
(Very) Basic Eliptic Curve Cryptography - block_chain_
https://blockchain.works-hub.com/learn/very-basic-elliptic-curve-cryptography-cb5c2
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meta_AU
I'm not really following the trapdoor reasoning. Both RSA and elliptic curves
are based on having a system where 'exponentiation' commutes and the
'logarithm' is computationally difficult. RSA only needs the two generator
primes to make finding the 'inverse' of the e exponent computationally
tractable, once that is done the 'trapdoor' isn't used any more. There isn't
an equivalent of that in elliptic curves in my understanding of them.

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FlyingAvatar
> A 256 bit key in ECC offers about the same security as 3072 bit key using
> RSA.

> This means that in systems with limited resources such as smartphones,
> embedded computers, cryptocurrency networks, it uses less than 10% of the
> hard disk space and bandwidth required using RSA.

What?

I could possibly understand CPU usage being significantly lower for an
equivalent level of security, but how could disk space and bandwidth be
affected to any significant measure?

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eboyjr
In this example, an EC private key is made up of 256 bits of "randomness".
Nearly every 256-bit number is a valid ECDSA private key.

However, an RSA private key is made of up specific numbers like a modulus,
private exponent, etc that contribute to its length. In principle this is all
you need. But usually other generation parameters are included that speed up
calculations for the Chinese Remainder Theorem.

When it comes to network bandwidth, the number one concern relates to the
symmetric algorithm used for message encryption and Message Authentication
Coding (MAC) for integrity checking (this is unrelated to the choice of RSA
versus ECC). Smaller embedded systems may start sessions more frequently, or
the asymmetric authentication may be a larger percentage of the overall
traffic and the size of the keys and signatures can make a difference. At the
128-bit security level, public keys and signatures are six-times larger for
RSA than for ECC. Private keys are 12-times larger for RSA compared to ECC at
the 128-bit security level. The key size generally has no impact on
performance, but size matters when it comes to the cost of secure storage of
the keys.

