Advanced bitflip: threat-adjusted, quantum-ready, battery-friendly, application-rich cipher

A method for secret communication and for mutual authentication among transmitting parties belonging to a secret-sharing group, wherein a secret communication of a message M written in an alphabet A comprised of t letters:

• {a1, a2, . . . at} where transmitting party and recipient party share a secret key K comprised of t bit strings k1, k2, . . . kt each comprised of n bits, and t positive integers f1, f2, . . . ft where 0≤fi≤n, for i=1, 2, . . . t, and where the transmitting party transmits the q letters in M in sequence m1, m2, . . . mj, . . . mq letter by letter such that letter mj (j=1, 2, . . . q) written as letter ai of the alphabet A is communicated to the recipient by the transmitter sending to the recipient string cj which is generated by a flip action defined as flipping fi bits in ki, then conducting a no equivocation test where one tests that for all l≠i the Hamming distance between cj and ki is not equal to fl;
• if the test fails the transmitting party repeats the flip action with different choice of fi bits to flip, then conducting the “no equivocation test” on the new output string of the flip action, cj,
• and repeating this loop until the no equivocation test does not fail, in which case cj is transmitted to the recipient party;
• repeating the same for j=1, 2 . . . q the entire message M is transmitted to the recipient party,
• and where the recipient party, receiving the sequence c1, c2, . . . cj, . . . cq, is extracting the corresponding value of ai for each cj by finding for each cj for j=1, 2, . . . q the letter ai where the corresponding string ki has a Hamming distance fi with cj, while for all l≠i the Hamming distance between cj and kl is not equal to fl,
• and where any party in the secret-sharing group will authenticate itself to any other party in the secret-sharing group, regarded as an authenticator, where the party to be authenticated is regarded as an authentication-candidate, and where all parties in the secret-sharing group share a secret comprised of an n-bits long string Ka and a secret integer s≤n, and whereby the authentication candidate will randomly flip s bits in Ka to generate an authentication candidate string R, and then send the R candidate string to the authenticator to evaluate (i) that the Hamming distance between R and Ka is s, H(R,Ka)=s, and (ii) that the Hamming distance between R and each and every authentication string used previously, is larger than a threshold distance d;
• failing either test the authenticator will reject R as a proof of the identity of the authentication candidate, and then the authenticator will instruct the authentication candidate to try with another, candidate string, R′, and try again, until both tests (i, ii) for authentication are satisfied.