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압수･수색 영장을 집행하는 경우에 스마트폰에 설정된 잠금을 해제 또는 해킹하는데 실패하면 어떻게 해야 할까? 우리나라의 경우 스마트폰의 잠금을 해제하라는 수 사기관의 요구를 거부하였다는 이유로 처벌하는 규정은 없다. 반면에 영국의 ｢수사 권한규제법｣ 제49조 제(2)항과, 프랑스의 ｢형법｣ 제434-15-2조와 호주의 ｢형법｣(The Crimes Act 1914 (Cth)) 제3LA조 등은 일정한 요건 아래 스마트폰의 잠금 해제에 협조하도록 강제하고 있다. 피의자에게 스마트폰의 잠금을 해제하여 제출하라고 강제하는 것이 수정헌법 제5 조가 보장하는 ‘자기부죄거부특권’을 침해하는 것인가에 대하여 미국 내 하급심들은 상반된 판단을 하고 있다. 그런데 미국의 법원들은 이른바 “예견된 결론의 원칙 (foregone conclusion doctrine)”을 충족하는 경우에는 피의자나 피고인의 자기부죄거 부특권에 예외를 인정하고 있다. 따라서 수사기관이 일정한 사실을 입증한 경우에 법원은 피의자나 피고인의 자기부죄거부특권에도 불구하고 이들에게 스마트폰의 잠 금을 해제하라고 명령한다. 만약 그러한 명령을 이행하지 않는 경우에 법원은 피의자나 피고인의 불이행을 ‘법원모욕’으로 처벌함으로써 간접적으로 그 이행을 강제하 고 있다. 우리 헌법상 진술거부권은 상대적 기본권이며, 헌법 제37조 제2항에 따라 “필요한 경우에 한하여 법률로써” 제한할 수 있다고 보아야 한다. 따라서 과잉금지의 원칙에 따라 피의자가 중대한 범죄를 범하였다는 혐의를 받는 경우에 한하여 검사가 제출한 청구서와 자료를 토대로 판단하여 볼 때 다른 수사기법을 통해서는 범죄의 증거를 수집하는 것이 불가능하거나 현저히 곤란하고, 피의자가 스마트폰의 잠금을 해제하 는 방법을 알고 있다고 볼 수 있으며, 피의자의 스마트폰에 범죄의 증거가 들어있다 는 것을 “합리적으로 특정”한 경우에는 ‘법원’이 피의자에게 잠금 해제를 명령하거나 잠금 해제에 협조하라는 내용의 영장을 발부할 수 있도록 하는 등의 새로운 입법을 할 것인지에 대하여 고민해 보아야 할 것이다.

What should the government do if they fail to unlock or hack suspect’s locked or encrypted smartphone when executing a legitimate search and seizure warrant? Currently, in South Korea, there is no criminal provision to punish someone for refusing the government’s request to unlock the smartphone. In contrast, Article 49(2) of the Regulation of Investigatory Powers Act 2000 in the U.K., Article 434-15-2 of the French Criminal Code, and Article 3LA of the Crimes Act 1914 in Australia allow the government to require anyone to cooperate in unlocking or decrypting his or her smartphone in limited conditions. The courts in the U.S. have laid down different decisions on the issue of whether compelling the suspect to produce the smartphone in a condition of being unlocked or encrypted is repugnant to his or her privilege against self-incrimination under the Fifth Amendment. The courts, then, have ruled that there would be an exception to the privilege when any potential testimonial communication is the “foregone conclusion doctrine” that adds little or nothing to the total sum of the government’s information. Courts, therefore, usually order suspect to unlock or decrypt his or her smartphone when the government can independently prove some facts regarding the doctrine despite the suspect’s privilege. The courts have indirectly compelled suspect to unlock or encrypt his or her smartphone by holding the suspect in contempt of court if he or she fails to do so. The right to remain silent under the Constitution of the Republic of Korea is not an absolute constitutional right, therefore the right may be limited only by a statutory Act if necessary. According to the proportionality doctrine, it is time to consider if we should adopt a new law which allows courts to order suspect to unlock or decrypt his or her smartphone or to issue a warrant requesting his or her to cooperate with the government by unlocking or decrypting it on condition that the government reasonably places his or her a suspicion of committing a serious felony viewed on the prosecution service’s request and submitted evidence showing the facts not only that it would be impossible or seriously difficult to collect evidence through other investigative methods but also that it seems reasonable to conclude that the suspect knows the passwords and the government identifies the contents it seeks with reasonable particularity.

