Address comments

Author: sipa

bip-0340.mediawiki

@@ -151,28 +151,29 @@ As an alternative to generating keys randomly, it is also possible and safe to r
 Input:
 * The secret key ''sk'': a 32-byte array
 * The message ''m'': a 32-byte array
-* Auxiliary data ''a'': a byte array of length 0 or more
+* Auxiliary random data ''a'': a byte array of length 0 to 32 (inclusive)
 
 The algorithm ''Sign(sk, m)'' is defined as:
 * Let ''d' = int(sk)''
 * Fail if ''d' = 0'' or ''d' ≥ n''
 * Let ''P = d'⋅G''
 * Let ''d = d' '' if ''has_even_y(P)'', otherwise let ''d = n - d' ''.
-* Let ''rand = hash<sub>BIP340/nonce</sub>(xor(bytes(d), H<sub>BIP340/aux</sub>(a)) || bytes(P) || m)''<ref>Including the [https://moderncrypto.org/mail-archive/curves/2020/001012.html public key as input to the nonce hash] helps ensure the robustness of the signing algorithm by preventing leakage of the secret key if the calculation of the public key ''P'' is performed incorrectly or maliciously, for example if it is left to the caller for performance reasons.</ref>, where ''xor(a,b)'' represents the byte-wise xor of ''a'' and ''b''.
+* Let ''t'' be the byte-wise xor of ''bytes(d)'' and ''H<sub>BIP340/aux</sub>(a)''<ref>The auxiliary random data is hashed (with a unique tag) as a precaution against situations where the randomness may be correlated with the private key itself. It is xored with the private key (rather than combined with it in a hash) to reduce the number of operations exposed to the actual secret key.</ref>.
+* Let ''rand = hash<sub>BIP340/nonce</sub>(t || bytes(P) || m)''<ref>Including the [https://moderncrypto.org/mail-archive/curves/2020/001012.html public key as input to the nonce hash] helps ensure the robustness of the signing algorithm by preventing leakage of the secret key if the calculation of the public key ''P'' is performed incorrectly or maliciously, for example if it is left to the caller for performance reasons.</ref>.
 * Let ''k' = int(rand) mod n''<ref>Note that in general, taking a uniformly random 256-bit integer modulo the curve order will produce an unacceptably biased result. However, for the secp256k1 curve, the order is sufficiently close to ''2<sup>256</sup>'' that this bias is not observable (''1 - n / 2<sup>256</sup>'' is around ''1.27 * 2<sup>-128</sup>'').</ref>.
 * Fail if ''k' = 0''.
 * Let ''R = k'⋅G''.
 * Let ''k = k' '' if ''has_square_y(R)'', otherwise let ''k = n - k' ''.
 * Let ''e = int(hash<sub>BIP340/challenge</sub>(bytes(R) || bytes(P) || m)) mod n''.
-* Return the signature ''bytes(R) || bytes((k + ed) mod n)''.
+* Let ''sig = bytes(R) || bytes((k + ed) mod n)''.
+* If ''Verify(bytes(P), m, sig)'' (see below) returns failure, abort<ref>Verifying the signature before leaving the signer prevents random or attacker provoked computation errors. This prevents publishing invalid signatures which may leak information about the secret key. It is recommended, but can be omitted if the computation cost is prohibitive.</ref>.
+* Return the signature ''sig''.
 
-When an RNG is available at signing time, up to 32 bytes of its output should be included in ''a''. The result is then called a ''synthetic nonce''. Doing so may improve protection against [https://moderncrypto.org/mail-archive/curves/2017/000925.html fault injection attacks and side-channel attacks]. Therefore, '''synthetic nonces are recommended in settings where these attacks are a concern''' - in particular on offline signing devices. Adding more than 32 bytes serves no security purpose. Note that while this means the resulting nonce is not deterministic, its normal security properties do not depend on the quality of the RNG, and in fact using a completely broken RNG is still secure.
+The auxiliary random data should be set to fresh randomness generated at signing time, resulting in what is called a ''synthetic nonce''. If no randomness is available, a simple counter can be used as well, or even nothing at all. Using any non-repeating value increases protection against [https://moderncrypto.org/mail-archive/curves/2017/000925.html fault injection attacks]. Using unpredictable randomness additionally increases protection against other side-channel attacks, and is '''recommended whenever available'''. Note that while this means the resulting nonce is not deterministic, the randomness is only supplemental to security. The normal security properties (excluding side-channel attacks) do not depend on the quality of the signing-time RNG.
 
 ==== Alternative Signing ====
 
-It should be noted that various alternative signing algorithms can be used to produce equally valid signatures. The 32-byte ''rand'' value may be generated in other ways, producing a different but still valid signature (in other words, this is not a ''unique'' signature scheme). '''No matter which method is used to generate the ''rand'' value, the value must be a fresh uniformly random 32-byte string which is not even partially predictable for the attacker.''' Nonce freshness with a derandomized nonce function implies that the same inputs must not be presented in another context. This can be most reliably accomplished by not reusing the same private key across different signing schemes. For example, if the ''rand'' value was computed as per RFC6979 and the same secret key is used in deterministic ECDSA with RFC6979, the signatures can leak the secret key through nonce reuse.
-
-'''Verifying the signing output''' To prevent random or attacker provoked computation errors, the signature can be verified with the verification algorithm defined below before leaving the signer. This prevents publishing invalid signatures which may leak information about the secret key. '''If the additional computational cost is not a concern, it is recommended to verify newly created signatures and reject them in case of failure.'''
+It should be noted that various alternative signing algorithms can be used to produce equally valid signatures. The 32-byte ''rand'' value may be generated in other ways, producing a different but still valid signature (in other words, this is not a ''unique'' signature scheme). '''No matter which method is used to generate the ''rand'' value, the value must be a fresh uniformly random 32-byte string which is not even partially predictable for the attacker.''' For nonces without randomness this implies that the same inputs must not be presented in another context. This can be most reliably accomplished by not reusing the same private key across different signing schemes. For example, if the ''rand'' value was computed as per RFC6979 and the same secret key is used in deterministic ECDSA with RFC6979, the signatures can leak the secret key through nonce reuse.
 
 '''Nonce exfiltration protection''' It is possible to strengthen the nonce generation algorithm using a second device. In this case, the second device contributes randomness which the actual signer provably incorporates into its nonce. This prevents certain attacks where the signer device is compromised and intentionally tries to leak the secret key through its nonce selection.