diff --git a/target/s390x/helper.h b/target/s390x/helper.h
index 83e5070821..18a3df6b07 100644
--- a/target/s390x/helper.h
+++ b/target/s390x/helper.h
@@ -156,6 +156,14 @@ DEF_HELPER_FLAGS_3(gvec_vclz8, TCG_CALL_NO_RWG, void, ptr, cptr, i32)
 DEF_HELPER_FLAGS_3(gvec_vclz16, TCG_CALL_NO_RWG, void, ptr, cptr, i32)
 DEF_HELPER_FLAGS_3(gvec_vctz8, TCG_CALL_NO_RWG, void, ptr, cptr, i32)
 DEF_HELPER_FLAGS_3(gvec_vctz16, TCG_CALL_NO_RWG, void, ptr, cptr, i32)
+DEF_HELPER_FLAGS_4(gvec_vgfm8, TCG_CALL_NO_RWG, void, ptr, cptr, cptr, i32)
+DEF_HELPER_FLAGS_4(gvec_vgfm16, TCG_CALL_NO_RWG, void, ptr, cptr, cptr, i32)
+DEF_HELPER_FLAGS_4(gvec_vgfm32, TCG_CALL_NO_RWG, void, ptr, cptr, cptr, i32)
+DEF_HELPER_FLAGS_4(gvec_vgfm64, TCG_CALL_NO_RWG, void, ptr, cptr, cptr, i32)
+DEF_HELPER_FLAGS_5(gvec_vgfma8, TCG_CALL_NO_RWG, void, ptr, cptr, cptr, cptr, i32)
+DEF_HELPER_FLAGS_5(gvec_vgfma16, TCG_CALL_NO_RWG, void, ptr, cptr, cptr, cptr, i32)
+DEF_HELPER_FLAGS_5(gvec_vgfma32, TCG_CALL_NO_RWG, void, ptr, cptr, cptr, cptr, i32)
+DEF_HELPER_FLAGS_5(gvec_vgfma64, TCG_CALL_NO_RWG, void, ptr, cptr, cptr, cptr, i32)
 
 #ifndef CONFIG_USER_ONLY
 DEF_HELPER_3(servc, i32, env, i64, i64)
diff --git a/target/s390x/insn-data.def b/target/s390x/insn-data.def
index b8400c191a..add174b793 100644
--- a/target/s390x/insn-data.def
+++ b/target/s390x/insn-data.def
@@ -1090,6 +1090,10 @@
     F(0xe752, VCTZ,    VRR_a, V,   0, 0, 0, 0, vctz, 0, IF_VEC)
 /* VECTOR EXCLUSIVE OR */
     F(0xe76d, VX,      VRR_c, V,   0, 0, 0, 0, vx, 0, IF_VEC)
+/* VECTOR GALOIS FIELD MULTIPLY SUM */
+    F(0xe7b4, VGFM,    VRR_c, V,   0, 0, 0, 0, vgfm, 0, IF_VEC)
+/* VECTOR GALOIS FIELD MULTIPLY SUM AND ACCUMULATE */
+    F(0xe7bc, VGFMA,   VRR_d, V,   0, 0, 0, 0, vgfma, 0, IF_VEC)
 
 #ifndef CONFIG_USER_ONLY
 /* COMPARE AND SWAP AND PURGE */
diff --git a/target/s390x/translate_vx.inc.c b/target/s390x/translate_vx.inc.c
index 85a0f20b90..fe36d027b6 100644
--- a/target/s390x/translate_vx.inc.c
+++ b/target/s390x/translate_vx.inc.c
@@ -1441,3 +1441,41 @@ static DisasJumpType op_vx(DisasContext *s, DisasOps *o)
                  get_field(s->fields, v3));
     return DISAS_NEXT;
 }
+
+static DisasJumpType op_vgfm(DisasContext *s, DisasOps *o)
+{
+    const uint8_t es = get_field(s->fields, m4);
+    static const GVecGen3 g[4] = {
+        { .fno = gen_helper_gvec_vgfm8, },
+        { .fno = gen_helper_gvec_vgfm16, },
+        { .fno = gen_helper_gvec_vgfm32, },
+        { .fno = gen_helper_gvec_vgfm64, },
+    };
+
+    if (es > ES_64) {
+        gen_program_exception(s, PGM_SPECIFICATION);
+        return DISAS_NORETURN;
+    }
+    gen_gvec_3(get_field(s->fields, v1), get_field(s->fields, v2),
+               get_field(s->fields, v3), &g[es]);
+    return DISAS_NEXT;
+}
+
+static DisasJumpType op_vgfma(DisasContext *s, DisasOps *o)
+{
+    const uint8_t es = get_field(s->fields, m5);
+    static const GVecGen4 g[4] = {
+        { .fno = gen_helper_gvec_vgfma8, },
+        { .fno = gen_helper_gvec_vgfma16, },
+        { .fno = gen_helper_gvec_vgfma32, },
+        { .fno = gen_helper_gvec_vgfma64, },
+    };
+
+    if (es > ES_64) {
+        gen_program_exception(s, PGM_SPECIFICATION);
+        return DISAS_NORETURN;
+    }
+    gen_gvec_4(get_field(s->fields, v1), get_field(s->fields, v2),
+               get_field(s->fields, v3), get_field(s->fields, v4), &g[es]);
+    return DISAS_NEXT;
+}
diff --git a/target/s390x/vec_int_helper.c b/target/s390x/vec_int_helper.c
index c589f92765..99dd0653f6 100644
--- a/target/s390x/vec_int_helper.c
+++ b/target/s390x/vec_int_helper.c
@@ -37,6 +37,60 @@ static bool s390_vec_add(S390Vector *d, const S390Vector *a,
     return high_carry;
 }
 
+static bool s390_vec_is_zero(const S390Vector *v)