최근 애플, 구글 등을 비롯한 IT기업들이 기술보안을 강화하면서 정부와 대립하는 일련의 사건들이 발생하였다. 특히 스마트 전자기기 등에 대한 암호화가 일반화된 상황에서 국가안보, 아동 성범죄, 그 밖의 생명 신체에 대한 중대하고 긴급한 수사 필요가 인정될 때에도 기업의 협조를 받지 못해 어려움을 겪었다. 이 연구에서는 우선 피의자 또는 피고인에 대한 스마트 전자기기 등의 암호해제 강제가 헌법 제12조 진술거부권의 침해가 되는지 여부를 살펴보았고, 스마트 전자기기의 특수성을 고려할 때 해당 행위는 위헌적으로 평가하여야 한다고 하였다. 그리고 피의자 또는 피고인에게 스마트 전자기기 등의 암호해제를 강제할 수 없기 때문에 기존 ｢통신비밀보호법｣상의 기업 협조 요청과 같이 IT제조업체에 대해서 필요 정보에 접근할 수 있도록 협조를 요청할 수 있어야 한다고 하였다. 또한 영장주의와 적법절차원칙에 따라 통신제한조치보다는 엄격하고 좁은 범위인 국가안보, 아동 성범죄, 그 밖의 생명 신체에 대한 중대하고 긴급한 수사 필요가 인정될 경우에는 정보 수집이 가능하도록 하여야 한다고 주장하였다. 나아가 정부의 정보 압수 수색 및 증거 수집 절차에서 피의자 또는 피고인의 기본권 침해 사항을 개정하여야 하고, 독립적 지위가 인정되는 감독기구를 통해 국가감시권력이 남용될 수 있는 우려를 실질적으로 견제할 수 있도록 법제화하여야 한다고 하였다.

Recently, as IT companies such as Apple and Google have strengthened their technology security, a series of incidents have occurred against the government. In particular, in a situation where encryption for smart electronic devices has become common, it was difficult to get cooperation from companies when there was a need for serious and urgent investigations on national security, child sex crimes, and other lives. In this study, first, it was examined whether the enforcement of encryption by smart electronic devices on the suspect or the accused violates Article 12 of the Constitution, the right to refuse statements. And considering the specificity of the smart electronic device, the action should be evaluated as unconstitutional. Decryption of passwords such as smart electronic devices should not be forced on the suspect or the accused. Therefore, it is necessary to request cooperation from the IT manufacturer so that the government can access necessary information within the scope of minimizing the infringement of corporate freedom, freedom of expression, and copyright, as in the request for corporate cooperation under the existing CommunicationsSecret Protection Act. In addition, in accordance with warrants and due process, when serious and urgent investigations on national security, child sex crimes, and other lives are required, it should be possible to collect information within a narrower scope than the communication restriction measures. Furthermore, the government's information seizure, search and evidence collection procedures must revise the violation of the basic rights of the suspect or the accused. The entire legal system should be thoroughly reviewed so that the supervisory body, which is recognized for its independent status, can procedurally evaluate and effectively contain the abuse of state surveillance power.

