Public Key Cryptosystem Based On Partitioning Of Galois Field Elements

A method of encrypting a digital message, the method comprising:

• (a) generating a private key polynomial having coefficients from a first sub-set of predefined Galois field elements;
• (b) constructing an inverse private key polynomial having coefficients which are an inverse of said private key polynomial where the polynomial product of the private key polynomial and the inverse private key polynomial modulo a third polynomial F(x) is equal to 1
• (c) generating a polynomial B1(x) having coefficients from a second sub-set of said Galois field elements;
• (d) generating a polynomial B2(x) having coefficients from a third sub-set of said Galois field elements;
• (e) generating a polynomial R1(x) having coefficients from a fourth sub-set of said Galois field elements;
• (f) generating a polynomial R2(x) having coefficients from a fifth sub-set of said Galois field elements;
• (g) constructing a public key polynomial by multiplying the inverse private key polynomial by the sum of the polynomial B1(x) and R1(x), modulo F(x), and then adding the polynomials B2(x) and R2(x);
• (h) representing the digital message as a polynomial M(x) having coefficients from a sixth sub-set of said Galois field elements;
• (i) generating a session key polynomial S(x) having coefficients from a seventh sub-set of said Galois field elements;
• and
• (j) generating an encrypted message by multiplying the session key polynomial S(x) by the public key polynomial, modulo a polynomial F(x), and adding the result to the message polynomial M(x) to produce a polynomial representation of a cipher text.

A system comprising at least one processor configured to encrypt a digital message, by:

• (a) generating a private key polynomial having coefficients from a first sub-set of predefined Galois field elements;
• (b) constructing an inverse private key polynomial having coefficients which are an inverse of said private key polynomial where the polynomial product of the private key polynomial and the inverse private key polynomial modulo a third polynomial F(x) is equal to 1;
• (c) generating a polynomial B(x) having coefficients from a second sub-set of said Galois field elements;
• (d) constructing a public key polynomial by multiplying the inverse private key polynomial by the polynomial B(x) modulo F(x);
• (e) representing the digital message as a polynomial M(x) having coefficients from a third sub-set of said Galois field elements;
• (f) generating a session key polynomial S(x) having coefficients from a fourth sub-set of said Galois field elements;
• and
• (g) generating an encrypted message by multiplying the session key polynomial S(x) by the public key polynomial, modulo F(x), and adding the result to the message polynomial M(x) to produce a polynomial representation of a cipher text.

A system comprising at least one processor configured to encrypt a digital message, by:

• (a) generating a private key polynomial having coefficients from a first sub-set of predefined Galois field elements;
• (b) constructing an inverse private key polynomial having coefficients which are an inverse of said private key polynomial where the polynomial product of the private key polynomial and the inverse private key polynomial modulo a third polynomial F(x) is equal to 1
• (c) generating a polynomial B1(x) having coefficients from a second sub-set of said Galois field elements;
• (d) generating a polynomial B2(x) having coefficients from a third sub-set of said Galois field elements;
• (e) generating a polynomial R1(x) having coefficients from a fourth sub-set of said Galois field elements;
• (f) generating a polynomial R2(x) having coefficients from a fifth sub-set of said Galois field elements;
• (g) constructing a public key polynomial by multiplying the inverse private key polynomial by the sum of the polynomial B1(x) and R1(x), modulo F(x), and then adding the polynomials B2(x) and R2(x);
• (h) representing the digital message as a polynomial M(x) having coefficients from a sixth sub-set of said Galois field elements;
• (i) generating a session key polynomial S(x) having coefficients from a seventh sub-set of said Galois field elements;
• and
• (j) generating an encrypted message by multiplying the session key polynomial S(x) by the public key polynomial, modulo a polynomial F(x), and adding the result to the message polynomial M(x) to produce a polynomial representation of a cipher text.