+{
+    return !v->doubleword[0] && !v->doubleword[1];
+}
+
+static void s390_vec_xor(S390Vector *res, const S390Vector *a,
+                         const S390Vector *b)
+{
+    res->doubleword[0] = a->doubleword[0] ^ b->doubleword[0];
+    res->doubleword[1] = a->doubleword[1] ^ b->doubleword[1];
+}
+
+static void s390_vec_shl(S390Vector *d, const S390Vector *a, uint64_t count)
+{
+    uint64_t tmp;
+
+    g_assert(count < 128);
+    if (count == 0) {
+        d->doubleword[0] = a->doubleword[0];
+        d->doubleword[1] = a->doubleword[1];
+    } else if (count == 64) {
+        d->doubleword[0] = a->doubleword[1];
+        d->doubleword[1] = 0;
+    } else if (count < 64) {
+        tmp = extract64(a->doubleword[1], 64 - count, count);
+        d->doubleword[1] = a->doubleword[1] << count;
+        d->doubleword[0] = (a->doubleword[0] << count) | tmp;
+    } else {
+        d->doubleword[0] = a->doubleword[1] << (count - 64);
+        d->doubleword[1] = 0;
+    }
+}
+
+static void s390_vec_shr(S390Vector *d, const S390Vector *a, uint64_t count)
+{
+    uint64_t tmp;
+
+    g_assert(count < 128);
+    if (count == 0) {
+        d->doubleword[0] = a->doubleword[0];
+        d->doubleword[1] = a->doubleword[1];
+    } else if (count == 64) {
+        d->doubleword[1] = a->doubleword[0];
+        d->doubleword[0] = 0;
+    } else if (count < 64) {
+        tmp = a->doubleword[1] >> count;
+        d->doubleword[1] = deposit64(tmp, 64 - count, count, a->doubleword[0]);
+        d->doubleword[0] = a->doubleword[0] >> count;
+    } else {
+        d->doubleword[1] = a->doubleword[0] >> (count - 64);
+        d->doubleword[0] = 0;
+    }
+}
+
 void HELPER(gvec_vacc128)(void *v1, const void *v2, const void *v3,
                           uint32_t desc)
 {
@@ -121,3 +175,117 @@ void HELPER(gvec_vctz##BITS)(void *v1, const void *v2, uint32_t desc)          \
 }
 DEF_VCTZ(8)
 DEF_VCTZ(16)
+
+/* like binary multiplication, but XOR instead of addition */
+#define DEF_GALOIS_MULTIPLY(BITS, TBITS)                                       \
+static uint##TBITS##_t galois_multiply##BITS(uint##TBITS##_t a,                \
+                                             uint##TBITS##_t b)                \
+{                                                                              \
+    uint##TBITS##_t res = 0;                                                   \
+                                                                               \
+    while (b) {                                                                \
+        if (b & 0x1) {                                                         \
+            res = res ^ a;                                                     \
+        }                                                                      \
+        a = a << 1;                                                            \
+        b = b >> 1;                                                            \
+    }                                                                          \
+    return res;                                                                \
+}
+DEF_GALOIS_MULTIPLY(8, 16)
+DEF_GALOIS_MULTIPLY(16, 32)
+DEF_GALOIS_MULTIPLY(32, 64)
+
+static S390Vector galois_multiply64(uint64_t a, uint64_t b)
+{
+    S390Vector res = {};
+    S390Vector va = {
+        .doubleword[1] = a,
+    };
+    S390Vector vb = {
+        .doubleword[1] = b,
+    };
+
+    while (!s390_vec_is_zero(&vb)) {
+        if (vb.doubleword[1] & 0x1) {
+            s390_vec_xor(&res, &res, &va);
+        }
+        s390_vec_shl(&va, &va, 1);
+        s390_vec_shr(&vb, &vb, 1);
+    }
+    return res;
+}
+
+#define DEF_VGFM(BITS, TBITS)                                                  \