최근에는 전자제품 및 웨어러블 기기를 포함한 IoT 제품들이 증가 추세에 있다. 하지만, IoT 기기가 증가할수록 보안 문제가 대두되면서 유선 및 무선 보안에 대한 관심이 증가하고 있다. 현재 많이 사용하고 있는 알 고리즘으로는 AES가 있으며, 임베디드 기반에서도 사용이 가능한 경량의 암복호화 알고리즘 들이 있다. 본 논문 은 임베디드 경량 블록 암호 알고리즘인의 응용에 관심이 있으며, 평문 데이터 대신에 실시간으로 측정한 심박 데 이터에 경량의 암복호화 알고리즘을 적용하는 실험을 수행하였다. 데이터를 분석한 결과, 본 데이터와 복호화 데 이터가 100% 일치하였다. LEA 알고리즘의 경우에 1개의 심박 데이터에 대한 샘플링 갯수는 초당 100개임을 확 인하였다. 향후, 샘플링 레이트를 높일 수 있도록 고성능의 임베디드 기기에서 실험을 수행할 예정이다.

In recent years, the number of IoT products, including electronics and wearable devices, has been on the rise. However, with the increase in IoT devices comes security concerns, which has led to an increased focus on wired and wireless security. Currently, AES is a popular algorithm, and there are lightweight encryption algorithms that can be used on an embedded basis. This paper is interested in the application of embedded lightweight block cipher algorithms, and experiments were conducted to apply lightweight decryption algorithms to real-time measured heart rate data instead of plain text data. After analyzing the data, we found that the original data and the decrypted data matched 100%. For the LEA algorithm, we found that the number of samples for one heart rate data is 100 per second. In the future, we will conduct experiments on high-performance embedded devices to increase the sampling rate.

데이터베이스는 중요한 정보를 저장·관리하는 핵심 IT 자산이며, 이를 보호하기 위한 대표적인 기술 중 하나가 암호화 기 술이다. 본 연구에서는 AES, RSA, 그리고 두 방식을 결합한 하이브리드 암호 시스템을 구현하고, 데이터베이스(MySQL, SQLite)와 데이터 유형(텍스트, 이미지)에 따른 암·복호화 성능을 비교 및 분석하였다. 특히, 텍스트 데이터셋(FIFA, Top5) 및 이미지 데이터셋(GTSRB, Chest_xray)을 사용하여 데이터 특성과 크기에 따른 성능 차이를 실험적으로 평가하였다. 실험 결 과, AES는 모든 조건에서 가장 짧은 처리 시간과 낮은 메모리 사용량을 보였으며, 하이브리드 방식은 중간 수준, RSA는 가장 낮은 성능을 나타냈다. 데이터 유형별로는 텍스트가 이미지보다 일관되게 빠르고 경량이었고, 데이터베이스별로는 SQLite가 MySQL보다 전반적으로 우수했다. 이러한 경향은 알고리즘 구조, 데이터 처리 과정의 복잡성, DBMS의 동작 방식 차이에 기 인한다. 본 연구의 성능 비교 결과는 데이터베이스 보안 기능 구현 시 효율적인 암호화 방식 선택을 위한 근거를 제공하며, 제 안한 하이브리드 방식은 보안성과 성능의 균형을 위한 실질적 참고 자료가 될 수 있다.

A database is a core IT asset for storing and managing critical information, and encryption is one of the representative technologies for its protection. This study implements AES, RSA, and a hybrid cryptosystem combining the two methods and compares and analyzes their encryption and decryption performance across different databases (MySQL and SQLite) and data types (text and image). In particular, the performance differences according to data characteristics and sizes were experimentally evaluated using text datasets (FIFA, Top5) and image datasets (GTSRB, Chest_xray). Experimental results show that AES consistently achieved the shortest processing time and lowest memory usage under all conditions, the hybrid approach demonstrated intermediate performance, and RSA exhibited the lowest performance. Text processing was consistently faster and lighter than image processing, whereas SQLite outperformed MySQL. These trends can be attributed to differences in the algorithm structure, complexity of data processing, and operational mechanisms of the DBMSs. The performance comparison results of this study provide a basis for selecting efficient encryption methods when implementing database security features, and the proposed hybrid approach can serve as a practical reference for balancing the security and performance.

