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    25b034ee
    Complete rewrite of PuTTY's bignum library. · 25b034ee
    Simon Tatham authored
    The old 'Bignum' data type is gone completely, and so is sshbn.c. In
    its place is a new thing called 'mp_int', handled by an entirely new
    library module mpint.c, with API differences both large and small.
    
    The main aim of this change is that the new library should be free of
    timing- and cache-related side channels. I've written the code so that
    it _should_ - assuming I haven't made any mistakes - do all of its
    work without either control flow or memory addressing depending on the
    data words of the input numbers. (Though, being an _arbitrary_
    precision library, it does have to at least depend on the sizes of the
    numbers - but there's a 'formal' size that can vary separately from
    the actual magnitude of the represented integer, so if you want to
    keep it secret that your number is actually small, it should work fine
    to have a very long mp_int and just happen to store 23 in it.) So I've
    done all my conditionalisation by means of computing both answers and
    doing bit-masking to swap the right one into place, and all loops over
    the words of an mp_int go up to the formal size rather than the actual
    size.
    
    I haven't actually tested the constant-time property in any rigorous
    way yet (I'm still considering the best way to do it). But this code
    is surely at the very least a big improvement on the old version, even
    if I later find a few more things to fix.
    
    I've also completely rewritten the low-level elliptic curve arithmetic
    from sshecc.c; the new ecc.c is closer to being an adjunct of mpint.c
    than it is to the SSH end of the code. The new elliptic curve code
    keeps all coordinates in Montgomery-multiplication transformed form to
    speed up all the multiplications mod the same prime, and only converts
    them back when you ask for the affine coordinates. Also, I adopted
    extended coordinates for the Edwards curve implementation.
    
    sshecc.c has also had a near-total rewrite in the course of switching
    it over to the new system. While I was there, I've separated ECDSA and
    EdDSA more completely - they now have separate vtables, instead of a
    single vtable in which nearly every function had a big if statement in
    it - and also made the externally exposed types for an ECDSA key and
    an ECDH context different.
    
    A minor new feature: since the new arithmetic code includes a modular
    square root function, we can now support the compressed point
    representation for the NIST curves. We seem to have been getting along
    fine without that so far, but it seemed a shame not to put it in,
    since it was suddenly easy.
    
    In sshrsa.c, one major change is that I've removed the RSA blinding
    step in rsa_privkey_op, in which we randomise the ciphertext before
    doing the decryption. The purpose of that was to avoid timing leaks
    giving away the plaintext - but the new arithmetic code should take
    that in its stride in the course of also being careful enough to avoid
    leaking the _private key_, which RSA blinding had no way to do
    anything about in any case.
    
    Apart from those specific points, most of the rest of the changes are
    more or less mechanical, just changing type names and translating code
    into the new API.
    25b034ee
    History
    Complete rewrite of PuTTY's bignum library.
    Simon Tatham authored
    The old 'Bignum' data type is gone completely, and so is sshbn.c. In
    its place is a new thing called 'mp_int', handled by an entirely new
    library module mpint.c, with API differences both large and small.
    
    The main aim of this change is that the new library should be free of
    timing- and cache-related side channels. I've written the code so that
    it _should_ - assuming I haven't made any mistakes - do all of its
    work without either control flow or memory addressing depending on the
    data words of the input numbers. (Though, being an _arbitrary_
    precision library, it does have to at least depend on the sizes of the
    numbers - but there's a 'formal' size that can vary separately from
    the actual magnitude of the represented integer, so if you want to
    keep it secret that your number is actually small, it should work fine
    to have a very long mp_int and just happen to store 23 in it.) So I've
    done all my conditionalisation by means of computing both answers and
    doing bit-masking to swap the right one into place, and all loops over
    the words of an mp_int go up to the formal size rather than the actual
    size.
    
    I haven't actually tested the constant-time property in any rigorous
    way yet (I'm still considering the best way to do it). But this code
    is surely at the very least a big improvement on the old version, even
    if I later find a few more things to fix.
    
    I've also completely rewritten the low-level elliptic curve arithmetic
    from sshecc.c; the new ecc.c is closer to being an adjunct of mpint.c
    than it is to the SSH end of the code. The new elliptic curve code
    keeps all coordinates in Montgomery-multiplication transformed form to
    speed up all the multiplications mod the same prime, and only converts
    them back when you ask for the affine coordinates. Also, I adopted
    extended coordinates for the Edwards curve implementation.
    
    sshecc.c has also had a near-total rewrite in the course of switching
    it over to the new system. While I was there, I've separated ECDSA and
    EdDSA more completely - they now have separate vtables, instead of a
    single vtable in which nearly every function had a big if statement in
    it - and also made the externally exposed types for an ECDSA key and
    an ECDH context different.
    
    A minor new feature: since the new arithmetic code includes a modular
    square root function, we can now support the compressed point
    representation for the NIST curves. We seem to have been getting along
    fine without that so far, but it seemed a shame not to put it in,
    since it was suddenly easy.
    
    In sshrsa.c, one major change is that I've removed the RSA blinding
    step in rsa_privkey_op, in which we randomise the ciphertext before
    doing the decryption. The purpose of that was to avoid timing leaks
    giving away the plaintext - but the new arithmetic code should take
    that in its stride in the course of also being careful enough to avoid
    leaking the _private key_, which RSA blinding had no way to do
    anything about in any case.
    
    Apart from those specific points, most of the rest of the changes are
    more or less mechanical, just changing type names and translating code
    into the new API.
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