bytes])
+
+    // the transcript is fixed-length, made up of 5 32-byte values:
+    // byte 0-31   : sha256(pw)
+    // byte 32-63  : sha256(idSymmetric)
+    // byte 64-95  : X_msg
+    // byte 96-127 : Y_msg
+    // byte 128-159: K_bytes
+    let mut transcript = [0u8; 5 * 32];
+
+    let mut pw_hash = Sha256::new();
+    pw_hash.input(password_vec);
+    transcript[0..32].copy_from_slice(&pw_hash.result());
+
+    let mut ids_hash = Sha256::new();
+    ids_hash.input(id_s);
+    transcript[32..64].copy_from_slice(&ids_hash.result());
+
+    if msg_u < msg_v {
+        transcript[64..96].copy_from_slice(msg_u);
+        transcript[96..128].copy_from_slice(msg_v);
+    } else {
+        transcript[64..96].copy_from_slice(msg_v);
+        transcript[96..128].copy_from_slice(msg_u);
+    }
+    transcript[128..160].copy_from_slice(key_bytes);
+
+    let mut hash = Sha256::new();
+    hash.input(&transcript);
+    hash.result().to_vec()
+}
+
+/* "session type pattern" */
+
+#[derive(Debug, PartialEq, Eq)]
+enum Side {
+    A,
+    B,
+    Symmetric,
+}
+
+// we implement a custom Debug below, to avoid revealing secrets in a dump
+#[derive(PartialEq, Eq)]
+pub struct SPAKE2<G: Group> {
+    //where &G::Scalar: Neg {
+    side: Side,
+    xy_scalar: G::Scalar,
+    password_vec: Vec<u8>,
+    id_a: Vec<u8>,
+    id_b: Vec<u8>,
+    id_s: Vec<u8>,
+    msg1: Vec<u8>,
+    password_scalar: G::Scalar,
+}
+
+impl<G: Group> SPAKE2<G> {
+    fn start_internal(
+        side: Side,
+        password: &Password,
+        id_a: &Identity,
+        id_b: &Identity,
+        id_s: &Identity,
+        xy_scalar: G::Scalar,
+    ) -> (SPAKE2<G>, Vec<u8>) {
+        //let password_scalar: G::Scalar = hash_to_scalar::<G::Scalar>(password);
+        let password_scalar: G::Scalar = G::hash_to_scalar(&password);
+
+        // a: X = B*x + M*pw
+        // b: Y = B*y + N*pw
+        // sym: X = B*x * S*pw
+        let blinding = match side {
+            Side::A => G::const_m(),
+            Side::B => G::const_n(),
+            Side::Symmetric => G::const_s(),
+        };
+        let m1: G::Element = G::add(
+            &G::basepoint_mult(&xy_scalar),
+            &G::scalarmult(&blinding, &password_scalar),
+        );
+        //let m1: G::Element = &G::basepoint_mult(&x) + &(blinding * &password_scalar);
+        let msg1: Vec<u8> = G::element_to_bytes(&m1);
+        let mut password_vec = Vec::new();
+        password_vec.extend_from_slice(&password);
+        let mut id_a_copy = Vec::new();
+        id_a_copy.extend_from_slice(&id_a);
+        let mut id_b_copy = Vec::new();
+        id_b_copy.extend_from_slice(&id_b);
+        let mut id_s_copy = Vec::new();
+        id_s_copy.extend_from_slice(&id_s);
+
+        let mut msg_and_side = Vec::new();
+        msg_and_side.push(match side {
+            Side::A => 0x41,         // 'A'
+            Side::B => 0x42,         // 'B'
+            Side::Symmetric => 0x53, // 'S'
+        });
+        msg_and_side.extend_from_slice(&msg1);
+
+        (
+            SPAKE2 {
+                side,
+                xy_scalar,
+                password_vec, // string
+                id_a: id_a_copy,
+                id_b: id_b_copy,
+                id_s: id_s_copy,
+                msg1: msg1.clone(),
+                password_scalar, // scalar
+            },
+            msg_and_side,
+        )
+    }
+
+    fn start_a_internal(
+        password: &Password,
+        id_a: &Identity,
+        id_b: &Identity,
+        xy_scalar: G::Scalar,
+    ) -> (SPAKE2<G>, Vec<u8>) {
+        Self::start_internal(
+            Side::A,
+            &password,
+            &id_a,
+            &id_b,
+            &Identity::new(b""),
+            xy_scalar,
+        )
+    }
+
+    fn start_b_internal(
+        password: &Password,
+        id_a: &Identity,
+        id_b: &Identity,
+        xy_scalar: G::Scalar,
+    ) -> (SPAKE2<G>, Vec<u8>) {
+        Self::start_internal(
+            Side::B,
+            &password,
+            &id_a,
+            &id_b,
+            &Identity::new(b""),
+            xy_scalar,
+        )
+    }
+
+    fn start_symmetric_internal(
+        password: &Password,
+        id_s: &Identity,
+        xy_scalar: G::Scalar,
+    ) -> (SPAKE2<G>, Vec<u8>) {
+        Self::start_internal(
+            Side::Symmetric,
+            &password,
+            &Identity::new(b""),
+            &Identity::new(b""),
+            &id_s,
+            xy_scalar,
+        )
+    }
+
+    pub fn start_a(password: &Password, id_a: &Identity, id_b: &Identity) -> (SPAKE2<G>, Vec<u8>) {
