diff --git a/halo2_gadgets/Cargo.toml b/halo2_gadgets/Cargo.toml
index 8299fedbe..5583b5baa 100644
--- a/halo2_gadgets/Cargo.toml
+++ b/halo2_gadgets/Cargo.toml
@@ -43,6 +43,13 @@ goldenfile = "1.5.2"
 criterion = { version = "0.3", features = ["html_reports"] }
 proptest = "1.0.0"
 seq-macro = "0.3.5"
+tempfile = "3.3.0"
+serde = { version = "1.0", features = ["derive"] }
+serde_json = "1.0"
+halo2curves = { git = "https://github.com/davidnevadoc/halo2curves", rev = "33b1d2fe0f4576fde180e171eeab24f3d8573f2e", features = ["bits", "derive_serde"] }
+# More recent versions of halo2curves enable ["pasta_curves/serde"], but our
+# version above is too old so we do it ourselves.
+pasta_curves = { version = "0.5.0", features = ["serde"] }
 
 [target.'cfg(unix)'.dev-dependencies]
 pprof = { version = "0.8", features = ["criterion", "flamegraph"] } # MSRV 1.56
@@ -55,6 +62,7 @@ dev-graph = ["halo2_proofs/dev-graph", "plotters"]
 circuit-params = ["halo2_proofs/circuit-params"]
 test-dependencies = ["proptest"]
 unstable = []
+cache-test-data = []
 
 [[bench]]
 name = "duplex"
diff --git a/halo2_gadgets/data/.gitattributes b/halo2_gadgets/data/.gitattributes
new file mode 100644
index 000000000..568262a8a
--- /dev/null
+++ b/halo2_gadgets/data/.gitattributes
@@ -0,0 +1 @@
+*.json binary
diff --git a/halo2_gadgets/data/README.md b/halo2_gadgets/data/README.md
new file mode 100644
index 000000000..33f012771
--- /dev/null
+++ b/halo2_gadgets/data/README.md
@@ -0,0 +1,7 @@
+This directory contains cached data used to speed up testing.
+
+The various `*fixed_point*.json` files are used to test fixed-base scalar multiplication. They are generated by running
+
+    cargo test -p halo2_gadgets cache_to_disk --features cache-test-data
+
+Warning: the full generation process is very slow, and took 17.5 hours on a 4 core Intel(R) Core(TM) i7-3520M CPU @ 2.90GHz with 16GB memory.
diff --git a/halo2_gadgets/data/eris_fixed_point_full.json b/halo2_gadgets/data/eris_fixed_point_full.json
new file mode 100644
index 000000000..ec7751d48
--- /dev/null
+++ b/halo2_gadgets/data/eris_fixed_point_full.json
@@ -0,0 +1 @@
+{"base":{"x":[16140848687369682959,3303000518133785677,7336339510640278931,18427053380302822210,15580445869929480324,1287220256266755429,2017612633062120448],"y":[16141072163108028367,278244751655364421,4319631844929734636,17281284067257564233,15512155490251416755,14241824569904817211,2017612633061530623]},"window_table":[[{"x":[141290146602931731,58169950517920144,8285739647965887213,1022447834604400972,17646577696771475320,11829202021308221904,1099981231435818025],"y":[12396109151202639772,15836570097909523174,14541106567469763716,14325922910344642127,12446541053519477231,16312224563545191435,621838129307739246]},{"x":[18345169745262495399,17059909907975099459,938534746051351514,14777290739238400882,10837879793859500128,4482824305312618945,599720334907459065],"y":[9803547579527930175,2838678288379469544,17061541883742547164,1712969047521934972,12416096576492547137,13152761240962065498,4902795729721253]},{"x":[2140391820397556318,12068357661938132938,10759026476134764069,8941374032090941033,358797649403898813,11143619397334881679,1574698191752137352],"y":[2191362570323914243,2449873677727089401,8762421211568703558,1529580879030784930,16203751102029516317,7697650513391213850,302183519404431632]},{"x":[8836901710214284669,11597851954865168569,6581538873967667061,3757981805636115656,7835222055981200330,16973307789193875100,1852220075680626275],"y":[18024166885699351142,14698748114529525377,5006557746199262276,17946415337648543270,17525393171564734562,10980011002772205782,1016520340178190438]},{"x":[7092380113072051022,8445816105733544806,5619532151828842583,1767599945316516777,3769262365513351142,2262731151357331486,1958747570827102332],"y":[11229368315337269389,6921538045549581420,6829859041492588677,2753811078143323661,10032738841866266708,8358107222146753412,969891662705783103]},{"x":[18239209866256723175,3916712609693285331,9768557937839647737,13091250973564830263,15202872039097949217,11436635869273711508,59091914665662362],"y":[6202866603754070444,8616218117316169794,8766283813489882290,3370627778343850592,3563105255101779564,13950231181265867798,796614627641126611]},{"x":[11614415388489562380,11554516650922406937,9206652815102680298,11314969403307313452,6349784866280329248,8216839725699032440,1799840364482048304],"y":[15861015331277261