--- a/crypto/crypto.c
+++ b/crypto/crypto.c
@@ -19,7 +19,7 @@
 // undesirable, so all assembly-referenced symbols should be hidden. CPU
 // capabilities are the only such symbols defined in C. Explicitly hide them,
 // rather than rely on being built with -fvisibility=hidden.
-#if defined(OPENSSL_WINDOWS)
+#if defined(OPENSSL_WINDOWS) || defined(__CYGWIN__)
 #define HIDDEN
 #else
 #define HIDDEN __attribute__((visibility("hidden")))
--- a/src/rand.rs
+++ b/src/rand.rs
@@ -128,6 +128,7 @@ impl SystemRandom {
     all(feature = "less-safe-getrandom-espidf", target_os = "espidf"),
     target_os = "aix",
     target_os = "android",
+    target_os = "cygwin",
     target_os = "dragonfly",
     target_os = "freebsd",
     target_os = "fuchsia",
--- a/build.rs
+++ b/build.rs
@@ -246,7 +247,7 @@ const ASM_TARGETS: &[AsmTarget] = &[
         perlasm_format: WIN32N,
     },
     AsmTarget {
-        oss: &[WINDOWS],
+        oss: &[WINDOWS, CYGWIN],
         arch: X86_64,
         perlasm_format: NASM,
     },
@@ -297,6 +298,7 @@ const NASM: &str = "nasm";
 const APPLE_ABI: &[&str] = &["ios", "macos", "tvos", "visionos", "watchos"];
 
 const WINDOWS: &str = "windows";
+const CYGWIN: &str = "cygwin";
 
 fn main() {
     // Avoid assuming the working directory is the same is the $CARGO_MANIFEST_DIR so that toolchains
@@ -651,7 +653,11 @@ fn nasm(file: &Path, arch: &str, include_dir: &Path, out_dir: &Path, c_root_dir:
     let mut include_dir = include_dir.as_os_str().to_os_string();
     include_dir.push(OsString::from(String::from(std::path::MAIN_SEPARATOR)));
 
-    let mut c = Command::new("./target/tools/windows/nasm/nasm");
+    let mut c = Command::new(if env::var("HOST").unwrap().contains("cygwin") {
+        "nasm"
+    } else {
+        "./target/tools/windows/nasm/nasm"
+    });
     let _ = c
         .arg("-o")
         .arg(out_file.to_str().expect("Invalid path"))
@@ -763,7 +769,19 @@ fn perlasm(
 }
 
 fn join_components_with_forward_slashes(path: &Path) -> OsString {
-    let parts = path.components().map(|c| c.as_os_str()).collect::<Vec<_>>();
+    let mut parts = path.components().map(|c| c.as_os_str()).collect::<Vec<_>>();
+    if env::var("HOST").unwrap().contains("cygwin") {
+        // Most platforms treat `//foo` the same as `/foo`, but POSIX allows `//`
+        // specifically to have an implementation-defined behavior. Most platforms
+        // treat them equal, but Cygwin is not one of them.
+        //
+        // - POSIX.1-2024: https://pubs.opengroup.org/onlinepubs/9799919799/basedefs/V1_chap04.html#tag_04_16
+        // - gnulib notes: https://cgit.git.savannah.gnu.org/cgit/gnulib.git/plain/m4/double-slash-root.m4?id=f4038dcb346fccb58d910e2f0a62c0f45022d2a8
+
+        if parts[0] == OsStr::new("/") {
+            parts[0] = OsStr::new("");
+        }
+    }
     parts.join(OsStr::new("/"))
 }
 
--- a/third_party/fiat/asm/fiat_curve25519_adx_mul.S
+++ b/third_party/fiat/asm/fiat_curve25519_adx_mul.S
@@ -1,7 +1,7 @@
 #include <ring-core/asm_base.h>
 
 #if !defined(OPENSSL_NO_ASM) && defined(OPENSSL_X86_64) && \
-    (defined(__APPLE__) || defined(__ELF__))
+    (defined(__APPLE__) || defined(__ELF__) || defined(__CYGWIN__))
 
 .intel_syntax noprefix
 .text
@@ -10,8 +10,10 @@
 .global _fiat_curve25519_adx_mul
 _fiat_curve25519_adx_mul:
 #else
+#if defined(__ELF__)
 .type fiat_curve25519_adx_mul, @function
 .hidden fiat_curve25519_adx_mul
+#endif
 .global fiat_curve25519_adx_mul
 fiat_curve25519_adx_mul:
 #endif
--- a/third_party/fiat/asm/fiat_curve25519_adx_square.S
+++ b/third_party/fiat/asm/fiat_curve25519_adx_square.S
@@ -1,7 +1,7 @@
 #include <ring-core/asm_base.h>
 
 #if !defined(OPENSSL_NO_ASM) && defined(OPENSSL_X86_64) && \
-    (defined(__APPLE__) || defined(__ELF__))
+    (defined(__APPLE__) || defined(__ELF__) || defined(__CYGWIN__))
 
 .intel_syntax noprefix
 .text
@@ -10,8 +10,10 @@
 .global _fiat_curve25519_adx_square
 _fiat_curve25519_adx_square:
 #else
+#if defined (__ELF__)
 .type fiat_curve25519_adx_square, @function
 .hidden fiat_curve25519_adx_square
+#endif
 .global fiat_curve25519_adx_square
 fiat_curve25519_adx_square:
 #endif