+        let mut cspring: OsRng = OsRng::new().unwrap();
+        let xy_scalar: G::Scalar = G::random_scalar(&mut cspring);
+        Self::start_a_internal(&password, &id_a, &id_b, xy_scalar)
+    }
+
+    pub fn start_b(password: &Password, id_a: &Identity, id_b: &Identity) -> (SPAKE2<G>, Vec<u8>) {
+        let mut cspring: OsRng = OsRng::new().unwrap();
+        let xy_scalar: G::Scalar = G::random_scalar(&mut cspring);
+        Self::start_b_internal(&password, &id_a, &id_b, xy_scalar)
+    }
+
+    pub fn start_symmetric(password: &Password, id_s: &Identity) -> (SPAKE2<G>, Vec<u8>) {
+        let mut cspring: OsRng = OsRng::new().unwrap();
+        let xy_scalar: G::Scalar = G::random_scalar(&mut cspring);
+        Self::start_symmetric_internal(&password, &id_s, xy_scalar)
+    }
+
+    pub fn finish(self, msg2: &[u8]) -> Result<Vec<u8>, SPAKEErr> {
+        if msg2.len() != 1 + G::element_length() {
+            return Err(SPAKEErr {
+                kind: ErrorType::WrongLength,
+            });
+        }
+        let msg_side = msg2[0];
+
+        match self.side {
+            Side::A => match msg_side {
+                0x42 => (), // 'B'
+                _ => {
+                    return Err(SPAKEErr {
+                        kind: ErrorType::BadSide,
+                    })
+                }
+            },
+            Side::B => match msg_side {
+                0x41 => (), // 'A'
+                _ => {
+                    return Err(SPAKEErr {
+                        kind: ErrorType::BadSide,
+                    })
+                }
+            },
+            Side::Symmetric => match msg_side {
+                0x53 => (), // 'S'
+                _ => {
+                    return Err(SPAKEErr {
+                        kind: ErrorType::BadSide,
+                    })
+                }
+            },
+        }
+
+        let msg2_element = match G::bytes_to_element(&msg2[1..]) {
+            Some(x) => x,
+            None => {
+                return Err(SPAKEErr {
+                    kind: ErrorType::CorruptMessage,
+                })
+            }
+        };
+
+        // a: K = (Y+N*(-pw))*x
+        // b: K = (X+M*(-pw))*y
+        let unblinding = match self.side {
+            Side::A => G::const_n(),
+            Side::B => G::const_m(),
+            Side::Symmetric => G::const_s(),
+        };
+        let tmp1 = G::scalarmult(&unblinding, &G::scalar_neg(&self.password_scalar));
+        let tmp2 = G::add(&msg2_element, &tmp1);
+        let key_element = G::scalarmult(&tmp2, &self.xy_scalar);
+        let key_bytes = G::element_to_bytes(&key_element);
+
+        // key = H(H(pw) + H(idA) + H(idB) + X + Y + K)
+        //transcript = b"".join([sha256(pw).digest(),
+        //                       sha256(idA).digest(), sha256(idB).digest(),
+        //                       X_msg, Y_msg, K_bytes])
+        //key = sha256(transcript).digest()
+        // note that both sides must use the same order
+
+        Ok(match self.side {
+            Side::A => ed25519_hash_ab(
+                &self.password_vec,
+                &self.id_a,
+                &self.id_b,
+                self.msg1.as_slice(),
+                &msg2[1..],
+                &key_bytes,
+            ),
+            Side::B => ed25519_hash_ab(
+                &self.password_vec,
+                &self.id_a,
+                &self.id_b,
+                &msg2[1..],
+                self.msg1.as_slice(),
+                &key_bytes,
+            ),
+            Side::Symmetric => ed25519_hash_symmetric(
+                &self.password_vec,
+                &self.id_s,
+                &self.msg1,
+                &msg2[1..],
+                &key_bytes,
+            ),
+        })
+    }
+}
+
+fn maybe_utf8(s: &[u8]) -> String {
+    match String::from_utf8(s.to_vec()) {
+        Ok(m) => format!("(s={})", m),
+        Err(_) => format!("(hex={})", hex::encode(s)),
+    }
+}
+
+impl<G: Group> fmt::Debug for SPAKE2<G> {
+    fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
+        write!(
+            f,
+            "SPAKE2(G=?, side={:?}, idA={}, idB={}, idS={})",
+            self.side,
+            maybe_utf8(&self.id_a),
+            maybe_utf8(&self.id_b),
+            maybe_utf8(&self.id_s)
+        )
+    }
+}
+
+#[cfg(test)]
+mod test {
+    /* This compares results against the python compatibility tests:
+    spake2.test.test_compat.SPAKE2.test_asymmetric . The python test passes a
+    deterministic RNG (used only for tests, of course) into the per-Group
+    "random_scalar()" function, which results in some particular scalar.
