Problem Description The current technological development allowed that ciphers previously known as unbreakable to be cracked due to increased computational power. Despite this fact, a question that arises towards this manner is whether the combination between different ciphers can lead to the design of stronger enciphering methods. The present research identifies some new ways of combining classical symmetric ciphers in order to obtain stronger encryption schemes. Besides this, there are referred previous papers that attempted to follow the same track and there are analyzed their obtained results. In the end of the paper the conclusion reveals that pure symmetric encryption is not able of offering neither the confidentiality nor integrity of data, although some of the improvements of classical symmetrical ciphers can be considered significant, especially for later research.Study Methods for the Strength of a Cipher The analysis is required within the project in order to know which the main objectives of the research are. In this case the purpose of the analysis is to study some attempts made for achieving the goal of designing stronger encryption schemes based on symmetric ciphers. Each of Project Contribution subsections follows the same model: statement of work (what is intended to be studied), methodology (how is the goal achieved), analysis (reasoning) and interpretation of the result. The theoretical support that each subsection is based on is inherited from presentation phase. The recent studies proved that greatest majority of symmetric ciphers can be compromised by a series of security attacks. Despite this fact, many current cryptosystems use a combination between symmetrical and public cryptography called hybrid systems (REF13). When it is studied the strength of a cipher, the analysis can be conducted on several directions that are summarized below: - study of the number of keys that must be tried by attacker/hacker/eavesdropper –this result must be combined with computational power of the systems that try to break the cryptosystem; - vulnerability to chosen/known plaintext attacks – this can be present even if the attacker must try a large number of keys before recovering the message/key; - An eventual analysis of perfect secrecy (this is not a must, because it can be used only when the other methods show the cipher strength holds). During the research there were studied various combinations between affine cipher and hill cipher, but also other modifications that can be operated on classical symmetric ciphers as well. Main objective was to obtain a certification whether it can be obtained a stronger combination with respect to the level of achieved security. Not last, it must be noted the research is not interesting in protection of the cryptosystem achieved by establishing a secure communication channel or in ways to achieve integrity of the messages (e.g. how to protect against Man-in-the-Middle attacks). At the same time, a cryptosystem based on symmetrical cipher is as secure as it can resist to the identified security attacks on it. What might be an insecure solution for a system, can be a safe approach for another system. Project Contribution Outline One question to be put is why the research is focused on combination between symmetric ciphers that are recognized to have vulnerabilities. In order to understand better the reasoning, it is needed to make the following observations: - regular affine cipher has only 311 usable keys; this is why it is vulnerable to exhaustive-search attacks based on brute-force when it is used alone. (REF11) Current computational power developed by computer systems (including the parallelism of multiprocessing units) makes this attack very likely to succeed. - traditional Hill cipher relies on invertible matrices that can recover the plaintext from ciphertext (REF12); if this operation can be somehow avoided (without increasing computational costs over reasonable limits), then it worth to design a variation of this cryptosystem, even if that implies the usage of other ciphers. - Cryptanalysis over Vigenere cipher can succeed because the key length can be identified based on Kasiski attack; if the process of key generation can be masked or more complicated, then identification of the key becomes more difficult; in the end this approach can lead to the design of a more powerful scheme; since the linear mapping used by affine cipher doesn't influence the speed of encryption process in a significant manner, the paper tried to use a combination between of the two ciphers. - One-Time Pad is a stream cipher considered to share the properties of perfect secrecy (REF14). Despite this fact, an observation about a certain used key had revealed a weakness for it. Project Contribution 1 One of simpler constructions in this direction can be considered the following (as well as related schemes): a block of plaintext represented by pairs of characters (x, y) is encrypted according the affine transformation, namely (x y) * + (a5 a6) = (x1 y1) (mod 26). At this point it can be even made the extension towards (mod 26). This can be replaced by any group. It was taken the example with 26 characters because it is widely used the basic alphabet of English language in case of almost all ciphers. Although the encryption key appear stronger than regular key used for affine cipher, the