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Homomorphic encryption
- 2. What Is Encryption ? • Encryption Is encoding messages or information with a key in such a way that only authorized parties can read it. • Used to protect data in transit.
- 3. How It Works ? Party A Party B Traditional Encryption Plain Text Cipher Text key
- 4. Problem With Traditional Encryption ? Party A Party B Data needs to be decrypted Whenever we have to perform any computation on the data.
- 5. Problem With Traditional Encryption ? Party A Party B • What If Party A does not trusts Party B, with its confidential data. ?
- 6. Homomorphic Encryption Party A Party B Party B does NOT requires the secret key for answering this query from A
- 7. Homomorphic Encryption • Homomorphic (Mathematical Term) describes the transformation of one data set into another while preserving relationships between elements in both sets. • Homomorphic is a Greek word for "same structure“. • Data in a Homomorphic encryption scheme retains the same encrypted structure.
- 8. Homomorphic Encryption • Definition: A crypto-system that allows another party to perform operations on cipher text(Encrypted Text) without having knowledge of your secret key/Password. • So if X1 and X2 are two numbers , E(X1) and E(X2) represents the encryption of these numbers with a secret key, another party would be able to compute E(X1 + X2) or E(X1 * X2) without knowing the secret key.
- 9. Homomorphic Encryption 1. PHE (Partially Homomorphic Encryption) 2. FHE (Fully Homomorphic Encryption) • Plenty of encryption schemes allow partial Homomorphic encryption which let users perform some mathematical functions on encrypted data, but not others. • A feasible FHE Has not been developed yet.
- 10. Partially Homomorphic Encryption • When You can only perform certain mathematical operations on the cipher text but not others. o RSA Cryptosystem is Partially Homomorphic with respect to Multiplication. o Caesar Cipher is Partially Homomorphic With respect to addition.
- 11. How It Works ! • Suppose I have a file with my phone number Message = [9, 0, 2, 6, 7, 2, 8, 1, 6, 8] • And I encrypt it with Caesar cipher* by adding 2 to each digit, Key = 2 Cipher = [11, 2, 4, 8, 9, 4, 10, 3, 8, 10] • Want to find the sum of all the numbers in Message. • Sum up all the elements of Cipher and give the encrypted result. Summation(Cipher) = 69 • Summation(Message) = 49 • Remove Encryption on Summation(Cipher) = 69 – 10*2 = 49 • This Is partially Homomorphic for only addition and subtraction. *Caesar cipher or any Substitution Cipher
- 12. How It Works ! A rudimentary Homomorphic cryptosystem
- 13. How It Works ! • RSA Cryptosystem : basic RSA scheme is partially Homomorphic, it allows multiplication but not addition on cipher text. • If we denote encrypted form of message x as • Then with encryption key pair (m, e) and encrypted message is Then this property proves RSA is partially Homomorphic
- 14. Advantages • Increased Security of offshore data, While computing on it. • Guarantees confidentiality of user data. • Will make distributed computing secure.
- 15. Applications • Encrypted Query Processing on an offshore server : o MIT CryptDB o It works by executing SQL queries over encrypted data. o Support six basic functions: Addition, multiplication, greater than, equality, search, and nesting these functions which are used to run Database queries. User Offshore Server
- 16. Applications • Building secure voting systems : Solves the tally problem with online votes. • Protection Of proprietary Algorithms : eg can be used by Stock Market Analysts to protect their algorithms. • Everyday Usage Where You need to send your confidential data to another computer. o For example you have to convert your confidential pdf document to another format (doc ) using an online service. o You want to search something on Google without letting Google know what you are searching. o Spam Filtering – in Encrypted Mail.
- 17. Applications One of most expensive part of the MRI machine is the chip which the machine uses to analyzes the magnetic resonance data. If an MRI maker could centralize MRI data computing It could Reduce the cost of MRI
- 18. Current Research • Companies like Fujitsu Laboratories (Japan) and IBM are moving forward with practical testing of this technology with a goal of commercial applications in 2015.
- 19. Thank You
Notas do Editor
- I Am Anon and I am here to discuss about Homomorphic encryption
- Before I describe what homomorphic encryption is we should first see what encryption is , what is the problem with our traditional encryption system that homomorphic encryption can solve . Encryption is basically encoding the data or message or information in such a way that no unauthorized party can view the data or message accept for the one for which the message is intended for called the receiver. ::Encoding is the process of putting a sequence of characters (letters, numbers, punctuation, and certain symbols) into a specialized digital format for efficient Handling of the data or information.
