Encryption is slower than decryption in elliptic curve cryptography (ECC), there are lots of Cryptography algorithms available to protect the data from intruders,Elliptic curve Cryptography algorithm and RSA algorithms are the most effective public key Cryptographic algorithm. The Elliptic curve Cryptography (ECC) algorithm meets the requirements encryption. The encoding/decoding operations for converting text message into points on the curve and vice versa are not considered asa simple process. RSA algorithm allows a sender to generate a public keys to encrypt the message and the receiver is sent a generated private key using a secured database.In this paper we are comparing the performance characteristics of the two-public key Cryptography techniques Elliptic Curve Cryptography and RSA used in digital Signature of each modern technologies. The analysis showed that ECC takes less time for encryption/decryption . ECC takes less time for encryption of data than RSA, it also generates smaller size of key than RSA. ECC is more efficient than RSA. The cost of key generation can be considered as a major factor in the choice of public key system to use when using digital signature, especially for smaller devices with lesser computational resources .

Dear Kgs Venkatesan ,

Thanks for your informative answer. But Is it possible to describe why "Encryption is slower than decryption in elliptic curve cryptography (ECC)" or that sentence is wrong?

For example: see diffie hellman algorithm:

In this algorithm for first see time is close for ENCRYPTE AND DECRYPTE

G - start point on Elliptic curve.

Alice have private key d_A

Bob have d_B

d_A, d_B \in N

Then we sum G point d_A and d_B times respectively and get: H_A = G*d_A and H_B = G * d_B.

H_A and H_B - points on Eliptic curves(public keys) for Alice and Bob.

Alice send H_A to Bob, Bob send H_B to Alice.

Alice and Bob count S = H_B*d_A = H_A* d_B - common point on eliptic curves.

(common secret key).

pub_key = S_x - first coordinate of S point

And now if Alice wish send message(integer number) use next:

message_hash = message*(pub_key%curve.p) - TIME ON ENCRYPTE

message = message_hash//(pub_key%curve.p) - TIME ON DECRYPTE

Wiki: https://en.wikipedia.org/wiki/Diffie%E2%80%93Hellman_key_exchange

Hi Andrey Nechesov ,

Thanks for a nice answer.

However, from this equation,

message_hash = message*(pub_key%curve.p) - TIME ON ENCRYPTE

message = message_hash/(pub_key%curve.p) - TIME ON DECRYPTE

Here, multiplication is more taking time?

Because decryption time is almost half of the encryption time.

ECC is not similar to RSA in the encryption phase. ECC take extra time in encryption due to selecting the curve , base point,the point multiplication and exponentiation which is costly , while the decryption phase based on DLP.

Dear diaa eldien mustafa ahmed

Thanks for your nice explanation. Can you provide the full form of DLP?

Thanks.

Discrete Logarithmic problem means, we will design a group of may numbers (high entropy), then we will select a number from the already builtin group, and this selected number must be the prime root of that group. Another integer should be selected, and pass from this formula

g=ax where g=group, a=integer number and x is a private key. is called discrete logarithmic problem.

Encryption process has many arguments while decryption is on a single entity, that is why encryption is slower then decryption (this is my own view, never seen, just imagine, but looking correct)

I have attached a response from another forum.

Hope that it will help.

Thanks.

What kind of protocol are you designing with ECC (Diffie-Hellman key exchange - ECDH or digital signature algorithm - ECDSA)? In ECDSA, two scalar multiplications are performed on both sides (signer and verifier), therefore ideally the performance should be same. However, the actual performance will depend on the size of the private key you choose (1 scalar multiplication operation) as well as the random number (other scalar multiplication) that is generated. Please evaluate the performance with different private keys/random numbers and see what you observe.

i think it's a good thing !! its important to decrepit faster if we exchange a message . but in the case of breaking the code not good at all.