diff --git a/cipher_suites.go b/cipher_suites.go
index 917a1ef..ec867ce 100644
--- a/cipher_suites.go
+++ b/cipher_suites.go
@@ -365,15 +365,13 @@ var tdesCiphers = map[uint16]bool{
 }
 
 var (
-	hasGCMAsmAMD64 = cpu.X86.HasAES && cpu.X86.HasPCLMULQDQ
+	// Keep in sync with crypto/internal/fips/aes/gcm.supportsAESGCM.
+	hasGCMAsmAMD64 = cpu.X86.HasAES && cpu.X86.HasPCLMULQDQ && cpu.X86.HasSSE41 && cpu.X86.HasSSSE3
 	hasGCMAsmARM64 = cpu.ARM64.HasAES && cpu.ARM64.HasPMULL
-	// Keep in sync with crypto/aes/cipher_s390x.go.
-	hasGCMAsmS390X = cpu.S390X.HasAES && cpu.S390X.HasAESCBC && cpu.S390X.HasAESCTR &&
-		(cpu.S390X.HasGHASH || cpu.S390X.HasAESGCM)
+	hasGCMAsmS390X = cpu.S390X.HasAES && cpu.S390X.HasAESCTR && cpu.S390X.HasGHASH
+	hasGCMAsmPPC64 = runtime.GOARCH == "ppc64" || runtime.GOARCH == "ppc64le"
 
-	hasAESGCMHardwareSupport = runtime.GOARCH == "amd64" && hasGCMAsmAMD64 ||
-		runtime.GOARCH == "arm64" && hasGCMAsmARM64 ||
-		runtime.GOARCH == "s390x" && hasGCMAsmS390X
+	hasAESGCMHardwareSupport = hasGCMAsmAMD64 || hasGCMAsmARM64 || hasGCMAsmS390X || hasGCMAsmPPC64
 )
 
 var aesgcmCiphers = map[uint16]bool{