Music has a versatile dimensionality; it can be used to express feelings, emotions and can also be used as a communicable language. Music and its attributes have been used in cryptography and steganography from a long time. Musical symbols and notes are used as replacement/substitution cipher. Using music as a cipher or cover media not only enhances the security of the message but also reduces its chance to be detected as an encoded or ciphered message. This paper proposes a hybrid Polybius and Playfair cipher which encodes the message into sequence of musical notes. The Playfair key matrix is generated using the Blum-Blum Shub generator. The bigrams of plain text message is first encrypted using Playfair cipher then individual character of the encrypted message is re-encrypted using Polybius cipher. The Playfair cipher enhances the security of the encrypted message over the simple substitution technique. The Polybius cipher then reduces the character set by appropriate number of symbols (here musical notes) for replacement. The basic 5X5 structure of key matrix in Polybius and Playfair is extended to 10X10 to hold the 95 prinTable characters of ASCII character set.

“Music can be used as a communicable language”. Musical symbols and musical notes have been used as codes and ciphers from early days. The art of encrypting messages using music is termed as Musical cryptography and it uses predefined set of notes and set of rules for composing musical pieces which in turn are musical cryptograms. Traditional algorithms applied to musical cryptography used simple substitution cipher which merely produced good musical sequences. To overcome this problem a fuzzy logic based algorithm for musical cryptography is proposed in this paper. The paper proposes a symmetric key substitution cipher which uses one of the n candidate notes to encrypt a particular character. The application of fuzzy logic in musical cryptography produces acceptable musical sequences which are hard to be suspected as cipher.

A black hole attack is one of the most serious attacks in mobile ad hoc networks. A malicious node can act as if it has a valid route to a destination and then respond with a false Route Reply (RREP) message to the source, when it receives a Route Request (RREQ). Then the malicious node absorbs data packets destined for the destination. We propose an Encrypted Verification Method (EVM) that effectively detects a black hole attack. It takes two steps. First, every node examines its neighbors by inspecting their data transmission behaviors. Second, a detection node that receives an RREP from the suspicious node sends an encrypted verification message directly to the destination along the path included in the RREP for verification. The approach not only pins down the black hole nodes, but also reduces control overhead significantly. We prove by resorting to simulation that the EVM is highly dependable against the black hole attack.

In recent years, there has been increasing trend for multimedia applications to use delegate service providers for content distributions. These delegate services have brought new challenges to the protection of multimedia content confidentiality. Encryption can be used to hide information from unauthorized individuals, either in transit or in storage. This technique transforms the content into unintelligible and unviewable format. This paper proposes image encryption using secret sharing scheme. According to this process there are two levels of encryption. The first level, generates the random polynomial of degree (t-1) , where t is a threshold value. The constant term is taken as the secret. In the second level construct the transformation matrix using secret and primitive root theorem. This matrix is used for encryption purpose. Experimental results and security analysis shows that the proposed algorithm offers good resistance against brute force attack and statistical crypt analysis.

We propose an Encrypted Verification Method (EVM) that effectively detects a black hole attack. A detection node that receives an RREP from a suspicious node sends an encrypted verification message directly to destination along the path included in the RREP for verification. The approach not only pins down the black hole nodes, but also reduces control overhead significantly. We prove by resorting to simulation that EVM is highly dependable against the black hole attack.

