System for implementing secure communication

A system for encoding a message, the system comprising:

• an encoder;
• and
• a communication channel operatively coupled to the encoder,
• wherein the encoder is configured to:
• receive a message (x), a plurality of encoding variables (y1, y2, . . . , yn), and a public encryption key (e);
• generate a ciphertext (c) based on the message (x), the plurality of encoding variables (y1, y2, . . . , yn), and the public encryption key (e), wherein c=( . . . ((xy1)y2) . . . )yn, wherein is a binary operation that satisfies an axiom of a quandle;
• and
• transmit the ciphertext (c) on the communication channel.

A method for encoding a message, the method comprising:

• receiving a message (x), a plurality of encoding variables (y1, y2, . . . , yn), and a public encryption key (e);
• generating a ciphertext (c) based on the message (x), the plurality of encoding variables (y1, y2, . . . , yn), and the public encryption key (e), wherein c=( . . . ((xy1)y2) . . . )yn, wherein is a binary operation that satisfies an axiom of a quandle;
• and
• transmitting, using the encoder, the ciphertext (c) to a communication channel.

A system for decoding a message, the system comprising:

• a decoder;
• and
• a communication channel operatively coupled to the decoder,
• wherein the decoder is configured to:
• receive, via the communication channel, a ciphertext (c), a plurality of encoding variables (y1, y2, . . . , yn), and a private encryption key (f);
• and
• generate a deciphered form (x′) of a message (x) based on the ciphertext (c), the plurality of encoding variables (y1, y2, . . . , yn), and the private encryption key (f), wherein x′=( . . . ((cyn)yn-1) . . . )y1, and wherein is a binary operation that satisfies an axiom of a quandle.

A system for implementing secure communication, the system comprising:

• an encoder, wherein the encoder is configured to:
• receive a message (x), a plurality of encoding variables (y1, y2, . . . , yn), and a plurality of public encryption keys (e1, e2, . . . , en);
• generate a ciphertext (c) based on the message (x), the plurality of encoding variables (y1, y2, . . . , yn), and the plurality of public encryption keys (e1, e2, . . . , en), wherein at each step, c=xyi;
• and
• transmit the ciphertext (c) on a communication channel, wherein the communication channel operatively coupled to the encoder;
• and
• a decoder operatively coupled to the communication channel, wherein the decoder is configured to:
• receive the ciphertext (c), the plurality of encoding variables (y1, y2, . . . , yn), and a plurality of private encryption keys (f1, f2, . . . , fn);
• and
• generate a deciphered form (x′) of the message (x) based on the ciphertext (c), the plurality of encoding variables (y1, y2, . . . , yn), and the plurality of private encryption keys (f1, f2, fn), wherein at each step, x′=cyi, and wherein and are binary operations that satisfy an axiom of a quandle.

A system for encoding a message, the system comprising:

• an encoder;
• and
• a communication channel operatively coupled to the encoder,
• wherein the encoder is configured to:
• receive a message (x), a plurality of encoding variables (y1, y2, . . . , yn), and a plurality of public encryption keys (e1, e2, . . . , en);
• generate a ciphertext (c) based on the message (x), the plurality of encoding variables (y1, y2, . . . , yn), and the plurality of public encryption keys (e1, e2, . . . , en), wherein at each step, c=xyi, and wherein is a binary operation that satisfies an axiom of a quandle;
• and
• transmit the ciphertext (c) on the communication channel.

A method for encoding a message, the method comprising:

• receiving a message (x), a plurality of encoding variables (y1, y2, . . . , yn), and a plurality of public encryption keys (e1, e2, . . . , en);
• generating a ciphertext (c) based on the message (x), the plurality of encoding variables (y1, y2, . . . , yn), and the plurality of public encryption keys (e1, e2, . . . , en), wherein c=xyi at each step, and wherein is a binary operation that satisfies an axiom of a quandle;
• and
• transmitting, using the encoder, the ciphertext (c) to a communication channel.

A system for decoding a message, the system comprising:

• a decoder;
• and
• a communication channel operatively coupled to the decoder,
• wherein the decoder is configured to:
• receive a ciphertext (c), a plurality of encoding variables (y1, y2, . . . , yn), and a plurality of private encryption keys (f1, f2, . . . , fn);
• and
• generate a deciphered form (x′) of a message (x) based on the ciphertext (c), the plurality of encoding variables (y1, y2, . . . , yn), and the plurality of private encryption keys (f1, f2, . . . , fn), wherein at each step, x′=cyi, and wherein is a binary operation that satisfies an axiom of a quandle.