crypto: remove slight bias in key generation due to modulo

2 files changed, 25 insertions, 4 deletions

diff --git a/src/crypto/crypto.cpp b/src/crypto/crypto.cpp
index f4ef751d3..9eafa0e28 100644
--- a/src/crypto/crypto.cpp
+++ b/src/crypto/crypto.cpp
@@ -93,6 +93,29 @@ namespace crypto {
     generate_random_bytes_not_thread_safe(N, bytes);
   }
 
+  static inline bool less32(const unsigned char *k0, const unsigned char *k1)
+  {
+    for (int n = 31; n >= 0; --n)
+    {
+      if (k0[n] < k1[n])
+        return true;
+      if (k0[n] > k1[n])
+        return false;
+    }
+    return false;
+  }
+
+  void random32_unbiased(unsigned char *bytes)
+  {
+    // l = 2^252 + 27742317777372353535851937790883648493.
+    // it fits 15 in 32 bytes
+    static const unsigned char limit[32] = { 0xe3, 0x6a, 0x67, 0x72, 0x8b, 0xce, 0x13, 0x29, 0x8f, 0x30, 0x82, 0x8c, 0x0b, 0xa4, 0x10, 0x39, 0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0xf0 };
+    do
+    {
+      generate_random_bytes_thread_safe(32, bytes);
+    } while (!less32(bytes, limit)); // should be good about 15/16 of the time
+    sc_reduce32(bytes);
+  }
   /* generate a random 32-byte (256-bit) integer and copy it to res */
   static inline void random_scalar_not_thread_safe(ec_scalar &res) {
     unsigned char tmp[64];
@@ -101,10 +124,7 @@ namespace crypto {
     memcpy(&res, tmp, 32);
   }
   static inline void random_scalar(ec_scalar &res) {
-    unsigned char tmp[64];
-    generate_random_bytes_thread_safe(64, tmp);
-    sc_reduce(tmp);
-    memcpy(&res, tmp, 32);
+    random32_unbiased((unsigned char*)res.data);
   }
 
   void hash_to_scalar(const void *data, size_t length, ec_scalar &res) {
diff --git a/src/crypto/crypto.h b/src/crypto/crypto.h
index 9ea0f2ec0..449af8f6d 100644
--- a/src/crypto/crypto.h
+++ b/src/crypto/crypto.h
@@ -99,6 +99,7 @@ namespace crypto {
 #pragma pack(pop)
 
   void hash_to_scalar(const void *data, size_t length, ec_scalar &res);
+  void random32_unbiased(unsigned char *bytes);
 
   static_assert(sizeof(ec_point) == 32 && sizeof(ec_scalar) == 32 &&
     sizeof(public_key) == 32 && sizeof(secret_key) == 32 &&