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-// Copyright 2015 The go-ethereum Authors
-// This file is part of the go-ethereum library.
-//
-// The go-ethereum library is free software: you can redistribute it and/or modify
-// it under the terms of the GNU Lesser General Public License as published by
-// the Free Software Foundation, either version 3 of the License, or
-// (at your option) any later version.
-//
-// The go-ethereum library is distributed in the hope that it will be useful,
-// but WITHOUT ANY WARRANTY; without even the implied warranty of
-// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
-// GNU Lesser General Public License for more details.
-//
-// You should have received a copy of the GNU Lesser General Public License
-// along with the go-ethereum library. If not, see <http://www.gnu.org/licenses/>.
-
-package secp256k1
-
-/*
-<HaltingState> sipa, int secp256k1_ecdsa_pubkey_create(unsigned char *pubkey, int *pubkeylen, const unsigned char *seckey, int compressed);
-<HaltingState> is that how i generate private/public keys?
-<sipa> HaltingState: you pass in a random 32-byte string as seckey
-<sipa> HaltingState: if it is valid, the corresponding pubkey is put in pubkey
-<sipa> and true is returned
-<sipa> otherwise, false is returned
-<sipa> around 1 in 2^128 32-byte strings are invalid, so the odds of even ever seeing one is extremely rare
-
-<sipa> private keys are mathematically numbers
-<sipa> each has a corresponding point on the curve as public key
-<sipa> a private key is just a number
-<sipa> a public key is a point with x/y coordinates
-<sipa> almost every 256-bit number is a valid private key (one with a point on the curve corresponding to it)
-<sipa> HaltingState: ok?
-
-<sipa> more than half of random points are not on the curve
-<sipa> and actually, it is less than the square root, not less than half, sorry :)
-!!!
-<sipa> a private key is a NUMBER
-<sipa> a public key is a POINT
-<gmaxwell> half the x,y values in the field are not on the curve, a private key is an integer.
-
-<sipa> HaltingState: yes, n,q = private keys; N,Q = corresponding public keys (N=n*G, Q=q*G); then it follows that n*Q = n*q*G = q*n*G = q*N
-<sipa> that's the reason ECDH works
-<sipa> multiplication is associative and commutativ
-*/
-
-/*
-<HaltingState> sipa, ok; i am doing compact signatures and I want to know; can someone change the signature to get another valid signature for same message without the private key
-<HaltingState> because i know they can do that for the normal 72 byte signatures that openssl was putting out
-<sipa> HaltingState: if you don't enforce non-malleability, yes
-<sipa> HaltingState: if you force the highest bit of t
-
-<sipa> it _creates_ signatures that already satisfy that condition
-<sipa> but it will accept ones that don't
-<sipa> maybe i should change that, and be strict
-<HaltingState> yes; i want some way to know signature is valid but fails malleability
-<sipa> well if the highest bit of S is 1, you can take its complement
-<sipa> and end up with a valid signature
-<sipa> that is canonical
-*/
-
-/*
-
-<HaltingState> sipa, I am signing messages and highest bit of the compact signature is 1!!!
-<HaltingState> if (b & 0x80) == 0x80 {
-<HaltingState> log.Panic("b= %v b2= %v \n", b, b&0x80)
-<HaltingState> }
-<sipa> what bit?
-* Pengoo has quit (Ping timeout: 272 seconds)
-<HaltingState> the highest bit of the first byte of signature
-<sipa> it's the highest bit of S
-<sipa> so the 32nd byte
-<HaltingState> wtf
-
-*/
-
-/*
- For instance, nonces are used in HTTP digest access authentication to calculate an MD5 digest
- of the password. The nonces are different each time the 401 authentication challenge
- response code is presented, thus making replay attacks virtually impossible.
-
-can verify client/server match without sending password over network
-*/
-
-/*
-<hanihani> one thing I dont get about armory for instance,
-is how the hot-wallet can generate new addresses without
-knowing the master key
-*/
-
-/*
-<HaltingState> i am yelling at the telehash people for using secp256r1
-instead of secp256k1; they thing r1 is "more secure" despite fact that
-there is no implementation that works and wrapping it is now taking
-up massive time, lol
-<gmaxwell> ...
-
-<gmaxwell> You know that the *r curves are selected via an undisclosed
-secret process, right?
-<gmaxwell> HaltingState: telehash is offtopic for this channel.
