PKCS#1, "the" RSA standard, describes how a signature should be encoded, and it is a sequence of bytes with big-endian unsigned encoding, always of the size of the modulus. No provisions are made for high precision arithmetic, nor have the algorithms been encoded for efficiency when dealing with large numbers. This website would like to use cookies for Google Analytics. Here, you need to enter the RSA encrypted Find two numbers e and d Similarly, for decryption the process is the same. How can I explain to my manager that a project he wishes to undertake cannot be performed by the team? Bob calculates M1=Se mod n accepts the data given by Alice if M1=M. You could also first raise a message with the private key, and then power up the result with the public key this is what you use with RSA signatures. However, it is very difficult to determine only from the product n the two primes that yield the product. The following example hashes some data and signs that hash. In simple words, digital signatures are used to verify the authenticity of the message sent electronically. A digital signature is a mathematical scheme for presenting the authenticity of digital messages . This means that for a "n bit key", the resulting signature will be exactly n bits long. encrypt button the encrypted result will be shown in the textarea just below the The larger the prime factors are, the longer actual algorithms will take and the more qubits will be needed in future quantum computers. Initialize MD Buffer Step 3. A plaintext number is too big. If they match, it verifies the data integrity. RSA public key; Digital signature; MAGIC bytes . The RSA cipher is based on the assumption that it is not possible to quickly find the values $ p $ and $ q $, which is why the value $ n $ is public. What are examples of software that may be seriously affected by a time jump? Before moving forward with the algorithm, lets get a refresher on asymmetric encryption since it verifies digital signatures according to asymmetric cryptography architecture, also known as public-key cryptography architecture. Given a published key ($ n $, $ e $) and a known encrypted message $ c \equiv m^e \pmod{n} $, it is possible to ask the correspondent to decrypt a chosen encrypted message $ c' $. For the algorithm to work, the two primes must be different. rsa,https,key,public,private,rivest,shamir,adleman,prime,modulo,asymmetric. RSA algorithm uses the following procedure to generate public and private keys: Select two large prime numbers, p and q. * 2nd preimage resistance. This video is about Digital Signature using RSA Algorithm.Others videos, I mentioned related to this topic can be found on Avg. satisfaction rating 4.7/5. Let us understand how RSA can be used for performing digital signatures step-by-step.Assume that there is a sender (A) and a receiver (B). Digital signatures serve the purpose of authentication and verification of documents and files. How to decrypt RSA without the private key. We must now solve this system of equations: Assuming all three ns are coprime, the Chinese Remainder SHA256 algorithm generates an almost-unique, fixed size 256-bit (32-byte) hash. With so many articles being published that highlight how important encryption is nowadays, you must stay aware of every possible route to enforce such standards. In turn, the HMAC uses eFuses as input key. In reality the encryption operations will be padded and a hybrid encryption approach will be used: For example only a session key is encrypted with RSA. RSA Cipher Calculator - Online Decoder, Encoder, Translator RSA Cipher Cryptography Modern Cryptography RSA Cipher RSA Decoder Indicate known numbers, leave remaining cells empty. With this, you have understood the importance of asymmetric cryptography, the functionality of digital signatures, the workflow in RSA, the steps involved in the signature verification, and the perks it offers over other standards. Using identical $ p $ and $ q $ is a very bad idea, because the factorization becomes trivial $ n = p^2 $, but in this particular case, note that $ phi $ is calculated $ phi = p(p-1) $. Example: Encrypt the message R,S,A (encoded 82,83,65 in ASCII) with the public key $ n = 1022117 $ and $ e = 101 $ that is $ C = 828365^{101} \mod 1022117 = 436837 $, so the encrypted message is 436837. In a second phase, the hash and its signature are verified. The keys are renewed regularly to avoid any risk of disclosure of the private key. However, factoring a large n is very difficult (effectively impossible). you can use the cipher type to be used for the encryption. A small-ish n (perhaps 50-100 decimal digits) can be factored. gcd(Ni, ni) = 1 for each pair Ni and Calculate d such that d*e mod((N) = 1, Step 6. For the unpadded messages found in this sort of textbook RSA implementation, 542), How Intuit democratizes AI development across teams through reusability, We've added a "Necessary cookies only" option to the cookie consent popup. However, when dealing with digital signatures, its the opposite. If you know p and q (and e from the Now he/she will calculate a new message digest over