Method and system for performing perfectly secure key exchange and authenticated messaging

A method for encrypting a message, comprising:

• establishing secret A, which is a number with an even number of digits that is at least 10 digits in length;
• converting each digit Ak of secret A into another value An through the use of the following formulas:
• (Ak+a)Mod q=Bk;
• and (Bk+Ck)Mod q=A;
• wherein q is hexadecimal or decimal, the two formulas use each single corresponding digits of A, B, and C, and C is randomly created by the sender;
• generating a random number Y which is twice as long as a system required message encryption strength;
• cutting the random number Y in half through the modular addition of adjacent digits;
• using the reduced random number as a message key to encrypt a language-based message;
• expanding the message key;
• cutting the expanded message key in half through the modular addition of adjacent digits to create Header Key;
• expanding the header key;
• adding a header including variables to indicate which of a plurality of techniques was used to expand the header key, the length of the message key and, if a one time pad was used, the length of the one time pad;
• building a random, one-time transpose matrix of ASCII elements;
• passing a plaintext message through transpose matrix to create a transposed plaintext;
• encrypting the transpose matrix using the extended header key in an exclusive OR operation to create an encrypted header output;
• encrypting the transposed plaintext using the extended message key in an exclusive OR operation to create a ciphertext output;
• and
• converting C for a subsequent message by transposing the digits in C with a digit-position-based one-way function to create a converted C, and then using the converted C as a next A in a subsequent communication.

A method for encrypting a message, comprising:

• establishing secret A, which is a number with an even number of digits that is at least 10 digits in length;
• converting each digit Ak of secret A into another value An through the use of the following formulas:
• (Ak+a)Mod q=Bk;
• and (Bk+Ck)Mod q=An
• wherein q is hexadecimal or decimal, the two formulas use each single corresponding digits of A, B, and C, and C is randomly created by the sender;
• generating a random number Y which is twice as long as a system required message encryption strength;
• cutting the random number Y in half through the modular addition of adjacent digits;
• using the reduced random number as a message key to encrypt a language-based message;
• expanding the message key;
• cutting the expanded message key in half through the modular addition of adjacent digits to create a header key;
• expanding the header key;
• adding a header including variables to indicate which of a plurality of techniques was used to expand the header key, the length of the message key and, if a one timepPad was used, the length of the one time pad;
• building a random, one-time transpose matrix of ASCII elements;
• passing a plaintext message through transpose matrix to create a transposed plaintext;
• encrypting the transpose matrix using the extended header key in an exclusive OR operation to create an encrypted header output;
• encrypting the transposed plaintext using the extended message key in an exclusive OR operation to create a ciphertext output;
• and
• converting C for a subsequent message by transposing C's digits by a digit-position-based one-way function and then using the converted C value as a next A in a subsequent communication.

A method, applicable to a system for exchanging secure communications based on an existing secret wherein each communication within the system contains a message identification number, for randomly and indecipherably exchanging a new secret upon demand to be used to replace an existing secret, the method comprising:

• providing a first number and a message identification number;
• providing an operator that is a function of first and second variables;
• providing a matrix lookup function which, on the basis of at least one given input number, uniquely determines a set of indices, and returns the element of a matrix defined by those indices;
• operating on the first number and the message identification number with the operator to generate a second number;
• generating first and second index numbers by applying the matrix lookup function to first and second digits, respectively, selected from the second number;
• operating on the sum of the two index numbers with the operator, thereby generating a result;
• and
• replacing the existing secret with the result.