-*/
-/*
- For instance, nonces are used in HTTP digest access authentication to calculate an MD5 digest
- of the password. The nonces are different each time the 401 authentication challenge
- response code is presented, thus making replay attacks virtually impossible.
-
-can verify client/server match without sending password over network
-*/
-
-/*
-void secp256k1_start(void);
-void secp256k1_stop(void);
-
- * Verify an ECDSA signature.
- * Returns: 1: correct signature
- * 0: incorrect signature
- * -1: invalid public key
- * -2: invalid signature
- *
-int secp256k1_ecdsa_verify(const unsigned char *msg, int msglen,
- const unsigned char *sig, int siglen,
- const unsigned char *pubkey, int pubkeylen);
-
-http://www.nilsschneider.net/2013/01/28/recovering-bitcoin-private-keys.html
-
-Why did this work? ECDSA requires a random number for each signature. If this random
-number is ever used twice with the same private key it can be recovered.
-This transaction was generated by a hardware bitcoin wallet using a pseudo-random number
-generator that was returning the same “random” number every time.
-
-Nonce is 32 bytes?
-
- * Create an ECDSA signature.
- * Returns: 1: signature created
- * 0: nonce invalid, try another one
- * In: msg: the message being signed
- * msglen: the length of the message being signed
- * seckey: pointer to a 32-byte secret key (assumed to be valid)
- * nonce: pointer to a 32-byte nonce (generated with a cryptographic PRNG)
- * Out: sig: pointer to a 72-byte array where the signature will be placed.
- * siglen: pointer to an int, which will be updated to the signature length (<=72).
- *
-int secp256k1_ecdsa_sign(const unsigned char *msg, int msglen,
- unsigned char *sig, int *siglen,
- const unsigned char *seckey,
- const unsigned char *nonce);
-
-
- * Create a compact ECDSA signature (64 byte + recovery id).
- * Returns: 1: signature created
- * 0: nonce invalid, try another one
- * In: msg: the message being signed
- * msglen: the length of the message being signed
- * seckey: pointer to a 32-byte secret key (assumed to be valid)
- * nonce: pointer to a 32-byte nonce (generated with a cryptographic PRNG)
- * Out: sig: pointer to a 64-byte array where the signature will be placed.
- * recid: pointer to an int, which will be updated to contain the recovery id.
- *
-int secp256k1_ecdsa_sign_compact(const unsigned char *msg, int msglen,
- unsigned char *sig64,
- const unsigned char *seckey,
- const unsigned char *nonce,
- int *recid);
-
- * Recover an ECDSA public key from a compact signature.
- * Returns: 1: public key successfully recovered (which guarantees a correct signature).
- * 0: otherwise.
- * In: msg: the message assumed to be signed
- * msglen: the length of the message
- * compressed: whether to recover a compressed or uncompressed pubkey
- * recid: the recovery id (as returned by ecdsa_sign_compact)
- * Out: pubkey: pointer to a 33 or 65 byte array to put the pubkey.
- * pubkeylen: pointer to an int that will contain the pubkey length.
- *
-
-recovery id is between 0 and 3
-
-int secp256k1_ecdsa_recover_compact(const unsigned char *msg, int msglen,
- const unsigned char *sig64,
- unsigned char *pubkey, int *pubkeylen,
- int compressed, int recid);
-
-
- * Verify an ECDSA secret key.
- * Returns: 1: secret key is valid
- * 0: secret key is invalid
- * In: seckey: pointer to a 32-byte secret key
- *
-int secp256k1_ecdsa_seckey_verify(const unsigned char *seckey);
-
-** Just validate a public key.
- * Returns: 1: valid public key
- * 0: invalid public key
- *
-int secp256k1_ecdsa_pubkey_verify(const unsigned char *pubkey, int pubkeylen);
-
-** Compute the public key for a secret key.
- * In: compressed: whether the computed public key should be compressed
- * seckey: pointer to a 32-byte private key.
- * Out: pubkey: pointer to a 33-byte (if compressed) or 65-byte (if uncompressed)
- * area to store the public key.
- * pubkeylen: pointer to int that will be updated to contains the pubkey's
- * length.
- * Returns: 1: secret was valid, public key stores
- * 0: secret was invalid, try again.
- *
-int secp256k1_ecdsa_pubkey_create(unsigned char *pubkey, int *pubkeylen, const unsigned char *seckey, int compressed);
-*/