Talk:Discrete logarithm records

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CPU-hours?

CPU-hours isn't a proper unit for measurement. Please either specify WHAT a CPU-hour is or use another unit which is directly compareable. --82.113.122.166 (talk) 07:56, 17 July 2013 (UTC)[reply]

ECC

No, it must be a joke! With less than 160 or even 164 bits Diffie–Hellman key exchange is not really secure against NSA as a matter of fact.

See for example Pollard's_rho_algorithm_for_logarithms.

But ok, it seems 113 is really the record today. Perfect, with the Mersenne Prime $p=2^{607}-1$ it is perfectly secure. 109.90.224.162 (talk) 09:25, 30 October 2015 (UTC) — Preceding unsigned comment added by 109.90.224.162 (talk) 09:44, 29 October 2015 (UTC)[reply]

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Pollard rho - but there might be a better method?

Yes, with Pollard rho method it very hard to find the discrete logarithm with more than 120 bits in case of elliptic curves.

But this is not my question.

My question is, might someone know a much better method? — Preceding unsigned comment added by Scheerer Software (Wiesbaden) (talk • contribs) 18:04, 23 March 2019 (UTC) Scheerer Software (Wiesbaden) (talk) 18:09, 23 March 2019 (UTC)[reply]

We can read now, "On 16 June 2020, Aleksander Zieniewicz (zielar) and Jean Luc Pons (JeanLucPons) announced the solution of a 114-bit interval elliptic curve discrete logarithm problem on the secp256k1 curve by solving a 114-bit private key in Bitcoin Puzzle Transactions Challenge. To set a new record, they used their own software [39] based on the Pollard Kangaroo on 256x NVIDIA Tesla V100 GPU processor and it took them 13 days. Two weeks earlier - They used the same number of graphics cards to solve a 109-bit interval ECDLP in just 3 days.", but what does it mean?

Is secp256k1 broken, is Bitcoin broken, might it be broken in near future?

For me personally secp256k1 looks really quite simple, because the term ax is just removed, compared to secp256r1. Why secp256k1 was choosen instead of secp245r1 for Bitcoin? It looks crazy. 95.222.84.67 (talk) 12:22, 22 October 2020 (UTC)[reply]

95.222.84.67 (talk) 14:47, 21 October 2020 (UTC) — Preceding unsigned comment added by 178.202.60.40 (talk) [reply]

My conclusion

Be careful, the private key must be chosen randomly from the entire interval. 128 bits are not enough! That's because of the birthday paradox. But all elliptic curves with p > 2^160 are safe. 178.202.60.40 (talk) 08:54, 29 November 2022 (UTC)[reply]

Prime exponents – clarification needed?

I don't think so, as "prime exponent" just means that the exponent is a prime number, which one can deduce 1279 is. Alfa-ketosav (talk) 15:52, 18 August 2023 (UTC)[reply]