634,5626101402372695137,3063298073660207424,17388172537584878919,14333120042945144370,1088680757879574412,2153178795859819909]},{"x":[12264555454338484914,17389293811173262971,1782637754471668261,12980128034774520403,1717019328938384253,1615648933887834411,627014445117135536],"y":[1057548267751216257,4797163311589939082,632712044486965802,12326350262673364398,16963132530168306716,1268631848286925270,284458315509738062]}],[{"x":[13822868821981143070,195456041741322589,9276100574707220668,1158767948776093352,10690939826794995473,6392493154874025797,2002110076651380506],"y":[13666662611530512968,14589162957521228322,16722098570277418857,6336849318554696779,11385913172149490595,7421362302071635589,1878743955341638832]},{"x":[12958493468703281366,6712468510850451154,3743619234214055099,15448007355495600892,10070474867432829595,10554368511630303231,2509238673158649606],"y":[1057186906824077870,12409038015446325134,17845763806775634202,7132776929309983338,8698892720530747203,1774002201492656368,2520760723252397743]},{"x":[5037449596040758526,7681642385585821726,15757657362752558058,6287972242542520172,13199930058768097122,9252687211416895521,562112960335182557],"y":[18018345315556500051,3624170455637966887,5593877609744108036,16400186904402656926,1918502952785735004,15825439777231008448,1013654609684617314]},{"x":[10480676877801723528,2700537510674417868,1579651520500064574,9934133585988219741,8739894575774392489,9228295382715282284,2356880912936467740],"y":[16586073158029838154,11406107003683695828,479031197755203056,11775122048677934087,6433860639266825925,12368216633600123533,223946380061069118]},{"x":[16985240031791747045,9586524170314671849,7288391546777747457,11262993415457125293,11822400003875877835,1179267184541088014,970580222605097576],"y":[9622249067627738945,2426471604862764933,5259984887668250057,2717625330356259318,12434604487546510206,3410887762682018660,570833002719210645]},{"x":[10328949610018628840,16456066470774438169,12692876757914324233,8507114404185199031,15826505856830672438,6090936782661383618,669258511564160468],"y":[16177383084358407884,15588846688256382882,17398366024891061443,12222483881272741728,12163269464782395453,11761701322393422634,891388516429600361]},{"x":[12442556344105928865,1087000330543539880,11457399518309619986,12406219253625387431,10665674159768524541,2223940925534474774,2098561203800585239],"y":[13600225333608843745,9895149202107615434,8268896914681227346,5012325763147512603,2725740732642896352,4168979433511384615,1824142225550534246]},{"x":[12082012141577988497,10664628112375761765,16052206494681669393,243077311379514706,11389860754510511758,11699956773486886826,2165631884927046882],"y":[17472651080127992060,10588750564225466089,10477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\ No newline at end of file
diff --git a/halo2_gadgets/data/eris_fixed_point_short.json b/halo2_gadgets/data/eris_fixed_point_short.json
new file mode 100644
index 000000000..65cdb123e
--- /dev/null
+++ b/halo2_gadgets/data/eris_fixed_point_short.json
@@ -0,0 +1 @@
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\ No newline at end of file
diff --git a/halo2_gadgets/data/pallas_fixed_point_full.json b/halo2_gadgets/data/pallas_fixed_point_full.json
new file mode 100644
index 000000000..907dfbf76
--- /dev/null
+++ b/halo2_gadgets/data/pallas_fixed_point_full.json
@@ -0,0 +1 @@
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\ No newline at end of file
diff --git a/halo2_gadgets/data/pallas_fixed_point_short.json b/halo2_gadgets/data/pallas_fixed_point_short.json
new file mode 100644
index 000000000..d9d3f296a
--- /dev/null
+++ b/halo2_gadgets/data/pallas_fixed_point_short.json
@@ -0,0 +1 @@
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\ No newline at end of file
diff --git a/halo2_gadgets/data/pluto_fixed_point_full.json b/halo2_gadgets/data/pluto_fixed_point_full.json
new file mode 100644
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@@ -0,0 +1 @@
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\ No newline at end of file
diff --git a/halo2_gadgets/data/pluto_fixed_point_short.json b/halo2_gadgets/data/pluto_fixed_point_short.json
new file mode 100644
index 000000000..f79c1a3ac
--- /dev/null
+++ b/halo2_gadgets/data/pluto_fixed_point_short.json
@@ -0,0 +1 @@
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\ No newline at end of file
