Start with Elliptic Curve point math. Slow, but it works.

test-generator/Database.hs

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+module Database(
+         Database,
+         emptyDatabase,
+         generateNum, genSign
+       )
+ where
+
+import           Crypto.Random(DRG(..),SystemDRG)
+import           Data.Bits(shiftL,testBit)
+import qualified Data.ByteString as S
+import           Data.Map.Strict(Map)
+import qualified Data.Map.Strict as Map
+
+type Database = (Map String [Integer], SystemDRG)
+
+emptyDatabase :: SystemDRG -> Database
+emptyDatabase g0 = (Map.empty, g0)
+
+generateNum :: Database -> String -> Int -> (Integer, Database)
+generateNum (db, rng0) varname size =
+  let (x, rng1) = randomBytesGenerate (size `div` 8) rng0
+      x'        = integerize x
+      before    = Map.findWithDefault [] varname db
+  in if length (filter (== x') before) < 10
+       then (x', (Map.insert varname (x':before) db, rng1))
+       else generateNum (db, rng1) varname size
+
+genSign :: (Integer, Database) -> (Integer, Database)
+genSign (x, (db, rng0)) =
+  let (n, rng1) = randomBytesGenerate 0 rng0
+      n' = integerize n 
+  in if testBit n' 0 then (0 - x, (db, rng1)) else (x, (db, rng1))
+
+integerize :: S.ByteString -> Integer
+integerize = go 0
+ where
+  go acc bstr =
+    case S.uncons bstr of
+      Nothing -> acc
+      Just (v,rest) ->
+        go ((acc `shiftL` 8) + fromIntegral v) rest