- So this is how our traditional encryption system works, The message to be sent is called plain text is encrypted using a key which is basically a password and the encrypted cipher text is sent to party B which uses its key to decrypt and view this data or information . Which is hello in this case. You should also note that the key of B is enclosed in the dotted black box while the key of A is outside his dotted black box this means that B’s key is his private key and the key with A’s side is the public key . I will get back to this when I discuss homomorphic encryption using RSA in a later slide.
- Now what if we want to do some computation on the encrypted data ? This is not possible with traditional encryption mechnanishms we have to decrypt the file first in order to compute on the file. Another Problem is basically if I have 100 numbers in this pendrive which are encrypted by my secret key and if I need to add all these numbers but I don’t have a computer I will have to give this encrypted file to another person B along with the key he will have to decrypt the file first before he starts adding the numbers and encrypt the file again. With the secret key. In early days of criptography Party A kept no Secret from party B it was the rest of the world they want to shut out.
- But What If I do not trust the person B with the secret key and the confidential data in the pendrive ? What can we do then ? There is no way person B can add all the numbers in encrypted form using traditional means of encryption. Consider another example Firm A has a offshore database with another Firm B that provides a Computing Facility, The database contains personal information of its employees which A does not wants B to see But A cannot encrypt the database either because if he encrypts the database and store it at B , B cannot compute on that data and cannot reply to A’s queries So A will have to download all the data and decrypt it for every query which defeats the purpose of outsourcing this computing work. Homomorphic encryption makes this possible ! Using homomorphic encryption we can do computation on encrypted data and get the result in encrypted format.
- The ability to perform computations on the ciphertext without decrypting it first is called homomorphic encryption ; In homomorphic encryption Party A will send encrypted Query to Party B which will search in its encrypted database and send out the encrypted result. All this without the need of decrypting the data anywhere in any phase. Because the data in a homomorphic encryption scheme retains the same structure, identical mathematical operations -- whether they are performed on encrypted or decrypted data -- will yield equivalent results.
- Homomorphic encryption is a term taken from mathematics which describe transformation of one data sets into another while keeping the set relation intact Homomorphic is a greek word meaning Same Structure .
- So Homomorphic encryption is a cryptosystem which allows another party to perform computation on cipher text without having any knowledge about the secret key. For example if we have two messages X1 and X2 the encryption of these messsages are denoted by E(X1) and E(X2) another party would be able to compute E(X1+X2) or E(X1*X2) without having any knowledge about the secret key. It is similar to homomorphism in mathematics Log(X) + log(y) =Log(Z) For example, it would allow a service to add two encrypted numbers and return the result without ever decrypting the two numbers.
- Before I show you how homomorphic encryption works, we need to understand that there are two kinds of homomorphic systems PHE and FHE FHE support the homomorphic propery for all the mathematical operations you can think of + - / * % & || ^ , Ie you can perform all these operations on cipher text …… PHE cryptosystems are those which supports only few kinds of mathematical operations ….
- As cryptosystems go, the doubling scheme is certainly simple, and it’s fully homomorphic. We can do all the arith - metic we want on ciphertexts. On the other hand, the system is not recom - mended if you actually want to keep secrets. Doubling a number does not thoroughly scramble the bits; it mere - ly shifts them left by one position
- Basic RSA cryptosystem is partially homomorphic because it allows only multiplications to be performed on cipher text but not addition or any other mathematical operation . ….
- These are some of the advantages of Homomorphic encryption
- Many reallife applications of Homomorphic encryption already exist such as Encrypted query systems, Mit’s CryptDB is one such example . Online applications are vulnerable to theft of sensitive information because adversaries can exploit software bugs to gain access to private data, and because curious or malicious administrators may capture and leak data. CryptDB is a system that provides practical and provable confidentiality in the face of these attacks for applications backed by SQL databases. It works by executing SQL queries over encrypted data using a collection of efficient SQL-aware encryption schemes. CryptDB can also chain encryption keys to user passwords, so that a data item can be decrypted only by using the password of one of the users with access to that data. As a result, a database administrator never gets access to decrypted data, and even if all servers are compromised, an adversary cannot decrypt the data of any user who is not logged in. An
- Okay these are more general uses of homomorphic encryption
- One of the best future application of a Fully Homomorphic system could make MRI machines less costly. One of the most expensive module of a MRI machine is the processing unit which contains the algorithms needed to analyze the MRI data and display it on monitors this algorithm is company’s secret and they spend a lot to protect it. If this processing could be done on an offshore computing facility of the company it would make MRI machines less expensive, For now company cannot do this because it is illegal to send patient data to some other company but if in future a fully Homomorphic encryption is made it can be used to protect the patient data while it is processed on a offshore computing facility and the encrypted results could be sent back to the hospital. If an MRI maker could centralize MRI data computing, it would be a fantastic reduction in risk of losing their algorithm. However, laws prevent them from accessing private patient data.