Secure and linear public-key cryptosystem based on parity-check error-correcting

A method according to any one of the preceding claims, wherein the ciphering and deciphering are utilized to configure other types of cryptosystems or types of error correcting codes, comprising:

• a) ciphering the parameters and other data required to configure communication utilizing a known error correcting code or cryptographic method, said ciphering being according to any one of the preceding claims;
• b) transmitting said ciphered parameters and other data to another participating party;
• c) decrypting said ciphered parameters and data information upon receipt, to reveal said parameters and other data;
• and
• d) initiating communications by configuring a known method according to said parameters and other data.

A method according to any one of the preceding claims, wherein the public-key [Ek] and the private-key are uniquely derived utilizing two sparse matrices [A] and [B], comprising:

• a) providing a first sparse and Boolean matrix [A] of dimensions M×N;
• b) providing a second sparse and Boolean matrix [B] which is invertible and of dimensions M×M;
• c) deriving the cryptographic public-key, [Ek], from the matrix multiplication result [Ek]=[B]−1[A];
• and
• d) constructing the cryptographic private-key, [Dk], from said pair of sparse matrices, [A] and [B], to obtain [Dk]=[A,B].

A method according to any one of the preceding claims, further comprising hiding the transmission utilizing Spread Spectrum techniques comprising:

• a) utilizing the recipient public-key to send a ciphered message comprising the Spread Spectrum parameters that will be utilized for the transmission of the message;
• b) receiving said message, deciphering said message, and revealing said Spread Spectrum parameters;
• c) sending a message utilizing Spread Spectrum techniques modulated with accordance to said parameters;
• and
• d) receiving said message and utilizing said parameters to demodulate the received Spread Signal;

A method for constructing a digital signature for the ciphertext t of the message “s”, comprising:

• a) producing a unique identifier, X(s,na), where said identifier is the combination of modifications made to the message “s” and the noise signal na that was utilized for the ciphering of said message s;
• b) encrypting said identifier X with the corrupted public key [Êk] to obtain the encrypted identifier c1=[Êk]X;
• c) producing a digital signature from a combination of another noise signal na1 and the encrypted identifier t1 to obtain the digital signature t1=c1+na1;
• d) publicizing a verification vector V constructed from a combination of said message “s” and noise signals, na and na1;
• e) verifying the transmission source and its integrity by the following steps:
• e.1) decrypting the received ciphertext t and the digital signature t1 utilizing decryption algorithm and obtaining the decrypted message s′, and the decrypted private noise signals na′ and na1′;
• e.2) constructing a verification vector V′ following a predetermined procedure;
• e.3) comparing verification vectors V′ and V;
• and
• e.4) assuring transmission integrity and source identity when said verification are found to be identical or slightly different.

A method for constructing a digital signature for the ciphertext t of the message “s”, comprising:

• a) producing a unique identifier, Vs(s,na), from a combination of modifications made to the message “s” and the noise signal that was utilized for the ciphering of said message s, na;
• b) permuting some of the rows of the recipient public key following a permutation procedure to obtain a permuted public key [ÊkP];
• c) encrypting said identifier, Vs, with the permuted public key [ÊkP], to obtain an encrypted signature t1=[ÊkP]Vs;
• and
• d) publicizing said permutation procedure.
• e) verifying the transmission source and its integrity by the following steps:
• e.1) decrypting the received ciphertext t utilizing decryption algorithm and obtaining the decrypted message s′, and the decrypted private noise na′;
• e.2) reconstructing the permuted public-mey [ÊkP] following a predetermined or publicized procedure;
• e.3) constructing an identifier Vs′=f(s′, na′) following a predetermined (or publicized) procedure;
• e.4) encrypting said identifier Vs′, with the permuted public key [ÊkP] to obtain its digital signature t1′=[ÊkP]Vs′;
• e.5) comparing the sender's digital signature, t1, and the digital signature of the received ciphertext t1′;
• and
• e.6) assuring transmission integrity and source identity when the identifiers t1 and t1′ are found to be identical or slightly different.

A method for constructing a digital signature for the ciphertext t of the message “s”, comprising:

• a) producing a unique identifier V of the same dimensions of the message “s”, where said identifier is the combination of modifications made to the message “s” and the noise signal na;
• b) encrypting the identifier V with the public-key to obtain the digital signature [Êk]V;
• and
• c) publicizing the procedure by which said digital signature was established.
• d) verifying the transmission source and its integrity by the following steps:
• d.1) decrypting the received ciphertext t and said digital signature utilizing decryption algorithm and obtaining the message s′, the private noise na′, and said identifier V;
• d.2) producing a new identifier V′ utilizing the decrypted message s′, and decrypted noise signal na′, and by following same procedure utilized for the production of V;
• and
• d.3) assuring transmission integrity and source identity when the identifiers V and V′ are found to be identical or slightly different.