diff --git a/halo2_gadgets/data/vesta_fixed_point_full.json b/halo2_gadgets/data/vesta_fixed_point_full.json
new file mode 100644
index 000000000..0f7c92ae3
--- /dev/null
+++ b/halo2_gadgets/data/vesta_fixed_point_full.json
@@ -0,0 +1 @@
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\ No newline at end of file
diff --git a/halo2_gadgets/data/vesta_fixed_point_short.json b/halo2_gadgets/data/vesta_fixed_point_short.json
new file mode 100644
index 000000000..0a0ba12a5
--- /dev/null
+++ b/halo2_gadgets/data/vesta_fixed_point_short.json
@@ -0,0 +1 @@
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\ No newline at end of file
diff --git a/halo2_gadgets/src/ecc.rs b/halo2_gadgets/src/ecc.rs
index eaed62cd5..6d6ec7b2c 100644
--- a/halo2_gadgets/src/ecc.rs
+++ b/halo2_gadgets/src/ecc.rs
@@ -637,12 +637,13 @@ pub(crate) mod tests {
 
     use super::{
         chip::{
-            find_zs_and_us, BaseFieldElem, EccChip, EccConfig, EccCurve, EccField, FixedPoint,
-            FullScalar, ShortScalar, H, NUM_WINDOWS_SHORT,
+            BaseFieldElem, EccChip, EccConfig, EccCurve, EccField, FixedPoint, FullScalar,
+            ShortScalar, H, NUM_WINDOWS_SHORT,
         },
         FixedPoints,
     };
     use crate::ecc::chip::mul_fixed::FbsmCurve;
+    use crate::ecc::chip::{compute_lagrange_coeffs, constants::serialize::CachedFixedPoint};
     use crate::utilities::{lookup_range_check::LookupRangeCheckConfig, pluto_eris::*};
 
     #[derive(Debug, Eq, PartialEq, Clone)]
@@ -653,45 +654,97 @@ pub(crate) mod tests {
     pub(crate) struct FullWidth<C: FbsmCurve> {
         base: C,
         zs_and_us: &'static [(u64, [C::Base; H])],
+        lagrange_coeffs: Vec<[C::Base; H]>,
     }
     #[derive(Debug, Eq, PartialEq, Clone)]
     pub(crate) struct BaseField<C: FbsmCurve> {
         base: C,
         zs_and_us: &'static [(u64, [C::Base; H])],
+        lagrange_coeffs: Vec<[C::Base; H]>,
     }
     #[derive(Debug, Eq, PartialEq, Clone)]
     pub(crate) struct Short<C: FbsmCurve> {
         base: C,
         zs_and_us: &'static [(u64, [C::Base; H])],
+        lagrange_coeffs: Vec<[C::Base; H]>,
     }
 
+    // Read very expensive test data from cache on disk.
     lazy_static! {
         static ref PALLAS_BASE: pallas::Affine = pallas::Point::generator().to_affine();
         static ref PALLAS_ZS_AND_US: Vec<(u64, [pallas::Base; H])> =
-            find_zs_and_us(*PALLAS_BASE, pallas::Affine::NUM_WINDOWS_FULL).unwrap();
+            CachedFixedPoint::read_zs_and_us_from_disk_and_verify(
+                *PALLAS_BASE,
+                pallas::Affine::NUM_WINDOWS_FULL,
+                "pallas_fixed_point_full",
+            );
         static ref PALLAS_ZS_AND_US_SHORT: Vec<(u64, [pallas::Base; H])> =
-            find_zs_and_us(*PALLAS_BASE, NUM_WINDOWS_SHORT).unwrap();
+            CachedFixedPoint::read_zs_and_us_from_disk_and_verify(
+                *PALLAS_BASE,
+                NUM_WINDOWS_SHORT,
+                "pallas_fixed_point_short",
+            );
+        static ref PALLAS_LAGRANGE_COEFFS_FULL: Vec<[pallas::Base; H]> =
+            compute_lagrange_coeffs(*PALLAS_BASE, pallas::Affine::NUM_WINDOWS_FULL);
+        static ref PALLAS_LAGRANGE_COEFFS_SHORT: Vec<[pallas::Base; H]> =
+            compute_lagrange_coeffs(*PALLAS_BASE, NUM_WINDOWS_SHORT);
     }
     lazy_static! {
         static ref VESTA_BASE: vesta::Affine = vesta::Point::generator().to_affine();
         static ref VESTA_ZS_AND_US: Vec<(u64, [vesta::Base; H])> =
-            find_zs_and_us(*VESTA_BASE, vesta::Affine::NUM_WINDOWS_FULL).unwrap();
+            CachedFixedPoint::read_zs_and_us_from_disk_and_verify(
+                *VESTA_BASE,
+                vesta::Affine::NUM_WINDOWS_FULL,
+                "vesta_fixed_point_full",
+            );
         static ref VESTA_ZS_AND_US_SHORT: Vec<(u64, [vesta::Base; H])> =
-            find_zs_and_us(*VESTA_BASE, NUM_WINDOWS_SHORT).unwrap();
+            CachedFixedPoint::read_zs_and_us_from_disk_and_verify(
+                *VESTA_BASE,
+                NUM_WINDOWS_SHORT,
+                "vesta_fixed_point_short",
+            );
+        static ref VESTA_LAGRANGE_COEFFS_FULL: Vec<[vesta::Base; H]> =
+            compute_lagrange_coeffs(*VESTA_BASE, vesta::Affine::NUM_WINDOWS_FULL);
+        static ref VESTA_LAGRANGE_COEFFS_SHORT: Vec<[vesta::Base; H]> =
+            compute_lagrange_coeffs(*VESTA_BASE, NUM_WINDOWS_SHORT);
     }