vulnerability of Hill cipher component is inherited for both chosen and known plaintext attacks. (REF1) For recovering the symmetric key, it is enough to see what happens for four plaintexts. For example, let the four plaintexts be (a b), (b c), (az) and (za) (it really doesn't matter if the chosen plaintext is other because in the end the objective is to have a number of equations that allow the revealing of the key; there can be chosen other plaintexts). In case of (a b), which is equivalent to (0 1), the above equation becomes: (0 1)* + (a5 a6) = (a3+a5 a4+a6) (mod 26). In case of (b a), which is equivalent to (1 0), the above equation becomes: (1 0)* + (a5 a6) = (a1+a5 a2+a6) (mod 26). If the chosen plaintext is (a z), or equivalently (0 25), the above equation becomes: (0 25)* + (a5 a6) =(25*a3+a5 25*a4+a6) (mod 26)= (-a3+a5 –a4+a6). Finally, for the plaintext (z a), or equivalently (25 0), the above equation becomes: (25 0)* + (a5 a6)=(25*a1+a5 25*a2+a6) (mod 26)=(-a1+a5 –a2+a6) (mod 26). From the values of a3+a5, -a3+a5, a1+a5 and –a1+a5 can be made a system of equations that will reveal each of a1, a3 and a5, while from the values of a4+a6, a2+a6,-a4+a6 and –a2+a6 can be made another system of equations that can be solved for discovering each of a2, a4 and a6. Therefore in the end all values that part of the encryption key are found, which shows the attack can succeed despite the fact that were combined initial Hill and affine transformation. Project Contribution 2 Another attempt to strengthen classical symmetric ciphers involves Vigenere cipher and affine cipher. Practically within Vigenere cipher, instead of using multiple shift ciphers, there are used affine ciphers. In technical terms, this means the symmetric key is formed by two keys (of the same length. We can regard these two keys as being (a1,a2,…ak) and (b1,b2,….bk). Since the example also considers the basic alphabet of English language, G.C.D. (ai, 26)=1 for all i=1,k (each ai is from the set {3,5,7,9,11,15,17,19,21,23 and 25}). The attempt consists of the following approach: the plaintext characters residing in positions j, key_length+j, 2*key_length+j and so on are encrypted using the pair (ai,bi). Therefore the enciphered character is (ai*p+bi) (mod 26), where p is the plaintext character. First of all, it must be recalled that affine cipher is a linear transformation. This means that a character from the plaintext is always encrypted in the same character from the ciphertext (there is no character to be encrypted in more than one values in the ciphertext). The focus of the security test in this case involves the discovery of the key length. A suitable attack that is based on finding some repeating patterns in the ciphertext is Kasiski attack. (REF2) This computes the distances (as number of characters) between the repeated patterns and checks the common divisors shared by these distances. One of the divisors will reveal the length of the key. In order to see if the "improved" cipher is secure, it is needed to design attacks that are commonly used on mono-substitution ciphers (like affine and/or its derivations). Such an attack is represented by the frequency table of all the "k" key-pairs. Each character can be decrypted in the following way: pi=*(ci-bi) (mod 26), with i=1,k. More generally, pi=pi mod k, since it is known the encryption is cyclic due the k positions of the key. As it could be seen, despite the replace of multiple shifts with affine linear mapping for building the keys, the resulted cipher still remains vulnerable to the same attacks as original versions. Project Contribution 3 At this point the focus of the performed research is on a modification of classical Vernam cipher. In practice this is known as One-Time Pad. The short study of a proposed modification starts from the observation that when it is used with the key equal to, Enck (message) =key message =message and the message is transmitted in clear form. The suggested improvement that is studied is whether the cipher can be more secure by only encrypting the message with a key ≠. This means that key to be chosen uniformly at random from the set of non-zero available keys of length l. In order to decide if the proposal represents an improvement for One-Time Pad cipher, it is needed to study what happens with respect to achieved perfect secrecy. We consider the uniform distribution of over M (messages group). In this case, for any fixed message called α , Pr[M= α| C= α]=0. But since Pr[M= α] is not 0, it means the two probabilities are distinct. This is equivalent with the fact that the modified scheme doesn't respect the definition of perfect secrecy. In conclusion, the modification is not actually an improvement for One-Time Pad cipher. Therefore the message must be encrypted with key in order to be obtained a perfect secret scheme (compliant with the formal definition). It must be said that although the key won't change the sent plaintext when the encryption operation is performed, a potential eavesdropper can't know which the used key is. Project Contribution 4 This approach starts from the situation outlined by the first contribution of the project. From there we can borrow the idea of mixing affine and Hill transformations, but based on a different encryption scheme. More exactly, the function can be the a polynomial function from Zn, like f(x,y,z,t)= *