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diff --git a/src/mux/muxi.h b/src/mux/muxi.h
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index 6b57eea..14fd6e2 100644
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--- a/src/mux/muxi.h
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+++ b/src/mux/muxi.h
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@@ -14,6 +14,7 @@
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 #ifndef WEBP_MUX_MUXI_H_
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 #define WEBP_MUX_MUXI_H_
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+#include <assert.h>
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 #include <stdlib.h>
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 #include "src/dec/vp8i_dec.h"
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 #include "src/dec/vp8li_dec.h"
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@@ -143,13 +144,13 @@
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 // Returns size of the chunk including chunk header and padding byte (if any).
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 static WEBP_INLINE size_t SizeWithPadding(size_t chunk_size) {
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+  assert(chunk_size <= MAX_CHUNK_PAYLOAD);
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   return CHUNK_HEADER_SIZE + ((chunk_size + 1) & ~1U);
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 }
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 // Size of a chunk including header and padding.
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 static WEBP_INLINE size_t ChunkDiskSize(const WebPChunk* chunk) {
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   const size_t data_size = chunk->data_.size;
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-  assert(data_size < MAX_CHUNK_PAYLOAD);
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   return SizeWithPadding(data_size);
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 }
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diff --git a/src/mux/muxread.c b/src/mux/muxread.c
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index eb5070b..ef50dae 100644
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--- a/src/mux/muxread.c
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+++ b/src/mux/muxread.c
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@@ -59,6 +59,7 @@
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   // Sanity checks.
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   if (data_size < CHUNK_HEADER_SIZE) return WEBP_MUX_NOT_ENOUGH_DATA;
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   chunk_size = GetLE32(data + TAG_SIZE);
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+  if (chunk_size > MAX_CHUNK_PAYLOAD) return WEBP_MUX_BAD_DATA;
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   {
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     const size_t chunk_disk_size = SizeWithPadding(chunk_size);
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@@ -203,9 +204,14 @@
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     goto Err;  // First chunk should be VP8, VP8L or VP8X.
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   }
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-  riff_size = SizeWithPadding(GetLE32(data + TAG_SIZE));
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+  riff_size = GetLE32(data + TAG_SIZE);
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+  if (riff_size > MAX_CHUNK_PAYLOAD) goto Err;
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+
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+  // Note this padding is historical and differs from demux.c which does not
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+  // pad the file size.
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+  riff_size = SizeWithPadding(riff_size);
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   if (riff_size < CHUNK_HEADER_SIZE) goto Err;
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-  if (riff_size > MAX_CHUNK_PAYLOAD || riff_size > size) goto Err;
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+  if (riff_size > size) goto Err;
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   // There's no point in reading past the end of the RIFF chunk.
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   if (size > riff_size + CHUNK_HEADER_SIZE) {
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     size = riff_size + CHUNK_HEADER_SIZE;
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