     lazy_static! {
         static ref PLUTO_BASE: pluto::Affine = pluto::Point::generator().to_affine();
         static ref PLUTO_ZS_AND_US: Vec<(u64, [pluto::Base; H])> =
-            find_zs_and_us(*PLUTO_BASE, pluto::Affine::NUM_WINDOWS_FULL).unwrap();
+            CachedFixedPoint::read_zs_and_us_from_disk_and_verify(
+                *PLUTO_BASE,
+                pluto::Affine::NUM_WINDOWS_FULL,
+                "pluto_fixed_point_full",
+            );
         static ref PLUTO_ZS_AND_US_SHORT: Vec<(u64, [pluto::Base; H])> =
-            find_zs_and_us(*PLUTO_BASE, NUM_WINDOWS_SHORT).unwrap();
+            CachedFixedPoint::read_zs_and_us_from_disk_and_verify(
+                *PLUTO_BASE,
+                NUM_WINDOWS_SHORT,
+                "pluto_fixed_point_short",
+            );
+        static ref PLUTO_LAGRANGE_COEFFS_FULL: Vec<[pluto::Base; H]> =
+            compute_lagrange_coeffs(*PLUTO_BASE, pluto::Affine::NUM_WINDOWS_FULL);
+        static ref PLUTO_LAGRANGE_COEFFS_SHORT: Vec<[pluto::Base; H]> =
+            compute_lagrange_coeffs(*PLUTO_BASE, NUM_WINDOWS_SHORT);
     }
     lazy_static! {
         static ref ERIS_BASE: eris::Affine = eris::Point::generator().to_affine();
         static ref ERIS_ZS_AND_US: Vec<(u64, [eris::Base; H])> =
-            find_zs_and_us(*ERIS_BASE, eris::Affine::NUM_WINDOWS_FULL).unwrap();
+            CachedFixedPoint::read_zs_and_us_from_disk_and_verify(
+                *ERIS_BASE,
+                eris::Affine::NUM_WINDOWS_FULL,
+                "eris_fixed_point_full",
+            );
         static ref ERIS_ZS_AND_US_SHORT: Vec<(u64, [eris::Base; H])> =
-            find_zs_and_us(*ERIS_BASE, NUM_WINDOWS_SHORT).unwrap();
+            CachedFixedPoint::read_zs_and_us_from_disk_and_verify(
+                *ERIS_BASE,
+                NUM_WINDOWS_SHORT,
+                "eris_fixed_point_short",
+            );
+        static ref ERIS_LAGRANGE_COEFFS_FULL: Vec<[eris::Base; H]> =
+            compute_lagrange_coeffs(*ERIS_BASE, eris::Affine::NUM_WINDOWS_FULL);
+        static ref ERIS_LAGRANGE_COEFFS_SHORT: Vec<[eris::Base; H]> =
+            compute_lagrange_coeffs(*ERIS_BASE, NUM_WINDOWS_SHORT);
     }
 
     /// A fixed point that can be computed from a distinguished generator.
@@ -702,7 +755,12 @@ pub(crate) mod tests {
     impl<C: FbsmCurve> FullWidth<C> {
         pub(crate) fn from_parts(base: C, zs_and_us: &'static [(u64, [C::Base; H])]) -> Self {
             assert_eq!(zs_and_us.len(), Self::NUM_WINDOWS);
-            FullWidth { base, zs_and_us }
+            let lagrange_coeffs = compute_lagrange_coeffs(base, Self::NUM_WINDOWS);
+            FullWidth {
+                base,
+                zs_and_us,
+                lagrange_coeffs,
+            }
         }
     }
 
@@ -716,6 +774,10 @@ pub(crate) mod tests {
         fn zs_and_us(&self) -> &'static [(u64, [C::Base; H])] {
             self.zs_and_us
         }
+
+        fn lagrange_coeffs(&self) -> Vec<[C::Base; H]> {
+            self.lagrange_coeffs.clone()
+        }
     }
 
     impl FromGenerator<pallas::Affine> for FullWidth<pallas::Affine> {
@@ -723,6 +785,7 @@ pub(crate) mod tests {
             FullWidth {
                 base: *PALLAS_BASE,
                 zs_and_us: &PALLAS_ZS_AND_US,
+                lagrange_coeffs: PALLAS_LAGRANGE_COEFFS_FULL.to_vec(),
             }
         }
     }
@@ -732,6 +795,7 @@ pub(crate) mod tests {
             FullWidth {
                 base: *VESTA_BASE,
                 zs_and_us: &VESTA_ZS_AND_US,
+                lagrange_coeffs: VESTA_LAGRANGE_COEFFS_FULL.to_vec(),
             }
         }
     }
@@ -741,6 +805,7 @@ pub(crate) mod tests {
             FullWidth {
                 base: *PLUTO_BASE,
                 zs_and_us: &PLUTO_ZS_AND_US,
+                lagrange_coeffs: PLUTO_LAGRANGE_COEFFS_FULL.to_vec(),
             }
         }
     }
@@ -750,6 +815,7 @@ pub(crate) mod tests {
             FullWidth {
                 base: *ERIS_BASE,
                 zs_and_us: &ERIS_ZS_AND_US,
+                lagrange_coeffs: ERIS_LAGRANGE_COEFFS_FULL.to_vec(),
             }
         }
     }
@@ -757,7 +823,12 @@ pub(crate) mod tests {
     impl<C: FbsmCurve> BaseField<C> {
         pub(crate) fn from_parts(base: C, zs_and_us: &'static [(u64, [C::Base; H])]) -> Self {
             assert_eq!(zs_and_us.len(), Self::NUM_WINDOWS);
