ECES (Elliptic Curve Encryption Scheme)
This chapter provides tutorial notes on ECES (Elliptic Curve Encryption Schema). Topics includes ECES plaintext encryption and ciphertext decryption processes; using Crypto.Cipher.AES module to test ECES.
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ECES Plaintext Encryption
ECES Ciphertext Decryption
Download and Install PyCryptodome
ECES Encryption with Crypto.Cipher.AES
ECES Decryption with Crypto.Cipher.AES
EC Encryption of Plaintext Point
- ECES (Elliptic Curve Encryption Scheme) is a schema
that uses elliptic curve subgroup properties to encrypt a
plaintext into a ciphertext using receiver's EC public key. The
ciphertext can only be decrypted back to the plaintext by the receiver
using his/her EC private key.
- ECES encryption process actually uses the ECDH Key Exchange protocol
to derive a shared secret key. Then a shared cipher function is used to
encrypt the plaintext message with the shared secret key.
- ECES decryption process actually uses the ECDH Key Exchange protocol
to recover the shared secret key. Then a shared cipher function is used to
decrypt the ciphertext message with the shared secret key.
- Crypto.Cipher.AES module from the PyCryptodome Python library
can be used to test the ECES encryption and decryption processes.
- Plaintext message can be mapped to a point on the elliptic curve and
encrypted to a ciphertext point using a shared secret point.
Table of Contents
About This Book
Geometric Introduction to Elliptic Curves
Algebraic Introduction to Elliptic Curves
Abelian Group and Elliptic Curves
Discrete Logarithm Problem (DLP)
Generators and Cyclic Subgroups
Reduced Elliptic Curve Groups
Elliptic Curve Subgroups
tinyec - Python Library for ECC
EC (Elliptic Curve) Key Pair
ECDH (Elliptic Curve Diffie-Hellman) Key Exchange
ECDSA (Elliptic Curve Digital Signature Algorithm)
►ECES (Elliptic Curve Encryption Scheme)
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