Nowadays, the network transmission and video encryption areas have urgently needed high-speed encryption systems for SM4 algorithm. To speed up the SM4 system in small area, three aspects in existing system is analyzed and optimized. Firstly, aiming at the prior encryption must wait long until completing all 32 rounds key expansion, a method is proposed for outputting round key in each key expansion to accelerate encryption response. Secondly, considering most user passwords are unchanged, we adopt additional memory for comparing old and new keys, so that key expansion can be cancelled sometimes. Thirdly, the paper analyses the relationship between key expansion and encryption/decryption algorithm in SM4. Using module reused technology, the designed key expansion module can also encrypt and decrypt, and the designed another two modules can both encrypt and decrypt. Therefore, the system can achieve three tasks’ synchronous encryption/decryption, which greatly improves the system's processing speed. This paper presents a hardware design scheme for the high-speed system. At last, the optimized design is realized in FPGA. The experimental results show that the design is feasible, and the SM4 encryption speed can increase fourfold.

In order to solve the problem of non-restoration of PVSS, in this paper, we propose a method to recover the secret image without using the Boolean operation of the matrix matrix. In the lossless recovery process, each column base matrix will be "and" and "exclusive or" operation to get the original image anti-color image, and then the image can be obtained by the lossless secret image, this method can be applied to the general ( k, n ) threshold lossless recovery. In the absence of a computing device, it can be decrypted by superimposing, in the XOR computing device, it can realize lossless recovery. Experimental results show that the proposed algorithm can guarantee the gradual visual secret sharing, complete the restoration of the secret image, the operation is simple and efficient, and has a strong practicability.

An optical encrypted color video sequence based on a spectral fusion of information has been proposed. Each color image of the sequence is decomposed into three basic color components. Pertinent information fusion is considered as segmentation. Encrypting consists in modulating each of these three components of the image spectrum by a corresponding phase mask. This phase mask includes pertinent information collected from various encrypted color keys according to a fusion criterion. As encrypting keys are formed by real images, it becomes an impossible task to get the target image by any trial and error random images techniques. For decrypting, a simple algorithm based on segmented correlation filters is proposed. Simulation results corroborate the effectiveness of our algorithm.

This paper proposed a algorithm for automatic key generation which generate from an integer value to create more secure communication over cloud architecture. Character based ASCII encryption scheme is used to satisfy the current requirement to establish secure communication. In this work we have a byte level security at each level of data transmission. It helps to create batter security to perform encryption & decryption over cloud infrastructure i.e., from this work we have technique through which we generate private key which help to establish secure communication between two or more node while they are communicating over cloud system.

A day-to-day use of cryptography in our life is increasing tremendously; this is because of necessity of our multimedia documents to be protected from unauthorized person. As the days are passing the old algorithms are not remained so strong as cryptanalyst are familiar with them. Today the computers are faster and in feature its speed will increase more and more. Brute force attacks are made to break the encryption and they are growing so faster. These attacks are the main drawbacks of older algorithm. But with feature this algorithms will be replaced by new techniques that will provide better protection. In this paper we are going to proposed new encryption technique which is more faster, better immune to attacks, more complex, easy to encrypt and many more advanced security feature included. This Document displays the comparison between PSR algorithm and RSA Algorithm which are used in the encryption of plaintext into cipher text that are generally used in cryptography.

In this paper, we introduce a novel approach to enhance document security by integrating Computer Generated Hologram(CGH) encryption technology with a system for document encryption, printing, and subsequent verification using a smartphone application. The proposed system enables the encryption of documents using CGH technology and their printing on the edges of the document, simplifying document verification and validation through a smartphone application. Furthermore, the system leverages highresolution smartphone cameras to perform online verification of the original document and supports offline document decryption, ensuring tamper detection even in environments without internet connectivity. This research contributes to the development of a comprehensive and versatile solution for document security and integrity, with applications in various domains.

