diff --git a/crypto/fipsmodule/aes/aes_nohw.c b/crypto/fipsmodule/aes/aes_nohw.c
index 308c7cca1c..7490ade194 100644
--- a/crypto/fipsmodule/aes/aes_nohw.c
+++ b/crypto/fipsmodule/aes/aes_nohw.c
@@ -338,15 +338,15 @@ static inline void aes_nohw_compact_block(aes_word_t out[AES_NOHW_BLOCK_WORDS],
 #if defined(OPENSSL_SSE2)
   // No conversions needed.
 #elif defined(OPENSSL_64_BIT)
-  uint64_t a0 = aes_nohw_compact_word(out[0]);
-  uint64_t a1 = aes_nohw_compact_word(out[1]);
+  uint64_t a0 = aes_nohw_compact_word(CRYPTO_bswap8_le(out[0]));
+  uint64_t a1 = aes_nohw_compact_word(CRYPTO_bswap8_le(out[1]));
   out[0] = (a0 & UINT64_C(0x00000000ffffffff)) | (a1 << 32);
   out[1] = (a1 & UINT64_C(0xffffffff00000000)) | (a0 >> 32);
 #else
-  uint32_t a0 = aes_nohw_compact_word(out[0]);
-  uint32_t a1 = aes_nohw_compact_word(out[1]);
-  uint32_t a2 = aes_nohw_compact_word(out[2]);
-  uint32_t a3 = aes_nohw_compact_word(out[3]);
+  uint32_t a0 = aes_nohw_compact_word(CRYPTO_bswap4_le(out[0]));
+  uint32_t a1 = aes_nohw_compact_word(CRYPTO_bswap4_le(out[1]));
+  uint32_t a2 = aes_nohw_compact_word(CRYPTO_bswap4_le(out[2]));
+  uint32_t a3 = aes_nohw_compact_word(CRYPTO_bswap4_le(out[3]));
   // Note clang, when building for ARM Thumb2, will sometimes miscompile
   // expressions such as (a0 & 0x0000ff00) << 8, particularly when building
   // without optimizations. This bug was introduced in
@@ -370,6 +370,8 @@ static inline void aes_nohw_uncompact_block(
       aes_nohw_uncompact_word((a0 & UINT64_C(0x00000000ffffffff)) | (a1 << 32));
   uint64_t b1 =
       aes_nohw_uncompact_word((a1 & UINT64_C(0xffffffff00000000)) | (a0 >> 32));
+  b0 = CRYPTO_bswap8_le(b0);
+  b1 = CRYPTO_bswap8_le(b1);
   OPENSSL_memcpy(out, &b0, 8);
   OPENSSL_memcpy(out + 8, &b1, 8);
 #else
@@ -392,6 +394,10 @@ static inline void aes_nohw_uncompact_block(
   b1 = aes_nohw_uncompact_word(b1);
   b2 = aes_nohw_uncompact_word(b2);
   b3 = aes_nohw_uncompact_word(b3);
+  b0 = CRYPTO_bswap4_le(b0);
+  b1 = CRYPTO_bswap4_le(b1);
+  b2 = CRYPTO_bswap4_le(b2);
+  b3 = CRYPTO_bswap4_le(b3);
   OPENSSL_memcpy(out, &b0, 4);
   OPENSSL_memcpy(out + 4, &b1, 4);
   OPENSSL_memcpy(out + 8, &b2, 4);
@@ -920,11 +926,11 @@ void aes_nohw_ctr32_encrypt_blocks(const uint8_t *in, uint8_t *out,
     OPENSSL_memcpy(ivs.u8 + 16 * i, ivec, 16);
   }
 
