# Cipher

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CIPHER. An arithmetical character, used for numerical notation. Vide Figures, and 13 Vin. Ab. 210; 18 Eng. C. L. R. 95; 1 Ch. Cr. Law, 176.
2. By cipher is also understood a mode of secret writing. Public ministers and other public agents frequently use ciphers in their correspondence, and it is sometimes very useful so to correspond in times of war. A key is given to each minister before his departure, namely, the cipher for writing ciphers, (chiffre chiffrant,) and the cipher for deciphering (chiffre dechiffrant.) Besides these, it is usual to give him a common cipher, (chiffre banal,) which is known to all the ministers of the same power, who occasionally use it in their correspondence with each other.
3. When it is suspected that, a cipher becomes known to the cabinet where the minister is residing, recourse is had to a preconcerted sign in order to annul, entirely or in part, what has been written in cipher, or rather to indicate that the contents are to be understood in an inverted or contrary sense. A cipher of reserve is also employed in extraordinary cases.

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1 presents the communication process in which the sender generates the ciphertext [sigma] for message m using his/her identity [ID.sub.s], private key [mathematical expression not reproducible], and the receiver's identity [ID.sub.r].
Given a data item m which is either 0 or 1 to be encrypted, choose a random subset S [mathematical expression not reproducible] {1,2,...,[tau]} and a random integer r [member of] (-[2.sup.[rho]]', [2.sup.[rho]]), and output the ciphertext:
4) Decryption: A caregiver's device decrypts the ciphertext [??] by the decryption algorithm Dec using a secret key sk.
given a seeming ciphertext, whether it is in fact a valid ciphertext
Decryption algorithm Decrypt (sk, c): Decrypt the ciphertext c with the private key sk to obtain the plaintext m.
Input : a ciphertext [CT.sub.F], a file tag value [Tag.sub.F], a master key [MK.sub.Srv], the highest challenge [mathematical expression not reproducible] Output : an expected response array [ResArr.sub.Srv] (1) for i in [1, 2] (2) [K.sub.own,i] [less than or equal to] KDF([MK.sub.Srv], i[parallel][Tag.sub.F]) (3) for j in [1, s] (4) [mathematical expression not reproducible] (5) [mathematical expression not reproducible] (6) [mathematical expression not reproducible] (7) [sigma] [left arrow] [CT.sub.F][[[pi].sub.k](1)] [parallel] ...
Encryption is carried out according to A and the ciphertext CT is the output.
Fig 6 and 7 describes the time to generate key generation and encryption in the Ciphertext -Policy Attribute Based Encryption method for collusion resistance.
The challenger obtains the public/secret key pair (pk,sk) by running Setup([l.sup.l]) and sends pk to the attacker, where the public key includes a message space M and a ciphertext space [XI].
(3) The decryption algorithm Dec(fc, m): on inputting a key k [member of] K and a ciphertext ce C, Dec outputs a message m [member of] M such that m = Dec(k, Enc(k, m))
(1) list the equation system of AES-256 algorithm; (2) select a known plaintext and ciphertext pair, and substitute it into the equation system; (3) construct Grobner basis Ggrelex of the ideal relative to degree lexicographical order using the method in Section 5.1; (4) judge the solution structure of the Grobner basis.
The purpose of the ciphertext scrambling and diffusion is realized.

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