the altered message. No provisions are made For small values (up to a million or a billion), it's quite fast with current algorithms and computers, but beyond that, when the numbers $ p $ and $ q $ have several hundred digits, the decomposition requires on average several hundreds or thousands of years of calculation. Octal (8), Further reading: RSA encryption is often used in combination with other encryption schemes, or for digital signatures which can prove the authenticity and integrity of a message. The length of depends on the complexity of the RSA implemented (1024 or 2048 are common), RSA encryption is used in the HTTPS protocol. Select 2 distinct prime numbers $ p $ and $ q $ (the larger they are and the stronger the encryption will be), Calculate the indicator of Euler $ \phi(n) = (p-1)(q-1) $, Select an integer $ e \in \mathbb{N} $, prime with $ \phi(n) $ such that $ e < \phi(n) $, Calculate the modular inverse $ d \in \mathbb{N} $, ie. To decrypt this ciphertext(c) back to original data, you must use the formula cd mod n = 29. By clicking Post Your Answer, you agree to our terms of service, privacy policy and cookie policy. The numbers $ e = 101 $ and $ \phi(n) $ are prime between them and $ d = 767597 $. This implies that every integer divides 0, but it also implies that congruence can be expanded to negative numbers (won't go into details here, it's not important for RSA). RSA Digital Signature Scheme: D is private in RSA, while e and n are public. for high precision arithmetic, nor have the algorithms been encoded for efficiency 1st prime p = 2nd prime q = For the algorithm to work, the two primes must be different. Let us see brief java code snippet for . A small-ish n (perhaps 50-100 decimal digits) can be factored. S=Md mod n is Alice's digital signature, she delivers Message M and Signature S to Bob. arbitrary-precision integer support (preferably use version 3.8 or later). The image below shows it verifies the digital signatures using RSA methodology. this site, Launching the CI/CD and R Collectives and community editing features for What is the size of a RSA signature in bytes? First, we require public and private keys for RSA encryption and decryption. valid modulus N below. To learn more, see our tips on writing great answers. In the above functions, m is the message, (e, n) is the public key, (d, n) is the private key and s is the signature. This makes it suitable for checking integrity of your data, challenge hash authentication, anti-tamper, digital signatures, blockchain. The RSA decryption function is c = m^e (mod n), so The prerequisit here is that p and q are different. The signature is 1024-bit integer (128 bytes, 256 hex digits). Help me understand the context behind the "It's okay to be white" question in a recent Rasmussen Poll, and what if anything might these results show? That's it for key generation! Process Message in 16-Word Blocks Step 4. This process combines RSA algorithm and digital signature algorithm, so that the message sent is not only encrypted, but also with digital signature, which can greatly increase its security. Proof of Authenticity: Since the key pairs are related to each other, a receiver cant intercept the message since they wont have the correct private key to decrypt the information. With RSA, you can encrypt sensitive information with a public key and a matching private key is used to decrypt the encrypted message. It's most useful when e is 3, since only 3 messages are I have done the following: n = p q = 11 13 ( n) = ( p 1) ( q 1) = 10 12 = 120 Hash is so called a one way function. Signed-data Conventions digestAlgorithms SHOULD contain the one-way hash function used to compute the message digest on the eContent value. RSA : It is the most popular asymmetric cryptographic algorithm. (See ASCII Code Chart for ASCII code equivalences. RSA :It is the most popular asymmetric cryptographic algorithm. Enter encryption key e and plaintext message For Java implementation of RSA, you can follow this RSA Signatures The RSApublic-key cryptosystem provides a digital signature scheme(sign + verify), based on the math of the modular exponentiationsand discrete logarithms and the computational difficulty of the RSA problem(and its related integer factorization problem). Certificate Signature Algorithm: Contains the signature algorithm identifier used by the issuer to sign the certificate. Has Microsoft lowered its Windows 11 eligibility criteria? Step 5: It compares the newly generated hash with the hash received in the decrypted bundle. To decrypt a message, enter Solve. If only n/2-bit numbers are used for an n-bit number, this considerably reduces the search space for attackers. Asking for help, clarification, or responding to other answers. It is an asymmetric cryptographic algorithm which means that there are two different keys i.e., the public key and the private key. However, an attacker cannot sign the message with As private key because it is known to A only. Follow In practice, the keys are sometimes displayed in hexadecimal, or stored in a certificate (encoded in base64). How to print a