Re: [Cfrg] Curve25519 lacks private/public homomorphism?

Dan Brown <danibrown@blackberry.com> Tue, 05 February 2019 19:38 UTC

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From: Dan Brown <danibrown@blackberry.com>
To: Tony Arcieri <bascule@gmail.com>
CC: Richard Barnes <rlb@ipv.sx>, CFRG <cfrg@irtf.org>
Thread-Topic: [Cfrg] Curve25519 lacks private/public homomorphism?
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Date: Tue, 5 Feb 2019 19:38:31 +0000
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Subject: Re: [Cfrg] Curve25519 lacks private/public homomorphism?
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Hi Tony, Richard,

Hmm, I thought that this question was about X25519, but now it seems to be about EdDSA (Ed25519)?

I see that BIP32 talks about updating the “after hash” private key?

Is such modification the key generation generally considered compliant to CFRG spec RFC 8032? 

Best regards,

Dan

 

From: Tony Arcieri <bascule@gmail.com> 
Sent: Tuesday, February 5, 2019 12:27 PM
To: Dan Brown <danibrown@blackberry.com>
Cc: Richard Barnes <rlb@ipv.sx>sx>; CFRG <cfrg@irtf.org>
Subject: Re: [Cfrg] Curve25519 lacks private/public homomorphism?

 

On Tue, Feb 5, 2019 at 9:20 AM Dan Brown <danibrown@blackberry.com <mailto:danibrown@blackberry.com> > wrote:

Could you not just add delta to the private key (instead of multiplying the private key)?  (Add [delta]G to the public key.)

 

Using addition instead of multiplication is the BIP32 method, and it has the same problems. See the Ed25519-BIP32 key recovery attack here:

 

https://forum.web3.foundation/t/key-recovery-attack-on-bip32-ed25519/44 <https://urldefense.proofpoint.com/v2/url?u=https-3A__forum.web3.foundation_t_key-2Drecovery-2Dattack-2Don-2Dbip32-2Ded25519_44&d=DwMFaQ&c=yzoHOc_ZK-sxl-kfGNSEvlJYanssXN3q-lhj0sp26wE&r=mf6j6fOClApRsArWE9wqI1rEGUVkfxZ0aXWmn35nK_c&m=ZDhvIILc-chTe68I4OmZ1clkTv10k3nhZwQz2dLJ6H8&s=Cye0i2Un5eqpM21QPjLvpL7e1YJtsEwXDhj57FUgL9o&e=> 

 

-- 

Tony Arcieri