큰 반소수 n = pq의 소인수 p,q를 나눗셈 시행법으로 직접 찾는 것은 현실적으로 거의 불가능하다. 따라서 대 부분의 소인수분해 알고리즘은 a2 ≡b2(mod n)의 제곱합동을 찾아 p = GCD(a-b,n), q=GCD(a+b,n)의 소인수를 찾는 간접 방법을 적용하고 있다. n = pq에 대해 p와 q를 선택한 영역은 l(p) = l(q) = l( ) = 0.5l(n)의 [10 ⋯ 01, 99 ⋯ 9] 범위에서  을 기준으로 10 ⋯ 00<p< 과 <q<99 ⋯ 9]에 존재한다는 사실만이 밝혀 졌다. 본 논문은 n으로 부터 획득한 정보를 이용하여 p의 범위를 보다 축소시키는 방법을 제안한다. 제안 방법은 n = nLR + nRL, l(nLR) = l(nRL) = L( )으로 분할하여 pmin = nLR, qmin = nRL로 설정하는 방법을 적 용하였다. 본 논문에서 제안한 n의 정보 로 p의 범위를 축소하는 방법은  의 정보로 p의 범위 축소 방법에 비해 최소 17.79%에서 최대 90.17%의 범위 축소 효과를 얻었다.

It is impossible directly to find a prime number p,q of a large semiprime n = pq using Trial Division method. So the most of the factorization algorithms use the indirection method which finds a prime number of p = GCD(a-b, n), q = GCD(a+b, n); get with a congruence of squares of a2 ≡ b2(mod n). It is just known the fact which the area that selects p and q about n = pq is between 10 ⋯ 00 < p <  and < q < 99 ⋯ 9 based on  in the range, [10 ⋯ 01, 99 ⋯ 9 of l(q) = l() = 0.5(n). This paper proposes the method that reduces the range of p using information obtained from n. The proposed method uses the method that sets to pmin = nLR, qmin = nRL ; divide into nLR + nRL, l(nLR) = l(nRL) = L( ). The proposed method is more effective from minimum 17.79% to maxmimum 90.17% than the method that reduces using  information.

본 논문에서는 다중 소스가 분리 된 노드에서 암호화되고 각각의 공개 통신 채널을 통해 공동 싱크 노드로전송되는 시스템을 고려한다. 우리는 상관 관계가 있는 암호화 키를 가진 것으로 알려진 기존 시스템의 보안 문제에관심이 있다. 특히, 우리는 추가적인 비밀 키를 도입하지 않고 해결책을 찾는데 초점을 맞추고 비용을 최소화하고 이미실행중인 시스템을 중단시키는 위험을 최소화하기 위해 최소한의 수정만으로. 우리는 도청자가 이용 가능한 공개 통신채널에 액세스함으로써 모든 암호문, 즉 암호화 된 소스를 획득하는 보안 모델 하에서의 해결책을 제안한다. 우리의 주요 기술은 암호문을 공개 통신 채널에 보내기 전에 특정 선형 코드의 유니버셜 함수를 사용하여 암호문을 인코딩하는것이다.

In this paper, we consider a system where multiple sources are encrypted in separated nodes and sent through their respective public communication channels into a joint sink node. We are interested at the problem on protecting the security of an already existing system such above, which is found out to have correlated encryption keys. In particular, we focus on finding a solution without introducing additional secret keys and with minimal modification to minimize the cost and the risk of bringing down an already running system. We propose a solution under a security model where an eavesdropper obtains all ciphertexts, i.e., encrypted sources, by accessing available public communication channels. Our main technique is to use encoders of universal function to encode the ciphertexts before sending them to public communication channels.

a ^{b} == c(mod``p)에서 a,c,p가 주어졌을 때 b를 구하는 이산대수 문제를 푸는 아기걸음-거인걸음 알고리즘은 p를 m= LEFT ⌈ sqrt {p} RIGHT ⌉개의 원소를 가진 m개의 블록으로 분할하고 거인 1명이 보폭 m으로 단방향으로만 a ^{0}로 걸어가면서 찾는 방법이다. 본 논문은 기본적으로 p를 p/l,`a ^{l} >p로 분할하고, 성인 1명이 보폭 l로 단방향으로 걸어가는 방법으로 변형시켰다. 또한, 성인 2 ^{k}명이 동시에 걸어가면서 b를 빠르게 찾는 방법으로 확장시켰다. 제안된 알고리즘을 1 LEQ b LEQ p-1의 범위에서 2 ^{k} ,`(k=2)를 적용한 결과 기본적인 성인걸음수의 1/4로 감소시키는 효과를 얻었다. 결론적으로, 제안된 알고리즘은 아기걸음-거인걸음 알고리즘의 보폭 수를 획기적으로 단축시킬 수 있었다.