+void HELPER(gvec_vgfm##BITS)(void *v1, const void *v2, const void *v3,         \
+                             uint32_t desc)                                    \
+{                                                                              \
+    int i;                                                                     \
+                                                                               \
+    for (i = 0; i < (128 / TBITS); i++) {                                      \
+        uint##BITS##_t a = s390_vec_read_element##BITS(v2, i * 2);             \
+        uint##BITS##_t b = s390_vec_read_element##BITS(v3, i * 2);             \
+        uint##TBITS##_t d = galois_multiply##BITS(a, b);                       \
+                                                                               \
+        a = s390_vec_read_element##BITS(v2, i * 2 + 1);                        \
+        b = s390_vec_read_element##BITS(v3, i * 2 + 1);                        \
+        d = d ^ galois_multiply32(a, b);                                       \
+        s390_vec_write_element##TBITS(v1, i, d);                               \
+    }                                                                          \
+}
+DEF_VGFM(8, 16)
+DEF_VGFM(16, 32)
+DEF_VGFM(32, 64)
+
+void HELPER(gvec_vgfm64)(void *v1, const void *v2, const void *v3,
+                         uint32_t desc)
+{
+    S390Vector tmp1, tmp2;
+    uint64_t a, b;
+
+    a = s390_vec_read_element64(v2, 0);
+    b = s390_vec_read_element64(v3, 0);
+    tmp1 = galois_multiply64(a, b);
+    a = s390_vec_read_element64(v2, 1);
+    b = s390_vec_read_element64(v3, 1);
+    tmp2 = galois_multiply64(a, b);
+    s390_vec_xor(v1, &tmp1, &tmp2);
+}
+
+#define DEF_VGFMA(BITS, TBITS)                                                 \
+void HELPER(gvec_vgfma##BITS)(void *v1, const void *v2, const void *v3,        \
+                              const void *v4, uint32_t desc)                   \
+{                                                                              \
+    int i;                                                                     \
+                                                                               \
+    for (i = 0; i < (128 / TBITS); i++) {                                      \
+        uint##BITS##_t a = s390_vec_read_element##BITS(v2, i * 2);             \
+        uint##BITS##_t b = s390_vec_read_element##BITS(v3, i * 2);             \
+        uint##TBITS##_t d = galois_multiply##BITS(a, b);                       \
+                                                                               \
+        a = s390_vec_read_element##BITS(v2, i * 2 + 1);                        \
+        b = s390_vec_read_element##BITS(v3, i * 2 + 1);                        \
+        d = d ^ galois_multiply32(a, b);                                       \
+        d = d ^ s390_vec_read_element##TBITS(v4, i);                           \
+        s390_vec_write_element##TBITS(v1, i, d);                               \
+    }                                                                          \
+}
+DEF_VGFMA(8, 16)
+DEF_VGFMA(16, 32)
+DEF_VGFMA(32, 64)
+
+void HELPER(gvec_vgfma64)(void *v1, const void *v2, const void *v3,
+                          const void *v4, uint32_t desc)
+{
+    S390Vector tmp1, tmp2;
+    uint64_t a, b;
+
+    a = s390_vec_read_element64(v2, 0);
+    b = s390_vec_read_element64(v3, 0);
+    tmp1 = galois_multiply64(a, b);
+    a = s390_vec_read_element64(v2, 1);
+    b = s390_vec_read_element64(v3, 1);
+    tmp2 = galois_multiply64(a, b);
+    s390_vec_xor(&tmp1, &tmp1, &tmp2);
+    s390_vec_xor(v1, &tmp1, v4);
+}