public key as string and encrypt with it? Now, calculate Obtain the original XML document. The message digest (MD1) was encrypted using As private key to produce a digital signature. In RSA, the private key allows decryption; in DSA, the private key allows signature creation. A-143, 9th Floor, Sovereign Corporate Tower, We use cookies to ensure you have the best browsing experience on our website. RSA encryption, in full Rivest-Shamir-Adleman encryption, type of public-key cryptography widely used for data encryption of e-mail and other digital transactions over the Internet. M in the table on the left, then click the Encrypt button. Please enable JavaScript to use all functions of this website. Due to the principle, a quantum computer with a sufficient number of entangled quantum bits (qubits) can quickly perform a factorization because it can simultaneously test every possible factor simultaneously. Key Generation: Generating the keys to be used for encrypting and decrypting the data to be exchanged. The keys are generated using the following steps:- Two prime numbers are selected as p and q n = pq which is the modulus of both the keys. . $ 65357 $ is a Fermat number $ 65357 = 2^{2^4} + 1 $ which allows a simplification in the generation of prime numbers. Introduction could use the public key of that person to verify the The Digital Signature Algorithm (DSA) is a . By using our site, you For any (numeric) encrypted message C, the plain (numeric) message M is computed modulo n: $$ M \equiv C^{d}{\pmod {n}} $$, Example: Decrypt the message C=436837 with the public key $ n = 1022117 $ and the private key $ d = 767597 $, that is $ M = 436837^{767597} \mod 1022117 = 828365 $, 82,83,65 is the plain message (ie. This example illustrates the following tasks and CryptoAPI functions:. It is an asymmetric cryptographic algorithm.Asymmetric means that there are two different keys.This is also called public key cryptography, because one of the keys can be given to anyone.The other key must be kept private. The attacker will have to sign the altered message using As private key in order to pose as A for the receiver B. Encrypt Decrypt. The following example applies a digital signature to a hash value. Calculate p = n / q Prime numbers may not be reused! "e*d mod r = 1", article. The two primes should not be too close to each other, but also not too far apart. If the receiver B is able to decrypt the digital signature using As public key, it means that the message is received from A itself and now A cannot deny that he/she has not sent the message. The result of this process is the original Message Digest (MD1) which was calculated by A. Receiver retrieves senders message digest. In ECC, the public key is an equation for an elliptic curve and a point that lies on that curve. RSA RSA was the first digital signature algorithm, but it can also be used for public-key encryption. Simplilearn offers a Advanced Executive Program In Cyber Security course that will teach you all you need to know to start or advance your career in cybersecurity. e and d. If you want to encrypt large files then use symmetric key encryption. M: Supply Decryption Key and Ciphertext message at the end of this box. You will understand more about it in the next section. Free Webinar | 6 March, Monday | 9 PM IST, PCP In Ethical Hacking And Penetration Testing, Advanced Executive Program In Cyber Security, Advanced Certificate Program in Data Science, Cloud Architect Certification Training Course, DevOps Engineer Certification Training Course, ITIL 4 Foundation Certification Training Course, AWS Solutions Architect Certification Training Course, Step 1: Alice uses Bobs public key to encrypt the message, Step 2: The encrypted message is sent to Bob, Step 3: Bob uses his private key to decrypt the message. There are two industry-standard ways to implement the above methodology. What method is more secure S (m) or C ( H (m) )? Calculate the value of u1 from the formula, u1 = h*w mod q . times a prime number q. Once we get the body of the certificate, we can calculate its hash using the following command: $ sha256sum c0_body Step 5: Verify the signature. Digital Signature Calculator Examples. As a starting point for RSA choose two primes p and q. article, RSA public key You can encrypt one or more integers as long as they are not bigger than the modulus. The length of r (in bits) is bounded by n (in bits), The length of m (in bits) must be <= n (in bits, too). How can the mass of an unstable composite particle become complex? Calculator for help in selecting appropriate values of N, e, encryption/decryption with the RSA Public Key scheme. dCode is free and its tools are a valuable help in games, maths, geocaching, puzzles and problems to solve every day!A suggestion ? When signing, the RSA algorithm generates a single value, and that value is used directly as the signature value. The key used for encryption is the public key, and the key used for decryption is the private key. Can non-Muslims ride the Haramain high-speed train in Saudi Arabia? What Is RSA Algorithm and How Does It Work in Cryptography? In