-  uint32_t ctr = CRYPTO_bswap4(ivs.u32[3]);
+  uint32_t ctr = CRYPTO_bswap4_be(ivs.u32[3]);
   for (;;) {
     // Update counters.
     for (uint32_t i = 0; i < AES_NOHW_BATCH_SIZE; i++) {
-      ivs.u32[4 * i + 3] = CRYPTO_bswap4(ctr + i);
+      ivs.u32[4 * i + 3] = CRYPTO_bswap4_be(ctr + i);
     }
 
     size_t todo = blocks >= AES_NOHW_BATCH_SIZE ? AES_NOHW_BATCH_SIZE : blocks;
diff --git a/crypto/fipsmodule/ec/p256_shared.h b/crypto/fipsmodule/ec/p256_shared.h
index 049b138085..0d37ea9cc5 100644
--- a/crypto/fipsmodule/ec/p256_shared.h
+++ b/crypto/fipsmodule/ec/p256_shared.h
@@ -51,7 +51,20 @@ typedef unsigned char P256_SCALAR_BYTES[33];
 
 static inline void p256_scalar_bytes_from_limbs(
     P256_SCALAR_BYTES bytes_out, const BN_ULONG limbs[P256_LIMBS]) {
+#ifdef RING_BIG_ENDIAN
+  for (int i = 0; i < P256_LIMBS; i++)
+  {
+#if BN_BITS2 == 64
+    BN_ULONG limb = CRYPTO_bswap8(limbs[i]);
+    OPENSSL_memcpy(bytes_out + i * 8, &limb, 8);
+#else
+    BN_ULONG limb = CRYPTO_bswap4(limbs[i]);
+    OPENSSL_memcpy(bytes_out + i * 4, &limb, 4);
+#endif
+  }
+#else
   OPENSSL_memcpy(bytes_out, limbs, 32);
+#endif
   bytes_out[32] = 0;
 }
 
diff --git a/crypto/internal.h b/crypto/internal.h
index dba229c399..22d0cab208 100644
--- a/crypto/internal.h
+++ b/crypto/internal.h
@@ -264,6 +264,10 @@ static inline crypto_word constant_time_select_w(crypto_word mask,
 static inline uint32_t CRYPTO_bswap4(uint32_t x) {
   return __builtin_bswap32(x);
 }
+
+static inline uint64_t CRYPTO_bswap8(uint64_t x) {
+  return __builtin_bswap64(x);
+}
 #elif defined(_MSC_VER)
 #pragma warning(push, 3)
 #include <stdlib.h>
@@ -272,8 +276,44 @@ static inline uint32_t CRYPTO_bswap4(uint32_t x) {
 static inline uint32_t CRYPTO_bswap4(uint32_t x) {
   return _byteswap_ulong(x);
 }
+
+static inline uint64_t CRYPTO_bswap8(uint64_t x) {
+  return _byteswap_uint64(x);
+}
+#else
+static inline uint32_t CRYPTO_bswap4(uint32_t x) {
+  x = (x >> 16) | (x << 16);
+  x = ((x & 0xff00ff00) >> 8) | ((x & 0x00ff00ff) << 8);
+  return x;
+}
+
+static inline uint64_t CRYPTO_bswap8(uint64_t x) {
+  return CRYPTO_bswap4(x >> 32) | (((uint64_t)CRYPTO_bswap4(x)) << 32);
+}
 #endif
 
+
+// Convert LE or BE values to/from native endianness.
+
+#if defined(__BYTE_ORDER__) && defined(__ORDER_BIG_ENDIAN__)
+#if __BYTE_ORDER__ == __ORDER_BIG_ENDIAN__
+#define RING_BIG_ENDIAN
+#endif
+#endif
+
+#ifdef RING_BIG_ENDIAN
+#define CRYPTO_bswap4_le(x) CRYPTO_bswap4((x))
+#define CRYPTO_bswap8_le(x) CRYPTO_bswap8((x))
+#define CRYPTO_bswap4_be(x) (x)
+#define CRYPTO_bswap8_be(x) (x)
+#else
+#define CRYPTO_bswap4_le(x) (x)
+#define CRYPTO_bswap8_le(x) (x)
+#define CRYPTO_bswap4_be(x) CRYPTO_bswap4((x))
+#define CRYPTO_bswap8_be(x) CRYPTO_bswap8((x))
+#endif
+
+
 #if !defined(RING_CORE_NOSTDLIBINC)
 #include <string.h>
 #endif
diff --git a/crypto/poly1305/poly1305.c b/crypto/poly1305/poly1305.c
index 5f0ab8d6b3..7f9c7dc0d5 100644
--- a/crypto/poly1305/poly1305.c
+++ b/crypto/poly1305/poly1305.c
@@ -29,14 +29,14 @@
 #pragma GCC diagnostic ignored "-Wconversion"
 #endif
 