-            BaseField { base, zs_and_us }
+            let lagrange_coeffs = compute_lagrange_coeffs(base, Self::NUM_WINDOWS);
+            BaseField {
+                base,
+                zs_and_us,
+                lagrange_coeffs,
+            }
         }
     }
 
@@ -771,6 +842,10 @@ pub(crate) mod tests {
         fn zs_and_us(&self) -> &'static [(u64, [C::Base; H])] {
             self.zs_and_us
         }
+
+        fn lagrange_coeffs(&self) -> Vec<[C::Base; H]> {
+            self.lagrange_coeffs.clone()
+        }
     }
 
     impl FromGenerator<pallas::Affine> for BaseField<pallas::Affine> {
@@ -778,6 +853,7 @@ pub(crate) mod tests {
             BaseField {
                 base: *PALLAS_BASE,
                 zs_and_us: &PALLAS_ZS_AND_US,
+                lagrange_coeffs: PALLAS_LAGRANGE_COEFFS_FULL.to_vec(),
             }
         }
     }
@@ -787,6 +863,7 @@ pub(crate) mod tests {
             BaseField {
                 base: *VESTA_BASE,
                 zs_and_us: &VESTA_ZS_AND_US,
+                lagrange_coeffs: VESTA_LAGRANGE_COEFFS_FULL.to_vec(),
             }
         }
     }
@@ -796,6 +873,7 @@ pub(crate) mod tests {
             BaseField {
                 base: *PLUTO_BASE,
                 zs_and_us: &PLUTO_ZS_AND_US,
+                lagrange_coeffs: PLUTO_LAGRANGE_COEFFS_FULL.to_vec(),
             }
         }
     }
@@ -805,6 +883,7 @@ pub(crate) mod tests {
             BaseField {
                 base: *ERIS_BASE,
                 zs_and_us: &ERIS_ZS_AND_US,
+                lagrange_coeffs: ERIS_LAGRANGE_COEFFS_FULL.to_vec(),
             }
         }
     }
@@ -812,7 +891,12 @@ pub(crate) mod tests {
     impl<C: FbsmCurve> Short<C> {
         pub(crate) fn from_parts(base: C, zs_and_us: &'static [(u64, [C::Base; H])]) -> Self {
             assert_eq!(zs_and_us.len(), Self::NUM_WINDOWS);
-            Short { base, zs_and_us }
+            let lagrange_coeffs = compute_lagrange_coeffs(base, Self::NUM_WINDOWS);
+            Short {
+                base,
+                zs_and_us,
+                lagrange_coeffs,
+            }
         }
     }
 
@@ -826,6 +910,10 @@ pub(crate) mod tests {
         fn zs_and_us(&self) -> &'static [(u64, [C::Base; H])] {
             self.zs_and_us
         }
+
+        fn lagrange_coeffs(&self) -> Vec<[C::Base; H]> {
+            self.lagrange_coeffs.clone()
+        }
     }
 
     impl FromGenerator<pallas::Affine> for Short<pallas::Affine> {
@@ -833,6 +921,7 @@ pub(crate) mod tests {
             Short {
                 base: *PALLAS_BASE,
                 zs_and_us: &PALLAS_ZS_AND_US_SHORT,
+                lagrange_coeffs: PALLAS_LAGRANGE_COEFFS_SHORT.to_vec(),
             }
         }
     }
@@ -842,6 +931,7 @@ pub(crate) mod tests {
             Short {
                 base: *VESTA_BASE,
                 zs_and_us: &VESTA_ZS_AND_US_SHORT,
+                lagrange_coeffs: VESTA_LAGRANGE_COEFFS_SHORT.to_vec(),
             }
         }
     }
@@ -851,6 +941,7 @@ pub(crate) mod tests {
             Short {
                 base: *PLUTO_BASE,
                 zs_and_us: &PLUTO_ZS_AND_US_SHORT,
+                lagrange_coeffs: PLUTO_LAGRANGE_COEFFS_SHORT.to_vec(),
             }
         }
     }
@@ -860,6 +951,7 @@ pub(crate) mod tests {
             Short {
                 base: *ERIS_BASE,
                 zs_and_us: &ERIS_ZS_AND_US_SHORT,
+                lagrange_coeffs: ERIS_LAGRANGE_COEFFS_SHORT.to_vec(),
             }
         }
     }
diff --git a/halo2_gadgets/src/ecc/chip/constants.rs b/halo2_gadgets/src/ecc/chip/constants.rs
index 1928c31a7..49ac4bfb5 100644
--- a/halo2_gadgets/src/ecc/chip/constants.rs
+++ b/halo2_gadgets/src/ecc/chip/constants.rs
@@ -118,6 +118,20 @@ pub fn find_zs_and_us<C: CurveAffine>(
             .iter()
             .map(|point| *point.coordinates().unwrap().y())
             .collect();
+        // This search should take `2^(2*H)` iterations on average: half the
+        // points in the field are squares, and assuming the `ys = {y_i}_i` are
+        // uniform random, each `y_i + z` and `-y_i + z` has a 1/2 chance of
+        // being a square. Pretending these are indep, and noting there are `H`
+        // points `y_i`, we get a `1/2^(2*H)` chance that all `y_i + z` are
+        // squares while at the same time no `-y_i + z` are squares. So, on
+        // average we will succeed after `2^(2*H)` iterations.