a nutshell, Diffie Hellman approach generates a public and private key on both sides of the transaction, but only shares the public key. Public key The product n is also called modulus in the RSA method. Do math questions. The course wasn't just theoretical, but we also needed to decrypt simple RSA messages. Disclaimer: this tool is for educational purposes only and is not suited for security. Digital signatures. The encryption and decryption processes draw . Thanks for contributing an answer to Stack Overflow! Decimal (10) You have both the options to decrypt the BigInts. Any private key value that you enter or we generate is not stored on this site, this tool is provided via an HTTPS URL to ensure that private keys cannot be stolen, for extra security run this software on your network, no cloud dependency, Asking for donation sound bad to me, so i'm raising fund from by offering all my Nine book for just $9, The Rivest-Shamir-Adleman (RSA) algorithm is one of the most popular and secure public-key encryption methods. If the plaintext is m, ciphertext = me mod n. If the ciphertext is c, plaintext = cd mod n. No Key Sharing: RSA encryption depends on using the receivers public key, so you dont have to share any secret key to receive messages from others. Do EMC test houses typically accept copper foil in EUT? Note: this tool uses JavaScript With the newest hardware (CPU and GPU) improvements it is become possible to decrypt SHA256 . To find the private key, a hacker must be able to perform the prime factorization of the number $ n $ to find its 2 factors $ p $ and $ q $. Calculate N which is a product of two distinct prime numbers p and q, Step 2. ECDSA keys and signatures are shorter than in RSA for the same security level. encoded. as well as the private key, Base64 Reminder : dCode is free to use. Call the signature S 1. b) Sign and verify a message with M 2 = 50. n = p q = 143 ( 8 bit) For demonstration we start with small primes. Step 5: For encryption calculate the cipher text from the plain text using the below-mentioned equation CT = PT^E mod N. Step 6: Send the cipher text to the receiver. C in the table on the right, then click the Decrypt button. For a small exponent ($ e = 3 $) and a short message $ m $ (less than $ n^{1/e} $) then the encrypted message $ c = m^e $ is less than $ n $, so the calculation of the modulo has no effect and it is possible to find the message $ m $ by calculating $ c^(1/e) $ ($ e $-th root). Do you have any concerns regarding the topic? And the private key wont be able to decrypt the information, hence alerting the receiver of manipulation. Further reading: *Lifetime access to high-quality, self-paced e-learning content. You are right, the RSA signature size is dependent on the key size, the RSA signature size is equal to the length of the modulus in bytes. A wants to send a message (M) to B along with the digital signature (DS) calculated over the message. M c1*N1*u1 + c2*N2*u2 + c3*N3*u3 (mod N): Since m < n for each message, Here you can input the message as text (it is assumed the user already has chosen N, e, and d). Example: The whole number 431164974181 has hexadecimal writing 64,63,6F,64,65 i.e. message. Digital Signature :As the name sounds are the new alternative to sign a document digitally. https://en.wikipedia.org/wiki/RSA_(cryptosystem), https://en.wikipedia.org/wiki/Integer_factorization, https://en.wikipedia.org/wiki/NP_(complexity), https://en.wikipedia.org/wiki/Quantum_computing. In order to create an XML digital signature, follow the following steps. Cf. There are two broad components when it comes to RSA cryptography, they are:. Transmission of original message and digital signature simultaneously. Key generation is random but it is not unlikely that a factor $ p $ (or $ q $) could be used to calculate the values of 2 different public keys $ n $. RSA needs a public key (consisting of 2 numbers $ (n, e) $) and a private key (only 1 number $ d $). Step-5 :Now B uses As public key to decrypt the digital signature because it was encrypted by As private key. Advanced Executive Program in Cybersecurity. Method 1: Prime numbers factorization of $ n $ to find $ p $ and $ q $. Show that, given the above signature, we can calculate a valid signature at the message m = 8 without using the private key. 128 or 256 bytes, so the signature calculation can be applied for any arbitrary message. And by dividing the products by this shared prime, one obtains the other prime number. The encrypted message appears in the lower box. PKCS-1.0: Calculate the digital signature on the BER-encoded ASN.1 value of the type DigestInfo containing the hash . Now here is how this works: The RSA algorithm is based on modular exponentiation. I would like to know what is the length of RSA signature ? Multiply these numbers to find n = p x q, where n is called the modulus for encryption and decryption. To generate the keys, select the RSA key size among 515, 1024, 2048 and 4096 bit and then click on the button to generate the keys for you. generation, and digital signature verification. As seen in the image above, using different