TL;DR: To overcome the drawbacks of the Hill cipher, a more secure number system with different bases and an enforced transformation of the enciphering matrix are provided.
Abstract: An improvement of the Hill cipher is proposed. In the Hill cipher, a randomly generated nonsingular matrix is used as an encryption key, and the inverse of the matrix is used as the decryption key. The weakness of Hill cipher is that the matrix may be revealed under known-plaintext attack. In the proposed cryptosystem a plaintext message is first partitioned into some suitable length of blocks and each block b concatenates with a random string r and a special control symbol c as r.//c//.b The new string is converted to a vector. The components of the vector are positive integers. To overcome the drawbacks of the Hill cipher, a more secure number system with different bases and an enforced transformation of the enciphering matrix are provided. >
TL;DR: Extensions are made to a class of transposition cipher based on continued shuffling that can generally replace the exclusive-OR combining function used in Vernam stream ciphers and be viewed as a cryptographic combiner.
Abstract: Extensions are made to a class of transposition cipher based on continued shuffling. These ciphers permute plaintext into ciphertext by swapping every message element with some message element selected at pseudo-random; elements can be characters (e.g., bytes) or bits. Extensions include operation on very large data blocks, cryptographic shuffling variations, and the efficient extraction of plaintext from ciphertext. In addition, selected extra data can be adjoined to the plaintext to eliminate the data-dependent weak encipherings otherwise inherent in transposition. This bit-balancing data is supposed to completely eliminate all normal usage-frequency statistics from bit-transposition ciphertext. The same mechanism can also be viewed as a cryptographic combiner, and, with sequence-to-block and block-to-sequence conversions, can generally replace the exclusive-OR combining function used in Vernam stream ciphers.
TL;DR: Two modifications of this cipher are discussed that may lead to practical provably-secure ciphers based on either of two assumptions that appear to be novel in cryptography, viz., the (sole) assumption that the enemy's memory capacity (but not his computing power) is restricted and the assumption that an explicit function is, in a specified sense, controllably-difficult to compute, but not necessarily one-way.
Abstract: Shannon's pessimistic theorem, which states that a cipher can be perfect only when the entropy of the secret key is at least, as great as that of the plaintext, is relativized by the demonstration of a randomized cipher in which the secret key is short but the plaintext can be very long. This cipher is shown to be "perfect with high probability". More precisely, the enemy is unable to obtain any information about the plaintext when a certain security event occurs, and the probability of this event is shown to be arbitrarily close to one unless the enemy performs an infeasible computation. This cipher exploits the existence of a publicly-accessible string of random bits whose length is much greater than that of all the plaintext to be encrypted before the secret key and the randomizer itself are changed. Two modifications of this cipher are discussed that may lead to practical provably-secure ciphers based on either of two assumptions that appear to be novel in cryptography, viz., the (sole) assumption that the enemy's memory capacity (but not his computing power) is restricted and the assumption that an explicit function is, in a specified sense, controllably-difficult to compute, but not necessarily one-way.