+        //
+        // The probability of failure after `1000*(2^(2*H))` iterations here is
+        // negligible, less than `(1/e)^1000`, using the bound
+        //
+        //     (1 - x) \le 1/e^x,
+        //
+        // which is true for all non-negative `x`.
         (0..(1000 * (1 << (2 * H)))).find_map(|z| {
             ys.iter()
                 .map(|&y| {
@@ -135,7 +149,11 @@ pub fn find_zs_and_us<C: CurveAffine>(
     let window_table = compute_window_table(base, num_windows);
     window_table
         .iter()
-        .map(|window_points| find_z_and_us(window_points))
+        .enumerate()
+        .map(|(i, window_points)| {
+            println!("Finding z and u's for window {}/{}...", i + 1, num_windows);
+            find_z_and_us(window_points)
+        })
         .collect()
 }
 
@@ -272,3 +290,208 @@ mod tests {
         }
     }
 }
+
+#[cfg(test)]
+pub(crate) mod serialize {
+    use halo2curves::pasta::pallas;
+    use serde::{Deserialize, Serialize};
+    use serde_json;
+    use std::{
+        env,
+        fs::File,
+        io,
+        path::{Path, PathBuf},
+    };
+
+    use super::*;
+    use crate::ecc::chip::FbsmCurve;
+
+    /// The data needed to compute an [`crate::ecc::chip::FixedPoint`] for a
+    /// given base and number of windows.
+    #[derive(Serialize, Deserialize, Debug, Eq, PartialEq)]
+    pub(crate) struct CachedFixedPoint<C: FbsmCurve>
+    where
+        C::Base: Serialize + for<'a> Deserialize<'a>,
+    {
+        base: C,
+        window_table: Vec<[C; H]>,
+        zs_and_us: Vec<(u64, [C::Base; H])>,
+    }
+
+    impl<C: FbsmCurve> CachedFixedPoint<C>
+    where
+        C: Serialize + for<'a> Deserialize<'a>,
+        C::Base: Serialize + for<'a> Deserialize<'a>,
+    {
+        /// Read `CachedFixedPoint` from disk and verify that it matches the
+        /// given parameters. Returns `zs_and_us`.
+        ///
+        /// Panics on failure.
+        pub(crate) fn read_zs_and_us_from_disk_and_verify(
+            base: C,
+            num_windows: usize,
+            name: &str,
+        ) -> Vec<(u64, [C::Base; H])> {
+            let file = CachedFixedPoint::<C>::get_cache_file_path(name);
+            let cache = CachedFixedPoint::<C>::read_from_disk(&file).unwrap();
+            assert_eq!(cache.base, base);
+            assert_eq!(cache.window_table.len(), num_windows);
+            assert_eq!(cache.zs_and_us.len(), num_windows);
+            cache.zs_and_us
+        }
+
+        /// Read a `CachedFixedPoint` from a file in `serde_json` format.
+        fn read_from_disk(file: &Path) -> io::Result<Self> {
+            let f = File::open(file)?;
+            let instance = serde_json::from_reader(f)
+                .map_err(|e| io::Error::new(io::ErrorKind::InvalidData, e))?;
+            Ok(instance)
+        }
+
+        /// Write a `CachedFixedPoint` to a file in `serde_json` format.
+        fn write_to_disk(&self, file: &Path) -> io::Result<()> {
+            let f = File::create(file)?;
+            serde_json::to_writer(f, &self).map_err(|e| io::Error::new(io::ErrorKind::Other, e))
+        }
+
+        /// Generate the cache file path for a given cache name.
