The Basic ABC Encryption Scheme

116 Pages·2013·0.9 MB·English

by  Jintai Ding

II Advanced School on Cryptology and Information
Security in Latin America, FlorianÃşpolis, Brazil, 2013
Simple Matrix Scheme for Encryption
Jintai Ding
JointworkwithChengdongTao,AdamaDiene,AlbrechtPetzoldt
October, 2013
Outline
1 Introduction
2 The Basic ABC Encryption Scheme
Key Generation
Encryption
Decryption
Security analysis and practical parameters
3 The Improved Scheme
A failed attempt
Key Generation
Encryption
Decryption
Outline
1 Introduction
2 The Basic ABC Encryption Scheme
Key Generation
Encryption
Decryption
Security analysis and practical parameters
3 The Improved Scheme
A failed attempt
Key Generation
Encryption
Decryption
Hash-based signature systems.
Lattice-based public key cryptosystems
Multivariate public key cryptosystems – MPKC
Post-quantum cryptography
Public key cryptosystems that could resist the future quantum
computer attack.
Code-based public key cryptosystems
Lattice-based public key cryptosystems
Multivariate public key cryptosystems – MPKC
Post-quantum cryptography
Public key cryptosystems that could resist the future quantum
computer attack.
Code-based public key cryptosystems
Hash-based signature systems.
Multivariate public key cryptosystems – MPKC
Post-quantum cryptography
Public key cryptosystems that could resist the future quantum
computer attack.
Code-based public key cryptosystems
Hash-based signature systems.
Lattice-based public key cryptosystems
Post-quantum cryptography
Public key cryptosystems that could resist the future quantum
computer attack.
Code-based public key cryptosystems
Hash-based signature systems.
Lattice-based public key cryptosystems
Multivariate public key cryptosystems – MPKC
G can be viewed as a map from kn to km.
G mostly quadratic maps, where g are quadratic polynomials:
i
X X
g (x ,..x ) = α x x + β x +γ .
i 1 n lij i j li i l
i,j i
What is a MPKC ?
Multivariate Public Key Cryptosystems
- Cryptosystems with public keys as a set of multivariate
functions
Public key: G(x ,...,x ) =
1 n
(g (x ,...,x ),...,g (x ,...,x )) = L ◦F ◦L .
1 1 n m 1 n 2 1
over k, a small finite field.
What is a MPKC ?
Multivariate Public Key Cryptosystems
- Cryptosystems with public keys as a set of multivariate
functions
Public key: G(x ,...,x ) =
1 n
(g (x ,...,x ),...,g (x ,...,x )) = L ◦F ◦L .
1 1 n m 1 n 2 1
over k, a small finite field.
G can be viewed as a map from kn to km.
G mostly quadratic maps, where g are quadratic polynomials:
i
X X
g (x ,..x ) = α x x + β x +γ .
i 1 n lij i j li i l
i,j i
Any plaintext M = (x0,...,x0) is encrypted via polynomial
1 n
evaluation:
G(M) = G(x0,...,x0) = (y0,...,y0 ).
1 n 1 m
To decrypt the ciphertext (y0,...,y0), one needs to know a
1 n
secret (the private key) to compute the inverse map
G−1 = L−1◦F−1◦L−1
1 2
to find the plaintext (x0,...,x0) = G−1(y0,..,y0).
1 n 1 n
What is MPKC for encryption
The public key is given as:
G(x ,...,x ) = (G (x ,...,x ),...,G (x ,...,x )) = L ◦F ◦L .
1 n 1 1 n m 1 n 2 1
F is called the central map and easy to invert. L and L
1 2
serve as ”locks”.