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*To*: [email protected]*Subject*: Re: Photuris Primality verification needed*From*: "William Allen Simpson" <[email protected]>*Date*: Tue, 7 Nov 95 15:00:15 GMT*Cc*: [email protected], [email protected]*Sender*: [email protected]

> From: "Brian A. LaMacchia" <[email protected]> > > Recently, someone asked for a smaller prime of only 512-bits for speed. > > This is more than enough for the strength of keys needed for DES, 3DES, > > MD5 and SHA. Perhaps this would be easier to have more complete and > > robust verification as well. > > Our practical experiences with discrete logs suggests that the effort > required to perform the discrete log precomputations in (a) is slightly > more difficult than factoring a composite of the same size in bits. In > 1990-91 we estimated that performing (a) for a k-bit prime modulus was > about as hard as factoring a k+32-bit composite. [Recent factoring work > has probably changed this a bit, but it's still a good estimate.] > Thanks. I have added the [from Schneier] estimate e ** ((ln p)**1/2 * (ln (ln p))**1/2) and number field sieve estimate e ** ((ln p)**1/3 * (ln (ln p))**2/3) to the Photuris draft, with a small amount of explanation. Hilarie Orman posted that 512-bits only gives an order of 56-bits strength, 1024-bits yeilds 80-bits strength, and 2048 yields 112-bits strength. I do not have the facilities to verify her numbers. As most of us agree that 56-bits is not enough (DES), the 512-bit prime seems a waste of time and a tempting target. I'd like to drop it, but Phil is inclined to keep it with a disclaimer. [email protected] Key fingerprint = 2E 07 23 03 C5 62 70 D3 59 B1 4F 5E 1D C2 C1 A2

**Follow-Ups**:**Re: Photuris Primality verification needed***From:*"Perry E. Metzger" <[email protected]>

**Re: Photuris Primality verification needed***From:*Phil Karn <[email protected]>

**Re: Photuris Primality verification needed***From:*Phil Karn <[email protected]>

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