+        fn get_cache_file_path(name: &str) -> PathBuf {
+            let manifest_dir = env::var("CARGO_MANIFEST_DIR").unwrap();
+            Path::new(&manifest_dir).join(format!("data/{name}.json"))
+        }
+
+        /// Generate and cache a `CachedFixedPoint` for a given base and number of windows.
+        fn cache_fixed_point(base: C, num_windows: usize, name: &str) -> io::Result<()> {
+            let file = CachedFixedPoint::<C>::get_cache_file_path(name);
+            if file.exists() {
+                println!(
+                    r"
+WARNING: Cache file
+
+    {}
+
+already exists! To avoid accidentally rerunning the expensive generation
+process, you must manually remove the existing cache file if you really want to
+proceed with generation.",
+                    file.display()
+                );
+                return Ok(());
+            }
+
+            let window_table = compute_window_table(base, num_windows);
+            let zs_and_us = find_zs_and_us(base, num_windows).unwrap();
+            let cache = CachedFixedPoint {
+                base,
+                window_table,
+                zs_and_us,
+            };
+            cache.write_to_disk(&file)
+        }
+    }
+
+    /// This module implements the caching of the expensive fbsm test
+    /// values. The `#[test]` functions in this module are not actual tests --
+    /// rather, they exist only to compute data used by other tests -- but
+    /// they're implemented as tests instead of a separate `[[bin]]` target
+    /// because this is much simpler than defining a seprate `[[bin]]` target:
+    ///
+    /// - we get parallelism for free and don't have to worry about command line
+    ///   arguments;
+    ///
+    /// - we don't have to worry about duplicating dependencies between dev and
+    ///   non-dev;
+    ///
+    /// This code is only ever expected to be run once, unless/until more curves
+    /// are added in the future.
+    ///
+    /// On a 4 core Intel(R) Core(TM) i7-3520M CPU @ 2.90GHz with 16GB memory
+    /// this generation process took about 17.5 hours, and on the beefier CI
+    /// machines 8 or 9 hours.
+    #[cfg(feature = "cache-test-data")]
+    mod cache_to_disk {
+        use super::*;
+        use crate::utilities::pluto_eris::{eris, pluto};
+        use halo2curves::pasta::{pallas, vesta};
+
+        fn cache_fixed_point_full<C: FbsmCurve>(name: &str) -> io::Result<()>
+        where
+            C: Serialize + for<'a> Deserialize<'a>,
+            C::Base: Serialize + for<'a> Deserialize<'a>,
+        {
+            let base = <C::CurveExt as group::Group>::generator().to_affine();
+            CachedFixedPoint::cache_fixed_point(base, C::NUM_WINDOWS_FULL, name)
+        }
+
+        fn cache_fixed_point_short<C: FbsmCurve>(name: &str) -> io::Result<()>
+        where
+            C: Serialize + for<'a> Deserialize<'a>,
+            C::Base: Serialize + for<'a> Deserialize<'a>,
+        {
+            let base = <C::CurveExt as group::Group>::generator().to_affine();
+            CachedFixedPoint::cache_fixed_point(base, NUM_WINDOWS_SHORT, name)
+        }
+
+        #[test]
+        fn pallas_cache_fixed_point_full() {
+            cache_fixed_point_full::<pallas::Affine>("pallas_fixed_point_full").unwrap();
+        }
+        #[test]
+        fn vesta_cache_fixed_point_full() {
+            cache_fixed_point_full::<vesta::Affine>("vesta_fixed_point_full").unwrap();
+        }
+        #[test]
+        fn pluto_cache_fixed_point_full() {
+            cache_fixed_point_full::<pluto::Affine>("pluto_fixed_point_full").unwrap();
+        }
+        #[test]
+        fn eris_cache_fixed_point_full() {
+            cache_fixed_point_full::<eris::Affine>("eris_fixed_point_full").unwrap();
+        }
+        #[test]
+        fn pallas_cache_fixed_point_short() {
+            cache_fixed_point_short::<pallas::Affine>("pallas_fixed_point_short").unwrap();
+        }
+        #[test]
+        fn vesta_cache_fixed_point_short() {
+            cache_fixed_point_short::<vesta::Affine>("vesta_fixed_point_short").unwrap();
+        }
+        #[test]
+        fn pluto_cache_fixed_point_short() {
+            cache_fixed_point_short::<pluto::Affine>("pluto_fixed_point_short").unwrap();
+        }
+        #[test]
+        fn eris_cache_fixed_point_short() {
+            cache_fixed_point_short::<eris::Affine>("eris_fixed_point_short").unwrap();
+        }
+    }
+
+    #[cfg(test)]
+    mod tests {
+        use group::Group;
+
+        use super::*;
+
+        /// Test that we can serialize and deserialize a `CachedFixedPoint` and
+        /// get back what we started with.
+        #[test]
+        #[ignore = "slow: ~1 minute"]
+        fn round_trip_serialize_cached_fixed_point() {
+            // Use minimum number of windows to make this fast; using one window
+            // is not supported by the window-table generation code.