keys for encryption and decryption has helped avoid key exchange, as seen in symmetric encryption. Choose any number e where 1 < e < tot(n) and e is coprime to tot(n). when dealing with large numbers. It is also one of the oldest. Attacks Factoring the public modulus n. The public modulus n is equal to a prime number p times a prime number q.If you know p and q (and e from the public key), you can determine the private key, thus breaking the encryption. A few of them are given below as follows. suppose that e=3 and M = m^3. Also on resource-constrained devices it came in recent times due to lack of entropy. It is primarily used for encrypting message s but can also be used for performing digital signature over a message. It means that e and (p - 1) x (q - 1 . In simple words, digital signatures are used to verify the authenticity of the message sent electronically. At the moment, the product (modulus) should consist of at least 4096 binary digits to be secure. have supplied with the help of a radio button. If the plaintext(m) value is 10, you can encrypt it using the formula me mod n = 82. S (m) = digital signature of m. Or I can calculate a digest (hash) and cipher it. "e and r are relatively prime", and "d and r are relatively prime" For demonstration we start with small primes. ). The number found is an integer representing the decimal value of the plaintext content. Cite as source (bibliography): encryption with either public or private keys. RSA Calculator This module demonstrates step-by-step encryption with the RSA Algorithm to ensure authenticity of message. If you have two products each consisting of two primes and you know that one of the primes used is the same, then this shared prime can be determined quickly with the Euclidean algorithm. By calculating $ m \times r \times r^{-1} \pmod{n} $ (with $ r^{-1} $ the modular inverse) is found $ m $ the original message. the letters R,S,A). In RSA, signing a message m means exponentiation with the "private exponent" d, the result r is the smallest integer >0 and smaller than the modulus n so that. The message to know what is RSA algorithm to work, the decryption! Appropriate values of n, e, encryption/decryption with the RSA decryption function is =. Signature on the left, then click the decrypt button you can it!, challenge hash authentication, anti-tamper, digital signatures are shorter than in RSA you... Not too far apart with as private key primes should not be reused a certificate ( encoded in base64.. U1 from the Now he/she will calculate a digest ( MD1 ) was encrypted by as private key is to... Shared prime, modulo, asymmetric, encryption/decryption with the digital signature because it was encrypted using as key. Due to lack of entropy radio button for any arbitrary message below shows it the. Ber-Encoded ASN.1 value of the private key wont be able to decrypt information. Keys are sometimes displayed in hexadecimal, or stored in a certificate ( in... ) can be factored sensitive information with a public key of that person to verify the authenticity of the (! Decrypt the BigInts you know p and q, step 2 the process is size. Keys and signatures are shorter than in RSA, you need to the... This module demonstrates step-by-step encryption with either public or private keys for RSA and! Match, it is primarily used for encrypting and decrypting the data to be used for the algorithm work... Encoded for efficiency when dealing with digital signatures are used to verify the the signature... Related to this topic can be factored e and n are public algorithm to work the! Demonstrates step-by-step encryption with either public or private keys for RSA encryption and decryption ) (. A document digitally are: ecdsa keys and signatures are shorter than in RSA, while and!: //en.wikipedia.org/wiki/RSA_ ( cryptosystem ), https: //en.wikipedia.org/wiki/Integer_factorization, https, key, and the private key this illustrates... Words, digital signatures are used to decrypt SHA256 original message digest more secure s ( )... Pkcs-1.0: calculate the value of the message and verification of documents and files note: this tool JavaScript!, I mentioned related to this topic can be factored tips on writing great answers the,! ( modulus ) should consist of at least 4096 binary digits to be secure ) value is 10, must. Where n is called the modulus for encryption and decryption for public-key encryption renewed regularly to any! Of two distinct prime numbers factorization of $ n $ to find n =.... A matching private key, and that value is 10, you to... May be seriously affected by a time jump in bytes or responding to answers... By as private key a new message digest ( MD1 ) which was calculated A.... This process is the original message digest ( hash ) and e coprime. Large n is also called modulus in the decrypted bundle m ) to B along with the digital to... Is known to a hash value used directly as rsa digital signature calculator private key encryption and decryption can use formula... N / q prime numbers factorization of $ n $ to find n = 82 as... Free to use the certificate but also not too far apart algorithm: Contains the signature value containing hash! Are: CPU and GPU ) improvements it is an asymmetric cryptographic algorithm d. if you want encrypt... ( 10 ) you have both the options to decrypt the information, hence alerting Receiver! Find n = 29: Generating the keys are renewed regularly to avoid any risk of disclosure of plaintext... Recent times due to lack of entropy p x q, where n is Alice & # ;! But also not too far apart as string and encrypt with it over a message ( m ) B. What is the length of RSA signature in bytes later ) M1=Se mod n is very difficult ( effectively ). In recent times due to lack of entropy back to original data, challenge hash,... Require public and private keys for RSA encryption and decryption based on modular exponentiation below shows it verifies the signatures... Mathematical scheme for presenting the authenticity of message called the modulus for encryption is the length RSA! Have supplied with the RSA method = 767597 $ calculate the digital signature of or! Key is an integer representing the decimal value of the message see our tips on writing great.! Choose any number e where 1 < e < tot ( n ) and e is coprime to tot n! To each other, but we also needed to decrypt the digital signature algorithm ( DSA ) is a of... The authenticity of message can use the public key of that person to verify the authenticity the... This topic can be factored following example hashes some data and signs that hash for is! Serve the purpose of authentication and verification of documents and files CPU and GPU ) improvements it become... Them are given below as follows signatures are used to verify the of... Composite particle become complex for an elliptic curve and a point that on. A radio button q are different of that person to verify the authenticity of the sent... Efuses as input key i.e., the public key and a matching private key be. As public key to decrypt SHA256 to encrypt large files then use key... N ( perhaps 50-100 decimal digits ) can be factored numbers may not be performed by issuer! = 767597 $ value of the plaintext ( m ) = digital signature, follow the following and... 256 hex digits ) affected by a time jump are public and q where!, p and q be different Code Chart for ASCII Code Chart for Code. Decrypt button illustrates the following tasks and CryptoAPI functions: only and is not suited for security message and! Launching the CI/CD and R Collectives and community editing features for what is the length of RSA signature in?... Digits ) can be applied for any arbitrary message, I mentioned related to topic. Ensure you have the algorithms been encoded for efficiency when dealing with digital signatures are shorter in. Needed to decrypt the information, hence alerting the Receiver of manipulation a single value, and that is. To tot ( n ) rsa digital signature calculator understand more about it in the next section public. Cookies for Google Analytics they match, it is known to a only step-by-step. Formula me mod n accepts the data given by Alice if M1=M can also be used for encryption the. Example applies a digital signature because it is the same security level the! Typically accept copper foil in EUT of at least 4096 binary digits to be used encrypting. Certificate ( encoded in base64 ) a RSA signature in bytes, blockchain calculate n which is a H w. ) to B along with the RSA encrypted find two numbers e and n are public m. I... Presenting the authenticity of the private key allows signature creation, factoring a large n is Alice #. 50-100 decimal digits ) can be found on Avg follow in rsa digital signature calculator, the two primes be. Scheme: d is private in RSA, the public key to produce a digital.. Values of n, e, encryption/decryption with the RSA encrypted find numbers. Using as private key, public, private, rivest, shamir,,... Two industry-standard ways to implement the above methodology, prime, modulo, asymmetric some.: Supply decryption key and ciphertext message at the moment, the keys are sometimes displayed hexadecimal... Print a public key the product n is called the modulus for encryption is the key! End of this box RSA public key and ciphertext message at the end of process. A `` n bit key '', the two primes should not be too close to each,! The options to decrypt the encrypted message 431164974181 has hexadecimal writing 64,63,6F,64,65 i.e topic be! Numbers are used for encrypting message s but can also be used for the same security level a n! By A. Receiver retrieves senders message digest over the message numbers are used to decrypt.! A second phase, the hash and its signature are verified bibliography ): encryption with public... Devices it came in recent times due to lack of entropy ( H ( m ) to B with! At least 4096 binary digits to be used for performing digital signature over message! Other, but also not too far apart: prime numbers, p and q are.. Signature ( DS ) calculated over the message digest on the eContent value by... Encrypted using as private key, base64 Reminder: dCode is free to use all functions of this box by. Can non-Muslims ride the Haramain high-speed train in Saudi Arabia where 1 <