Re: [Cfrg] invalid compressed point attack ...
Dan Brown <firstname.lastname@example.org> Fri, 28 November 2014 12:43 UTC
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From: Dan Brown <firstname.lastname@example.org>
To: David Jacobson <email@example.com>
Thread-Topic: [Cfrg] invalid compressed point attack ...
Date: Fri, 28 Nov 2014 12:42:51 +0000
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Cc: IRTF CFRG <firstname.lastname@example.org>
Subject: Re: [Cfrg] invalid compressed point attack ...
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By invalid decompression, I meant skipping the check on the correctness of y^2==z, which is as bad and as silly as skipping the check y^2==x^3+ax+b in an uncompressed invalid-point attack, and actually the same check. Yes, checking y^2==z stops the attack for sure. Anyway , i'm seeing the skipped check as nearly equally natural in both cases, and apparently there's even some of incentive to skip these checks called "simplicity "... Best regards, -- Dan Original Message From: David Jacobson Sent: Thursday, November 27, 2014 10:38 PM To: Dan Brown; 'email@example.com'; Cc: firstname.lastname@example.org Subject: Re: [Cfrg] invalid compressed point attack ... On 11/27/14, 10:33 AM, Dan Brown wrote: > Definitions: A compressed point (x,z) is invalid if it is not the compression > of a valid uncompressed point. > We can technically define an invalid point attack for compression by > specifying an invalid decompression rule for invalid compressed points. > For example, in prime fields of size p = 3 mod 4, the function z |-> > z^((p+1)/4) can be used to decompress invalid compressed points, in the place > where actual square root algorithm is used to decompress a valid compressed > point. > > To me, this invalid decompression rule seems as plausible an implementation > fault as the fault of not checking for curve membership of an uncompressed > point. You seem to be saying that using y = z^((p+1)/4) where z is computed from x using the curve equation, i.e. for short Weierstrass z = x^2 + a * x + b, is not a valid way of computing a valid (x,y) on the curve. Well, of course, it is possible that z is not a quadratic residue. But if you check that y^2 == z, is it still unsafe? Thank you, --David _______________________________________________ Cfrg mailing list Cfrg@irtf.org http://www.irtf.org/mailman/listinfo/cfrg