+            const NUM_WINDOWS: usize = 2;
+            let base = pallas::Point::random(rand::rngs::OsRng);
+            let window_table = compute_window_table(base.to_affine(), NUM_WINDOWS);
+            let zs_and_us = find_zs_and_us(base.to_affine(), NUM_WINDOWS).unwrap();
+            let cached = CachedFixedPoint {
+                base: base.to_affine(),
+                window_table,
+                zs_and_us,
+            };
+
+            let file = tempfile::NamedTempFile::new().unwrap();
+            cached.write_to_disk(file.path()).unwrap();
+            let deserialized = CachedFixedPoint::read_from_disk(file.path()).unwrap();
+            assert_eq!(cached, deserialized);
+        }
+    }
+}
diff --git a/halo2_gadgets/src/ecc/chip/mul_fixed.rs b/halo2_gadgets/src/ecc/chip/mul_fixed.rs
index 66173add1..c3723cf43 100644
--- a/halo2_gadgets/src/ecc/chip/mul_fixed.rs
+++ b/halo2_gadgets/src/ecc/chip/mul_fixed.rs
@@ -875,78 +875,51 @@ pub mod tests {
         }
     }
 
-    // Test both base-field and scalar-field fbsm.
-    //
-    // We combine these into one function, since both base-field and
-    // scalar-field use the same `find_zs_and_us` output behind the scenes, the
-    // computation of which takes about 8 - 16 hours (depending on computer
-    // used; the computation is deterministic), so combining these into a single
-    // test avoids computing that expensive input twice. Better would be to
-    // cache the expensive input, since it's computed out of circuit anyway ...
-    fn test_base_field_and_full_width<C: FbsmCurve>(
-        base_base: BaseField<C>,
-        full_width_base: FullWidth<C>,
-    ) where
-        C::Base: ScalarOrBase<C> + PrimeFieldBits + FromUniformBytes<64>,
-        C::Scalar: ScalarOrBase<C> + PrimeFieldBits + FromUniformBytes<64>,
-    {
-        test_base_field(base_base);
-        test_full_width(full_width_base);
+    #[test]
+    fn pallas_base_field_fbsm() {
+        test_base_field::<pallas::Affine>(BaseField::from_generator())
     }
-
     #[test]
-    #[ignore] // Slow (10+ minutes)
-    fn pallas_base_field_and_full_width_fbsm() {
-        test_base_field_and_full_width::<pallas::Affine>(
-            BaseField::from_generator(),
-            FullWidth::from_generator(),
-        )
+    fn pallas_full_width_fbsm() {
+        test_full_width::<pallas::Affine>(FullWidth::from_generator())
     }
-
     #[test]
-    #[ignore] // Slow (10+ minutes)
-    fn vesta_base_field_and_full_width_fbsm() {
-        test_base_field_and_full_width::<vesta::Affine>(
-            BaseField::from_generator(),
-            FullWidth::from_generator(),
-        )
+    fn vesta_base_field_fbsm() {
+        test_base_field::<vesta::Affine>(BaseField::from_generator())
     }
-
     #[test]
-    #[ignore] // Slow (8+ hours)
-    fn pluto_base_field_and_full_width_fbsm() {
-        test_base_field_and_full_width::<pluto::Affine>(
-            BaseField::from_generator(),
-            FullWidth::from_generator(),
-        )
+    fn vesta_full_width_fbsm() {
+        test_full_width::<vesta::Affine>(FullWidth::from_generator())
     }
-
     #[test]
-    #[ignore] // Slow (8+ hours)
-    fn eris_base_field_and_full_width_fbsm() {
-        test_base_field_and_full_width::<eris::Affine>(
-            BaseField::from_generator(),
-            FullWidth::from_generator(),
-        )
+    fn pluto_base_field_fbsm() {
+        test_base_field::<pluto::Affine>(BaseField::from_generator())
+    }
+    #[test]
+    fn pluto_full_width_fbsm() {
+        test_full_width::<pluto::Affine>(FullWidth::from_generator())
+    }
+    #[test]
+    fn eris_base_field_fbsm() {
+        test_base_field::<eris::Affine>(BaseField::from_generator())
+    }
+    #[test]
+    fn eris_full_width_fbsm() {
+        test_full_width::<eris::Affine>(FullWidth::from_generator())
     }
-
     #[test]
-    #[ignore] // Slow (10+ minutes)
     fn pallas_short_fbsm() {
         test_short::<pallas::Affine>(Short::from_generator())
     }
     #[test]
-    #[ignore] // Slow (10+ minutes)
     fn vesta_short_fbsm() {
         test_short::<vesta::Affine>(Short::from_generator())
     }
     #[test]
-    #[ignore] // Slow (10+ minutes)
     fn pluto_short_fbsm() {
         test_short::<pluto::Affine>(Short::from_generator())
     }
     #[test]
-    #[ignore] // Slow (10+ minutes)
     fn eris_short_fbsm() {
         test_short::<eris::Affine>(Short::from_generator())
     }