+     */
+    use super::*;
+    use curve25519_dalek::constants::ED25519_BASEPOINT_POINT;
+    use hex;
+    use spake2::{Ed25519Group, SPAKE2};
+
+    // the python tests show the long-integer form of scalars. the rust code
+    // wants an array of bytes (little-endian). Make sure the way we convert
+    // things works correctly.
+
+    #[test]
+    fn test_convert() {
+        let t1_decimal =
+            b"2238329342913194256032495932344128051776374960164957527413114840482143558222";
+        let t1_scalar = decimal_to_scalar(t1_decimal);
+        let t1_bytes = t1_scalar.to_bytes();
+        let expected = [
+            0x4e, 0x5a, 0xb4, 0x34, 0x5d, 0x47, 0x08, 0x84, 0x59, 0x13, 0xb4, 0x64, 0x1b, 0xc2,
+            0x7d, 0x52, 0x52, 0xa5, 0x85, 0x10, 0x1b, 0xcc, 0x42, 0x44, 0xd4, 0x49, 0xf4, 0xa8,
+            0x79, 0xd9, 0xf2, 0x04,
+        ];
+        assert_eq!(t1_bytes, expected);
+        //println!("t1_scalar is {:?}", t1_scalar);
+    }
+
+    #[test]
+    fn test_serialize_basepoint() {
+        // make sure elements are serialized same as the python library
+        let exp = "5866666666666666666666666666666666666666666666666666666666666666";
+        let base_vec = ED25519_BASEPOINT_POINT.compress().as_bytes().to_vec();
+        let base_hex = hex::encode(base_vec);
+        println!("exp: {:?}", exp);
+        println!("got: {:?}", base_hex);
+        assert_eq!(exp, base_hex);
+    }
+
+    #[test]
+    fn test_password_to_scalar() {
+        let password = Password::new(b"password");
+        let expected_pw_scalar = decimal_to_scalar(
+            b"3515301705789368674385125653994241092664323519848410154015274772661223168839",
+        );
+        let pw_scalar = Ed25519Group::hash_to_scalar(&password);
+        println!("exp: {:?}", hex::encode(expected_pw_scalar.as_bytes()));
+        println!("got: {:?}", hex::encode(pw_scalar.as_bytes()));
+        assert_eq!(&pw_scalar, &expected_pw_scalar);
+    }
+
+    #[test]
+    fn test_sizes() {
+        let (s1, msg1) = SPAKE2::<Ed25519Group>::start_a(
+            &Password::new(b"password"),
+            &Identity::new(b"idA"),
+            &Identity::new(b"idB"),
+        );
+        assert_eq!(msg1.len(), 1 + 32);
+        let (s2, msg2) = SPAKE2::<Ed25519Group>::start_b(
+            &Password::new(b"password"),
+            &Identity::new(b"idA"),
+            &Identity::new(b"idB"),
+        );
+        assert_eq!(msg2.len(), 1 + 32);
+        let key1 = s1.finish(&msg2).unwrap();
+        let key2 = s2.finish(&msg1).unwrap();
+        assert_eq!(key1.len(), 32);
+        assert_eq!(key2.len(), 32);
+
+        let (s1, msg1) = SPAKE2::<Ed25519Group>::start_symmetric(
+            &Password::new(b"password"),
+            &Identity::new(b"idS"),
+        );
+        assert_eq!(msg1.len(), 1 + 32);
+        let (s2, msg2) = SPAKE2::<Ed25519Group>::start_symmetric(
+            &Password::new(b"password"),
+            &Identity::new(b"idS"),
+        );
+        assert_eq!(msg2.len(), 1 + 32);
+        let key1 = s1.finish(&msg2).unwrap();
+        let key2 = s2.finish(&msg1).unwrap();
+        assert_eq!(key1.len(), 32);
+        assert_eq!(key2.len(), 32);
+    }
+
+    #[test]
+    fn test_hash_ab() {
+        let key = ed25519_hash_ab(
+            b"pw",
+            b"idA",
+            b"idB",
+            b"XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX", // len=32
+            b"YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY",