-// We can assume little-endian.
 static uint32_t U8TO32_LE(const uint8_t *m) {
   uint32_t r;
   OPENSSL_memcpy(&r, m, sizeof(r));
-  return r;
+  return CRYPTO_bswap4_le(r);
 }
 
 static void U32TO8_LE(uint8_t *m, uint32_t v) {
+  v = CRYPTO_bswap4_le(v);
   OPENSSL_memcpy(m, &v, sizeof(v));
 }
 
diff --git a/include/ring-core/base.h b/include/ring-core/base.h
index f1a027d1a4..0f58a9096c 100644
--- a/include/ring-core/base.h
+++ b/include/ring-core/base.h
@@ -89,6 +89,12 @@
 #elif defined(__MIPSEL__) && defined(__LP64__)
 #define OPENSSL_64_BIT
 #define OPENSSL_MIPS64
+#elif defined(__s390x__)
+#define OPENSSL_64_BIT
+#define OPENSSL_S390X
+#elif defined(__powerpc64__)
+#define OPENSSL_64_BIT
+#define OPENSSL_PPC64
 #elif defined(__wasm__)
 #define OPENSSL_32_BIT
 #else
diff --git a/mk/cargo.sh b/mk/cargo.sh
index 7ddb5dd628..5ff0960a4d 100755
--- a/mk/cargo.sh
+++ b/mk/cargo.sh
@@ -21,6 +21,7 @@ rustflags_self_contained="-Clink-self-contained=yes -Clinker=rust-lld"
 qemu_aarch64="qemu-aarch64 -L /usr/aarch64-linux-gnu"
 qemu_arm="qemu-arm -L /usr/arm-linux-gnueabihf"
 qemu_mipsel="qemu-mipsel -L /usr/mipsel-linux-gnu"
+qemu_s390x="qemu-s390x -L /usr/s390x-linux-gnu"
 
 # Avoid putting the Android tools in `$PATH` because there are tools in this
 # directory like `clang` that would conflict with the same-named tools that may
@@ -109,6 +110,13 @@ case $target in
       export CARGO_TARGET_X86_64_UNKNOWN_LINUX_MUSL_RUSTFLAGS="$rustflags_self_contained"
     fi
     ;;
+  s390x-unknown-linux-gnu)
+    export CC_s390x_unknown_linux_gnu=clang-$llvm_version
+    export AR_s390x_unknown_linux_gnu=llvm-ar-$llvm_version
+    export CFLAGS_s390x_unknown_linux_gnu="--sysroot=/usr/s390x-linux-gnu"
+    export CARGO_TARGET_S390X_UNKNOWN_LINUX_GNU_LINKER=s390x-linux-gnu-gcc
+    export CARGO_TARGET_S390X_UNKNOWN_LINUX_GNU_RUNNER="$qemu_s390x"
+    ;;
   wasm32-unknown-unknown)
     # The first two are only needed for when the "wasm_c" feature is enabled.
     export CC_wasm32_unknown_unknown=clang-$llvm_version
diff --git a/mk/install-build-tools.sh b/mk/install-build-tools.sh
index 77b01cdcb8..e30a6c7cbe 100755
--- a/mk/install-build-tools.sh
+++ b/mk/install-build-tools.sh
@@ -91,6 +91,14 @@ case $target in
     libc6-dev-mipsel-cross \
     qemu-user
   ;;
+--target=s390x-unknown-linux-gnu)
+  # Clang is needed for code coverage.
+  use_clang=1
+  install_packages \
+    qemu-user \
+    gcc-s390x-linux-gnu \
+    libc6-dev-s390x-cross
+  ;;
 --target=wasm32-unknown-unknown)
   cargo install wasm-bindgen-cli --bin wasm-bindgen-test-runner
   use_clang=1
diff --git a/src/lib.rs b/src/lib.rs
index 644708c828..2fe127e2dc 100644
--- a/src/lib.rs
+++ b/src/lib.rs
@@ -115,5 +115,3 @@ mod sealed {
     pub trait Sealed {}
 }
 
-// TODO: https://github.com/briansmith/ring/issues/1555.
-const _LITTLE_ENDIAN_ONLY: () = assert!(cfg!(target_endian = "little"));