The baby-step giant-step algorithm seeks b in a discrete logarithm problem when a,c,p of a ^{b} == c(mod``p) are already given. It does so by dividing p by m block of m= LEFT ⌈ sqrt {p} RIGHT ⌉length and letting one giant walk straight toward a ^{0} with constant m strides in search for b. In this paper, I basically reduce m= LEFT ⌈ sqrt {p} RIGHT ⌉to p/l,`a ^{l} >p and replace a giant with an adult who is designed to walk straight with constant l strides. I also extend the algorithm to allow 2 ^{k} adults to walk simultaneously. As a consequence, the proposed algorithm quarters the execution time of the basic adult-walk method when applied to 2 ^{k} ,`(k=2) in the range of 1 LEQ b LEQ p-1. In conclusion, the proposed algorithm greatly shorten the step number of baby-step giant-step.

비대칭키 RSA의 공개키 e와 합성수 n=pq 은 알고 있고 개인키 d를 모를 때, ∅(n)=(p-1)(q-1)=n+1-(p+q) 을 구하여 d=e^{-1} (mod ∅(n))으로 개인키 d를 해독한다. 암호해독은 일반적으로 n/p=q 또는 a^{2}≡b^{2} (mod n), a=(p+q)/ 2, b=(q-p)/2 를 구하는 소인수 분해법이 널리 적용되고 있다. 그러나 아직까지도 많은 RSA 수들이 해독되지 않고 있다. 본 논문은 ∅(n)을 직접 구하는 알고리즘을 제안하였다. 제안된 알고리즘은 이산대수의 아기걸음-거인걸음법과 모듈러 지수연산의 2^{k}-ary법을 적용하였다. 이 알고리즘은 역-아기걸음과 2^{k}-ary 성인걸음법을 적용하여 기본적인 성인걸음법 수행횟수를 1/2^{k} 로 줄이고, m=⌊sqrt {n}⌋의 저장 메모리 용량도 l, a^{l} >n로 감소시켜 ∅(n)을 l회 이내로 구하였다.

When the public key e and the composite number n=pq are disclosed but not the private key d in an asymmetric-key RSA, message decryption is carried out by obtaining ∅(n)=(p-1)(q-1)=n+1-(p+q) and subsequently computing d=e^{-1} (mod ∅(n)). The most commonly used decryption algorithm is integer factorization of n/p=q or a^{2}≡b^{2} (mod n), a=(p+q)/ 2, b=(q-p)/2. But many of the RSA numbers remain unfactorable. This paper therefore applies baby-step giant-step discrete logarithm and 2^{k}-ary modular exponentiation to directly obtain ∅(n). The proposed algorithm performs a reverse baby-step and 2^{k}-ary adult-step. As a results, it reduces the execution time of basic adult-step to 1/2^{k} times and the memory m=⌊sqrt {n}⌋ to l, a^{l} >n, hence obtaining ∅(n) by executing within l times.

In this paper, we discuss optical encryption and decryption considering wireless communication channels. In wireless communication systems, the wireless channel causes noise and fading effects of the transmitted information. Optical encryption technique such as double-random-phase encryption (DRPE) is used for encrypting transmitted data. When the encrypted data is transmitted, the information may be lost or distorted because there are a lot of factors such as channel noise, propagation fading, etc. Thus, using digital modulation and maximum likelihood (ML) detection, the noise and fading effects are mitigated, and the encrypted data is estimated well at the receiver. To the best of our knowledge, this is the first report that considers the wireless channel characteristics of the optical encryption technique.