+            b"KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK",
+        );
+        let expected_key = "d59d9ba920f7092565cec747b08d5b2e981d553ac32fde0f25e5b4a4cfca3efd";
+        assert_eq!(hex::encode(key), expected_key);
+    }
+
+    #[test]
+    fn test_hash_symmetric() {
+        let key = ed25519_hash_symmetric(
+            b"pw",
+            b"idSymmetric",
+            b"XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX",
+            b"YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY",
+            b"KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK",
+        );
+        let expected_key = "b0b31e4401aae37d91a9a8bf6fbb1298cafc005ff9142e3ffc5b9799fb11128b";
+        assert_eq!(hex::encode(key), expected_key);
+    }
+
+    #[test]
+    fn test_asymmetric() {
+        let scalar_a = decimal_to_scalar(
+            b"2611694063369306139794446498317402240796898290761098242657700742213257926693",
+        );
+        let scalar_b = decimal_to_scalar(
+            b"7002393159576182977806091886122272758628412261510164356026361256515836884383",
+        );
+        let expected_pw_scalar = decimal_to_scalar(
+            b"3515301705789368674385125653994241092664323519848410154015274772661223168839",
+        );
+
+        println!("scalar_a is {}", hex::encode(scalar_a.as_bytes()));
+
+        let (s1, msg1) = SPAKE2::<Ed25519Group>::start_a_internal(
+            &Password::new(b"password"),
+            &Identity::new(b"idA"),
+            &Identity::new(b"idB"),
+            scalar_a,
+        );
+        let expected_msg1 = "416fc960df73c9cf8ed7198b0c9534e2e96a5984bfc5edc023fd24dacf371f2af9";
+
+        println!();
+        println!("xys1: {:?}", hex::encode(s1.xy_scalar.as_bytes()));
+        println!();
+        println!("pws1: {:?}", hex::encode(s1.password_scalar.as_bytes()));
+        println!("exp : {:?}", hex::encode(expected_pw_scalar.as_bytes()));
+        println!();
+        println!("msg1: {:?}", hex::encode(&msg1));
+        println!("exp : {:?}", expected_msg1);
+        println!();
+
+        assert_eq!(
+            hex::encode(expected_pw_scalar.as_bytes()),
+            hex::encode(s1.password_scalar.as_bytes())
+        );
+        assert_eq!(hex::encode(&msg1), expected_msg1);
+
+        let (s2, msg2) = SPAKE2::<Ed25519Group>::start_b_internal(
+            &Password::new(b"password"),
+            &Identity::new(b"idA"),
+            &Identity::new(b"idB"),
+            scalar_b,
+        );
+        assert_eq!(expected_pw_scalar, s2.password_scalar);
+        assert_eq!(
+            hex::encode(&msg2),
+            "42354e97b88406922b1df4bea1d7870f17aed3dba7c720b313edae315b00959309"
+        );
+
+        let key1 = s1.finish(&msg2).unwrap();
+        let key2 = s2.finish(&msg1).unwrap();
+        assert_eq!(key1, key2);
+        assert_eq!(
+            hex::encode(key1),
+            "712295de7219c675ddd31942184aa26e0a957cf216bc230d165b215047b520c1"
+        );
+    }
+
+    #[test]
+    fn test_debug() {
+        let (s1, _msg1) = SPAKE2::<Ed25519Group>::start_a(
+            &Password::new(b"password"),
+            &Identity::new(b"idA"),
+            &Identity::new(b"idB"),
+        );
+        println!("s1: {:?}", s1);
+        let (s2, _msg1) = SPAKE2::<Ed25519Group>::start_symmetric(
+            &Password::new(b"password"),
+            &Identity::new(b"idS"),
+        );
+        println!("s2: {:?}", s2);
+    }
+
+}