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On the discrete logarithm problem for prime-field elliptic curves
elliptic curve discrete logarithm problem prime field
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2017/6/27
In recent years several papers have appeared investigating the classical discrete logarithm problem for elliptic curves by means of the multivariate polynomial approach based on the celebrated summati...
This paper reports on the number field sieve computation of a 768-bit prime field discrete logarithm, describes the different parameter optimizations and resulting algorithmic changes compared to the ...
CM55: special prime-field elliptic curves almost optimizing den Boer's reduction between Diffie-Hellman and discrete logs
public-key cryptography elliptic curve
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2016/1/6
Using the Pohlig–Hellman algorithm, den Boer reduced the discrete logarithm problem
to the Diffie–Hellman problem in groups of an order whose prime factors were each
one plus a smooth number. This r...
Fast Prime Field Elliptic Curve Cryptography with 256 Bit Primes
Elliptic Curve Cryptography
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2014/3/5
This paper studies software optimization of Elliptic Curve Cryptography with 256-bit prime fields. We propose a constant-time implementation of the NIST and SECG standardized curve P-256, that can be ...
Security of Prime Field Pairing Cryptoprocessor Against Differential Power Attack
implementation / Pairing Based Cryptography Side-channel Analysis Power Analysis Attack DPA Attack Prime Fields
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2012/3/28
This paper deals with the differential power attack on a pairing cryptoprocessor. The cryptoprocessor is designed for pairing computations on elliptic curves defined over finite fields with large prim...
Small Odd Prime Field Multivariate PKCs
Gr¨obner basis multivariate public key cryptosystem TTS
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2009/6/10
We show that Multivariate Public Key Cryptosystems (MPKCs)
over fields of small odd prime characteristic, say 31, can be highly
efficient. Indeed, at the same design security of 280 under the best k...